Modeling method and system of automatic lunar ladder based on gravitational siphon effect

Abstract

The present invention discloses a method and system for modeling an automatically operating lunar ladder based on the gravitational siphon effect. The method includes: constructing a gravitational siphon lunar ladder model; performing bead point simplification processing on the gravitational siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravitational siphon lunar ladder; performing coordinate system construction processing and dynamic analysis on the simplified multi-body dynamics model of the gravitational siphon lunar ladder to obtain a gravitational siphon effect lunar ladder dynamics model. By using the present invention, the gravitational siphon effect can be used to realize the transfer of matter from the surface of a rotating body to an orbital collection spacecraft, thereby avoiding the need for a traditional propulsion system and greatly reducing the energy consumption required to lift the payload. As a method and system for modeling an automatically operating lunar ladder based on the gravitational siphon effect, the present invention can be widely used in the field of aerospace modeling technology.

Description

Technical Field

[0001] The present invention relates to the technical field of aerospace modeling, and in particular to a method and system for modeling an automatically operating lunar ladder based on a gravitational siphon effect. Background Art

[0002] Currently, human exploration of space resources relies primarily on rocket launches, which consume vast amounts of fuel and are extremely costly. Furthermore, the technology involved in space resource development is complex, including deep space exploration, sample collection and return, and in-situ resource utilization, which are technically challenging and high-risk. As a potential means of space transportation, a space elevator holds great potential and carries significant strategic significance. It is envisioned as an efficient and sustainable means of transport between the Earth and the Moon, providing the infrastructure necessary for space travel, resource development, and future human habitation. The basic principle of a space elevator is to use a tether from the Earth's surface to the Earth-Moon L1 point near Earth, creating a long suspended rope between the two Earth-Moon connections. Space travel is achieved through the tension of the rope. Compared to traditional rocket launches, space elevators offer numerous advantages, including low cost, reduced energy consumption, and reusability. They are considered a key breakthrough for future space exploration. However, current methods require a propulsion system, which significantly increases payload consumption. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide an automatically operated lunar ladder modeling method and system based on the gravitational siphon effect, which can use the gravitational siphon effect to realize the transfer of matter from the surface of a rotating body to an orbital collection spacecraft, thereby avoiding the need for a traditional propulsion system and greatly reducing the energy consumption required to lift the payload.

[0004] The first technical solution adopted by the present invention is: a method for modeling an automatically operating lunar ladder based on the gravitational siphon effect, comprising the following steps:

[0005] Construct a gravitational siphon lunar ladder model;

[0006] The gravity siphon lunar ladder model is simplified by bead point processing to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder.

[0007] The coordinate system construction and dynamic analysis of the simplified multi-body dynamics model of the gravitational siphon lunar ladder are carried out to obtain the dynamics model of the gravitational siphon effect lunar ladder.

[0008] Furthermore, the gravity siphon lunar ladder model specifically includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-Earth surface of the moon, and the movable pulley is distributed on the near-Earth surface of the earth. The closed-loop rope runs around the two ends of the fixed pulley and the movable pulley respectively. The closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction. Cargo boxes are distributed at equal intervals on the upper surface of the closed-loop rope.

[0009] Furthermore, the step of performing bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder specifically includes:

[0010] The closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node;

[0011] Assume that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravitational siphon lunar ladder model are regarded as nodes;

[0012] Assume that the fixed pulley node is connected to the closed-loop rope node and the movable pulley node is connected to the closed-loop rope node. Set the previous node of the fixed pulley in the gravity siphon lunar ladder model to The last node of the fixed pulley in the gravitational siphon lunar ladder model is , the previous node of the movable pulley in the gravitational siphon lunar ladder model is The next node of the movable pulley in the gravitational siphon lunar ladder model is , and obtained a simplified multi-body dynamics model of the gravitational siphon lunar ladder.

[0013] Furthermore, the step of constructing a coordinate system and performing dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain the dynamics model of the gravity siphon lunar ladder specifically includes:

[0014] Based on the Earth-Moon rotating coordinate system, a simplified multi-body dynamics model of the gravitational siphon lunar ladder with a coordinate system is constructed to obtain the position vectors of the model parameters;

[0015] Based on the position vector of the model parameters, the dynamic equations of the node parameters are constructed by considering the interaction force factors, gravity factors, centrifugal force factors, Coriolis force factors and damping force factors;

[0016] Characteristic node identification rules are introduced, and the dynamic equations of node parameters are transformed to obtain the dynamic model of the lunar ladder with gravitational siphon effect.

[0017] Furthermore, the position vector of the model parameter specifically includes the closed-loop rope node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley , the position vector of the movable pulley is , the position vector of the previous node of the fixed pulley , the position vector of the next node of the fixed pulley , the position vector of the previous node of the movable pulley The position vector of the next node of the movable pulley .

[0018] Furthermore, the dynamic equation of the node parameters specifically includes the closed-loop rope node The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the previous node of the fixed pulley, the dynamic equation of the next node of the fixed pulley, the dynamic equation of the previous node of the movable pulley and the dynamic equation of the next node of the movable pulley, where:

[0019] The closed-loop rope node The expression of the kinetic equation is:

[0020]

[0021] In the above formula, represents the i-th closed-loop rope node The concentrated mass, represents the i-th closed-loop rope node The second derivative of the position vector with respect to time, represents the gravitational force of the earth on the nodes of the closed-loop rope, represents the gravitational force of the moon on the nodes of the closed-loop rope, 、 represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, represents the centrifugal force on the closed-loop rope node, represents the Coriolis force on the closed-loop rope node, represents the damping force on the closed-loop rope node;

[0022] The dynamic equation of the movable pulley is expressed as:

[0023]

[0024] In the above formula, represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, represents the earth's gravitational force on the movable pulley, represents the gravitational force of the moon on the movable pulley, is the centrifugal force on the movable pulley, represents the Coriolis force on the movable pulley, represents the friction force on the movable pulley, represents the elastic force of the connecting rod between the movable pulley and the node before the movable pulley, It represents the elastic force of the connecting rod between the movable pulley and the next node after the movable pulley;

[0025] The expression of the dynamic equation of the previous node of the fixed pulley is:

[0026]

[0027] In the above formula, represents the concentrated mass of the previous rope node of the fixed pulley, represents the second-order derivative of the position vector of the previous rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the previous node of the fixed pulley, represents the lunar gravitational force on the previous node of the fixed pulley, represents the centrifugal force on the previous node of the fixed pulley, represents the Coriolis force on the previous node of the fixed pulley, represents the friction force on the previous node of the fixed pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the fixed pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away;

[0028] The expression of the dynamic equation of the last node of the fixed pulley is:

[0029]

[0030] In the above formula, represents the concentrated mass of the last rope node of the fixed pulley, represents the second-order derivative of the position vector of the next rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the last node of the fixed pulley, represents the lunar gravitational force on the last node of the fixed pulley, It represents the centrifugal force on the last node of the fixed pulley. represents the Coriolis force on the last node of the fixed pulley, represents the friction force on the last node of the fixed pulley, represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the last node of the fixed pulley and the node further away;

[0031] The expression of the dynamic equation of the previous node of the movable pulley is:

[0032]

[0033] In the above formula, represents the concentrated mass of the previous rope node of the movable pulley, represents the second-order derivative of the position vector of the previous rope node of the movable pulley with respect to time, represents the earth's gravitational force on the previous node of the movable pulley, represents the gravitational force of the moon on the previous node of the movable pulley, represents the centrifugal force on the previous node of the movable pulley, represents the Coriolis force on the previous node of the movable pulley, represents the friction force on the previous node of the movable pulley, represents the elastic force of the connecting rod between the previous node of the movable pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and the node further away;

[0034] The expression of the dynamic equation of the last node of the movable pulley is:

[0035]

[0036] In the above formula, represents the concentrated mass of the last rope node of the movable pulley, represents the second-order derivative of the position vector of the next rope node of the movable pulley with respect to time, represents the earth's gravitational force on the last node of the movable pulley, represents the lunar gravitational force on the last node of the movable pulley, It represents the centrifugal force on the last node of the movable pulley. represents the Coriolis force on the last node of the movable pulley, represents the friction force on the last node of the movable pulley, represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, Represents the elastic force of the connecting rod between the adjacent node of the next node of the movable pulley and the node further away.

[0037] Furthermore, the introduced characteristic node identification rule is specifically as follows:

[0038] Determine the closed-loop rope node closest to the pulley, number it, and determine the target node, wherein the pulley is a fixed pulley or a movable pulley;

[0039] Determine the next node of the target node and the previous node of the target node, determine the distance between the next node of the target node and the pulley, and determine the distance between the previous node of the target node and the pulley;

[0040] Determine the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley;

[0041] If the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then the next node of the target node is determined to be the previous node of the pulley and the target node is determined to be the next node of the pulley;

[0042] If the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, the target node is determined to be the previous node of the pulley and the previous node of the target node is the next node of the pulley.

[0043] The second technical solution adopted by the present invention is: an automatically operated lunar ladder modeling system based on the gravitational siphon effect, comprising:

[0044] The first module is used to construct a gravitational siphon lunar ladder model;

[0045] The second module is used to perform bead point simplification on the gravitational siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravitational siphon lunar ladder;

[0046] The third module is used to construct the coordinate system and conduct dynamic analysis on the simplified multi-body dynamics model of the gravitational siphon lunar ladder, and obtain the dynamics model of the gravitational siphon effect lunar ladder.

[0047] The beneficial effects of the method and system of the present invention are as follows: the present invention constructs a gravity siphon lunar ladder model, utilizes gravity siphon as a power source of the power system, and then realizes the use of the rotational kinetic energy of the asteroid to realize propellant-free payload transfer, realizes the transfer of matter from the lunar surface to the orbital collection spacecraft, performs bead point simplification processing on the gravity siphon lunar ladder model, obtains a simplified multi-body dynamics model of the gravity siphon lunar ladder, discretizes the continuous ladder structure into a series of nodes and elastic connection segments, and then performs coordinate system construction processing and dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder, designs a criterion for determining the node coupled with the pulley, and converts the differential algebraic equation into a pure differential equation through continuous judgment, thereby realizing the uninterrupted continuous practical process integral solution of the differential equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flowchart of the steps of the method for automatically operating the lunar ladder modeling based on the gravitational siphon effect of the present invention;

[0049] Figure 2 This is a structural block diagram of the automatic lunar ladder modeling system based on the gravitational siphon effect of the present invention;

[0050] Figure 3 Schematic diagram of an automatically operated lunar ladder based on the gravitational siphon effect provided by a specific embodiment of the present invention;

[0051] Figure 4 is a schematic diagram of kinetic modeling provided by a specific embodiment of the present invention;

[0052] Figure 5 Schematic diagram of a simplified multi-body dynamics model of a siphon lunar ladder provided by a specific embodiment of the present invention;

[0053] Figure 6 Schematic diagram of force analysis of nodes in the overall inertial coordinate system provided by a specific embodiment of the present invention;

[0054] Figure 7 Schematic diagrams of two results of special node judgment provided by a specific embodiment of the present invention;

[0055] Figure 8 This is a schematic diagram of a special node determination process provided by a specific embodiment of the present invention;

[0056] Figure 9 It is a schematic diagram of the instantaneous configuration of the system at 0 o'clock every day in a typical example provided by a specific embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted based on the understanding of those skilled in the art.

[0058] Reference Figure 1 The present invention provides a method for modeling an automatically operated lunar ladder based on the gravitational siphon effect, the method comprising the following steps:

[0059] S100, construct a gravitational siphon lunar ladder model;

[0060] Specifically, the gravitational siphon lunar ladder model includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-Earth surface of the moon, and the movable pulley is distributed on the near-Earth surface of the earth. The closed-loop rope runs around the two ends of the fixed pulley and the movable pulley respectively. The closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction. Cargo boxes are distributed at equal intervals on the upper surface of the closed-loop rope.

[0061] In this embodiment, if Figure 3 As shown, this ladder can be viewed as an extremely long, closed-loop rope running around a two-pulley system, similar to a conveyor belt. A fixed pulley is installed at the center of the lunar surface, directly opposite the Earth. A movable pulley is located near Earth. Based on statics and material mechanics analysis, the movable pulley cannot be too close to Earth, nor more than 110,000 kilometers away. This ensures that the system's internal forces are tensile, allowing it to maintain its shape and avoid falling to the Moon. An extremely long rope, connected end to end, winds around these two pulleys. Obviously, one side will travel toward the Moon, known as the upward movement, while the other side will travel toward Earth, known as the downward movement. A series of cargo boxes are evenly spaced along the entire rope. When a box ascends and reaches the lunar surface and then descends (from the Moon's perspective, it moves upward and away from the lunar surface), it is loaded with a certain mass of cargo. When the box descends to the fixed pulley at the end, the cargo is unloaded and deposited at the terminal space station, or simply removed from the ladder system. The cargo then falls to Earth under the influence of gravity. This constitutes the gravitational siphon lunar ladder, which will be referred to as the "siphon ladder" or "ladder" below.

[0062] S200, performing bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder;

[0063] Specifically, the closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; it is assumed that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravity siphon lunar ladder model are both regarded as nodes; it is assumed that the fixed pulley node is connected to the closed-loop rope node and the movable pulley node is connected to the closed-loop rope node, and the previous node of the fixed pulley in the gravity siphon lunar ladder model is set to The last node of the fixed pulley in the gravitational siphon lunar ladder model is , the previous node of the movable pulley in the gravitational siphon lunar ladder model is The next node of the movable pulley in the gravitational siphon lunar ladder model is , and obtained a simplified multi-body dynamics model of the gravitational siphon lunar ladder.

[0064] In this embodiment, if Figure 4As shown, first simplify the model, assuming the total number of cargo boxes is , the model assumes that the mass of the cargo box and the goods inside are evenly distributed on the upper rope in the counterclockwise direction, and then the entire rope is divided into equal intervals. segment, each segment The mass (the collection of ropes, boxes, and cargo) is concentrated at its nodes In this process, Not necessarily Equal, of course in principle cannot be greater than , in order to facilitate the simulation calculation with higher precision. In actual engineering, The number should not be too small to ensure smooth operation of the system as a whole; nor too large to take into account the carrying capacity of the system. For example, if a cargo box is set up approximately every 1,000 kilometers, then when the terminal movable pulley is about 50,000 kilometers from the ground, Set to 700, at the same time The value is also set to 700, which can basically guarantee the calculation accuracy and make each node correspond to a container. Number them in sequence. At the initial moment, for convenience, the node closest to the fixed pulley on the lunar surface can be numbered 1. On the uplink side, the mass of each node is , on the downstream side, the quality of each node is . Contains the mass of the rope and empty container in the node set, It increases the quality of the goods. .

[0065] Furthermore, each of the two pulleys is simplified to two nodes. Given that the pulley radius is much smaller than the overall system, its radius is also omitted. The mass of the fixed pulley PM (M represents the lunar side) is effectively irrelevant, as its motion is known and follows the lunar surface. Furthermore, the gravitational forces acting on its mass are completely balanced by the lunar surface's reaction forces and are not transferred to other nodes. As for the movable pulley PE (E represents the Earth side), the mass of its simplified node is set to the combined mass of the pulley and the space station to which it is attached.

[0066] It should be further explained that the model requires special treatment of the four nodes closest to the two pulleys in the clockwise and counterclockwise directions. Although these two pairs of nodes are actually directly connected by ropes passing around the pulleys, since the rod is assumed to be a straight rod without bending, these two pairs of nodes are connected to the pulley nodes, and the forces between them and the pulleys are transmitted through the rod. The node before the fixed pulley PM is (b stands for before), the next node is (a stands for after); the node before the movable pulley PE is , the next node is , the corresponding four-link is marked as 、 、 、 Of course we know that and It is actually connected directly around the pulley and The two points are only considered as two sections due to our settings here. and The situation is similar. Figure 5 As shown in the figure 、 、 、 As the name suggests, it represents a previous or next node.

[0067] S300. Perform coordinate system construction and dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain a dynamics model of the gravity siphon effect lunar ladder.

[0068] S310. Based on the Earth-Moon rotating coordinate system, construct a simplified multi-body dynamics model of a gravitational siphon lunar ladder with a coordinate system, and obtain position vectors of model parameters;

[0069] Among them, it should be noted that the position vector of the model parameter specifically includes the closed-loop rope node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley , the position vector of the movable pulley is , the position vector of the previous node of the fixed pulley , the position vector of the next node of the fixed pulley , the position vector of the previous node of the movable pulley The position vector of the next node of the movable pulley .

[0070] Furthermore, in this embodiment, the Earth-Moon rotating coordinate system is used, that is, the origin is set at the common center of mass of the Earth and the Moon, the x-axis points to the Moon and rotates with the revolution of the Moon, the z-axis is the direction of the angular velocity of the Earth-Moon system, and finally the y-axis is determined by the right-hand rule of the three-dimensional coordinate system, as shown in FIG. Figure 2 In such a coordinate system, the positions of the Earth and the Moon remain fixed, but the coordinate system as a whole rotates around the z-axis, so the inertial forces (centrifugal force, Coriolis force) need to be explicitly given in the dynamic equations.

[0071] The main dynamic activities in the Earth-Moon system occur in the ecliptic plane, so the present invention does not consider the movement in the z direction. Therefore, in this coordinate system, the node The position vector is , the Earth's position vector , the moon's position vector , the position vector of the fixed pulley PM are all constant vectors, and the position vector of the movable pulley is Then the position vector of the special node connected to the pulley is recorded as 、 、 、 Etc. Each of the above vectors contains components in two directions, for example .

[0072] S320, based on the position vector of the model parameters, considering the interaction force factor, the gravitational force factor, the centrifugal force factor, the Coriolis force factor and the damping force factor, constructing the dynamic equation of the node parameters;

[0073] Among them, it should be noted that the dynamic equation of the node parameters specifically includes the closed-loop rope node The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the previous node of the fixed pulley, the dynamic equation of the next node of the fixed pulley, the dynamic equation of the previous node of the movable pulley and the dynamic equation of the next node of the movable pulley.

[0074] like Figure 6 As shown, the closed-loop rope node The expression of the kinetic equation is:

[0075]

[0076] In the above formula, represents the i-th closed-loop rope node The concentrated mass, represents the i-th closed-loop rope node The second derivative of the position vector with respect to time, represents the gravitational force of the earth on the nodes of the closed-loop rope, represents the gravitational force of the moon on the nodes of the closed-loop rope, 、 represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, represents the centrifugal force on the closed-loop rope node, represents the Coriolis force on the closed-loop rope node, represents the damping force on the closed-loop rope node;

[0077] The expression of the earth's gravitational force on the closed-loop rope node is:

[0078]

[0079] The expression of the moon's gravitational force on the closed-loop rope node is:

[0080]

[0081] represent and connecting rod between The elastic force points to , then the expression of the elastic force of the connecting rod between adjacent closed-loop rope nodes is:

[0082]

[0083] represent and connecting rod between The elastic force points to , then the expression of the elastic force of the connecting rod between adjacent closed-loop rope nodes is:

[0084]

[0085] The expression of the centrifugal force on the closed-loop rope node is:

[0086]

[0087] The expression of the Coriolis force on the closed-loop rope node is:

[0088]

[0089] In the absence of air, sunlight pressure and other external forces, the main source of damping force is the viscosity of the material. Its specific expression can be obtained through material mechanics experiments. This structure directly uses the linear damping assumption, that is, the damping force is proportional to the speed, and the viscosity coefficient is set to , the direction is always opposite to the direction of node movement, so the damping force on the closed-loop rope node is expressed as:

[0090]

[0091] In addition, it should be noted that, for the fixed pulley PM, its position in the selected coordinate system remains unchanged, and its velocity and acceleration remain zero.

[0092] The dynamic equation of the movable pulley is expressed as:

[0093]

[0094] In the above formula, represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, represents the earth's gravitational force on the movable pulley, represents the gravitational force of the moon on the movable pulley, is the centrifugal force on the movable pulley, is the Coriolis force on the movable pulley, represents the friction force on the movable pulley, represents the elastic force of the connecting rod between the movable pulley and the node before the movable pulley, It represents the elastic force of the connecting rod between the movable pulley and the next node after the movable pulley;

[0095] in, and They represent PE and the two nodes before and after respectively 、 Interconnecting rod 、 The two connecting rods are actually the same rope that goes around the pulley, so their elastic forces should be equal and point to 、 , whose expression is:

[0096]

[0097]

[0098] represents the elongation of a rope section around the pulley, and its expression is:

[0099]

[0100] That is, after the length of this section is less than the original length after deformation, the elastic force is set to 0 to ensure that the rope as a whole is not under pressure. All have this provision, namely .

[0101] The expression of the dynamic equation of the previous node of the fixed pulley is:

[0102]

[0103] In the above formula, represents the concentrated mass of the previous rope node of the fixed pulley, represents the second-order derivative of the position vector of the previous rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the previous node of the fixed pulley, represents the lunar gravitational force on the previous node of the fixed pulley, represents the centrifugal force on the previous node of the fixed pulley, represents the Coriolis force on the previous node of the fixed pulley, represents the friction force on the previous node of the fixed pulley, represents the elastic force of the connecting rod between the previous node and the adjacent node of the fixed pulley, represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away;

[0104] The expression of the dynamic equation of the last node of the fixed pulley is:

[0105]

[0106] In the above formula, represents the concentrated mass of the last rope node of the fixed pulley, represents the second-order derivative of the position vector of the next rope node of the fixed pulley with respect to time, represents the earth's gravitational force on the last node of the fixed pulley, represents the lunar gravitational force on the last node of the fixed pulley, It represents the centrifugal force on the last node of the fixed pulley. represents the Coriolis force on the last node of the fixed pulley, represents the friction force on the last node of the fixed pulley, represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the last node of the fixed pulley and the node further away;

[0107] The expression of the dynamic equation of the previous node of the movable pulley is:

[0108]

[0109] In the above formula, represents the concentrated mass of the previous rope node of the movable pulley, represents the second-order derivative of the position vector of the previous rope node of the movable pulley with respect to time, represents the earth's gravitational force on the previous node of the movable pulley, represents the gravitational force of the moon on the previous node of the movable pulley, represents the centrifugal force on the previous node of the movable pulley, represents the Coriolis force on the previous node of the movable pulley, represents the friction force on the previous node of the movable pulley, represents the elastic force of the connecting rod between the previous node of the movable pulley and the adjacent node, represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and the node further away;

[0110] The expression of the dynamic equation of the last node of the movable pulley is:

[0111]

[0112] In the above formula, represents the concentrated mass of the last rope node of the movable pulley, represents the second-order derivative of the position vector of the next rope node of the movable pulley with respect to time, represents the earth's gravitational force on the last node of the movable pulley, represents the lunar gravitational force on the last node of the movable pulley, It represents the centrifugal force on the last node of the movable pulley. represents the Coriolis force on the last node of the movable pulley, represents the friction force on the last node of the movable pulley, represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, Represents the elastic force of the connecting rod between the adjacent node of the next node of the movable pulley and the node further away.

[0113] Finally, it should be noted that 、 、 、 Each item represents the elastic force of the connecting rod between the adjacent node and the node farther away, and all points in the counterclockwise direction of the node.

[0114] S330. Introduce characteristic node identification rules, transform the dynamic equations of node parameters, and obtain the gravitational siphon effect lunar ladder dynamics model.

[0115] First, it's important to note that the numbers corresponding to special nodes will obviously change during motion, necessitating a mechanism to determine the node numbers at a specific moment. This determination mechanism is not unique and has a critical impact on the algorithm's execution mode and efficiency. Existing methods use a global array variable to store these special node numbers. During the computational process, the algorithm then sequentially determines whether the next node in the direction of motion has become the corresponding special node. This method is highly efficient, but it places demands on the smoothness of the dynamic process. In particular, during the early transient phase, the system experiences significant jitter, making it prone to situations where the next node arrives at the pulley out of sequence, resulting in singularities and computational failure. To overcome this difficulty, an interrupted integration approach can be employed. Upon detecting a singularity, the time history integration calculation is halted, the current result is stored as the initial value for the next calculation, and the position and velocity of the singular node are then forcibly adjusted before the integration is restarted. However, this approach significantly reduces computational efficiency.

[0116] Therefore, an embodiment of the present invention introduces a characteristic node discrimination rule, specifically, determines the closed-loop rope node closest to the pulley, numbers it, determines the target node, and the pulley is a fixed pulley or a movable pulley; determines the next node of the target node and the previous node of the target node, determines the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley; judges the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley; if the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then determines that the next node of the target node is the previous node of the pulley, and the target node is the next node of the pulley; if the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, then determines that the target node is the previous node of the pulley, and the previous node of the target node is the next node of the pulley.

[0117] In this embodiment, if Figure 7 and Figure 8 As shown, take the PE side of the movable pulley as an example. First determine the node closest to PE and get its number , then calculate 、 The distance between two nodes and PE, when the ladder is running in order (that is, the node with a smaller number moves towards the adjacent node with a larger number), if Compare If it is closer to PE, for , For Pea, for On the contrary, if Compare The distance from PE is farther, then Pmin is , For Pea, is .

[0118] A similar method is used to determine the PM side of the fixed pulley 、 The node number.

[0119] In addition, in Python and most programming languages, node numbers can only be one-dimensional arrays, so pay attention to the problem of connecting the beginning and the end. The last number plus one returns to the first number, and the first number minus one is defined as the last number.

[0120] Finally, the embodiment of the present invention also discloses that when a node passes over the pulley, that is, from ( )become ( ), its velocity is no longer given by the integral of the acceleration according to the dynamic equation, but is directly set to a constant rate, and the direction is changed from toward the pulley PM (PE) directly to toward ( ). Without affecting the accuracy, for the sake of simplicity, we can even directly stipulate that its speed becomes ( ) speed. This setting directly gives the equation ( ) are as follows:

[0121]

[0122]

[0123] When a node is become When the quality is changed from become ; When a node mass is become When it is become That is to say, and The node masses between , while the masses of other nodes are all .exist and The relationship in the ordinal array is Greater than When the two are connected, it is necessary to carefully define them as [1~Pea]U[Pmb~N]. This is actually to ensure that the quality of the uplink node is , the downstream node is loaded with goods Increased to .

[0124] The first node after passing the fixed pulley , provided to goods in motion Momentum, thus receiving a reaction force. Until the cargo and the node have the same speed. The actual loading process of this force is relatively complex, and this section uses the overall analysis method to approximate it. First, it is assumed that the cargo just uses one section of travel to reach the same linear speed as the system. This assumption is to avoid dealing with multiple nodes and cargo coupling processes at the same time. In addition, considering only the steady state, the final overall linear speed of the system is , that is, the speed of the goods increases from 0 to , assuming that the force on the cargo remains constant during acceleration, is , then:

[0125]

[0126] and It is mainly composed of the gravity of the earth, the gravity of the moon, cargo and nodes The force between The three items are composed, and at this time the earth's gravity is in the same direction as the movement, the moon's gravity is in the opposite direction of the movement, and when dealing with gravity, it is considered that the cargo and the node At the same location, we can get:

[0127]

[0128] Therefore, the above expression needs to be further modified to become:

[0129]

[0130] It should be said that here The symbol represents assignment, which means modifying the variable based on the previous expression. It can be expressed more conveniently in a sequentially compiled programming language. The expression of has a certain approximation. In computing practice, its direction is always defined as The direction of motion acceleration is opposite. Of course, such approximate processing is reasonable and convenient, and the error can be ignored.

[0131] By combining the above equations, we can obtain the dynamic equation of the system. This dynamic equation is a differential algebraic equation. It can be further degenerated into an ordinary differential equation as follows:

[0132]

[0133] In addition, since the embodiment of the present invention adopts a rotating coordinate system and does not study the case of the moon's elliptical orbit, the time independent variable t is not explicitly included in the equation, and it is a nonlinear autonomous system.

[0134] Furthermore, a simulation experiment was conducted on the embodiment of the present invention. First, a typical reasonable working condition was selected for simulation and post-processing analysis. The natural parameters of the Earth-Moon system are shown in Table 1:

[0135] Table 1 Parameter values ​​used in static calculations

[0136]

[0137] Its main material indicators are shown in Table 2 below:

[0138] Table 2 Material index data table

[0139]

[0140] The movable pulley end of the siphon ladder is located at At 10,000 kilometers, that is, about 63,000 kilometers above the ground, the one-way length of the siphon ladder is about 313,260 kilometers.

[0141] The ladder is divided into 340 nodes in one direction according to the method in Section 5.3, and there are 680 nodes in both directions. An empty container is set at each node. In the simulation, the mass of the container and the mass of the material of the next section of the ladder in the counterclockwise direction are combined and assigned to the node, which is This is equivalent to the density of the material or a corresponding increase in value. In this example, the length of each segment is calculated. , the quality of each node Because each container has a high mass Unchanged, for the convenience of general comparison, the goods and nodes are given the same quality A ratio called the cargo-box mass ratio , in this case =0.1, then the corresponding =9343kg.

[0142] In order to start the numerical simulation smoothly, all nodes are given an initial velocity of 10 in the counterclockwise direction. The Rouge-Kutta 4-5 method is used for simulation, and the time history is from time 0 to day 120, as shown in Figure 9 Figure 2 shows screenshots of typical simulation results from an embodiment of the present invention, along with post-processing of some key parameters and a brief analysis. The results demonstrate that the gravity siphon lunar ladder successfully starts and operates under the operating conditions of this typical example, reaching a stable operating state and effectively transporting cargo, achieving the design objectives. The ladder begins at a low, preset initial speed and gradually accelerates under the influence of the gravity siphon. During operation, the Coriolis forces acting on the ascending and descending sections act in opposite directions, causing the two sides of the ladder to open in opposite directions, just avoiding a collision. Initially, the ladder's opening is affected by elastic forces, but since the elastic forces are a reaction to the Coriolis forces, they are insufficient to cause collisions. Once the ladder reaches a certain speed, the opening remains relatively wide. Eventually, the ladder reaches its steady-state speed, maintaining stable operation for extended periods while continuously loading and unloading cargo.

[0143] Finally, the relationship between steady-state speed and ladder length

[0144] The above results show that the steady-state speed It has little to do with the cargo-to-box mass ratio, which is the most important operating indicator. Which design or operating parameters are mainly affected and what is the relationship? The following attempts to use the principle of conservation of energy to conduct a brief analysis.

[0145] Since in most cases the opening The total length of the ladder is very small, and the deflection angles relative to the Earth-Moon line are also very small. The opening angle will be ignored in this analysis. , the system is approximately considered to be moving up and down along the line connecting the Earth and the Moon.

[0146] First, in steady-state operation, the speed of all nodes in the siphon ladder is the steady-state speed. , the distance between adjacent nodes remains unchanged, and it can be considered that the total elastic potential energy of the system remains unchanged.

[0147] Secondly, the overall gravitational potential energy of the cargo in the downlink section decreases from the lunar surface to the end, which is converted into the kinetic energy of the cargo, increasing the overall kinetic energy of the system.

[0148] Finally, the cargo is thrown away at the end, which is equivalent to the system losing kinetic energy. The lost kinetic energy is equal to the kinetic energy increased by potential energy conversion, so that the overall kinetic energy of the system remains unchanged, that is, the system movement maintains a stable rate. .

[0149] Further increase the mass of the empty node , the quality of single box cargo Evenly distributed on the siphon ladder system, there is a corresponding line density 、 , in unit time Internal, the overall potential energy of the system The changes are as follows:

[0150]

[0151] The first term on the right side of the above formula represents the upward direction, and the second term represents the downward direction. The integral directions of the two are opposite. is the gravitational field intensity gradient of the Earth-Moon system, that is, the gravitational acceleration. The above formula can be simplified to:

[0152]

[0153] In unit time The kinetic energy lost by the system as follows:

[0154]

[0155] equal , and perform the integral operation to obtain:

[0156]

[0157] In the above formula, 、 、 、 、 、 are all constants, only the coordinates of the end movable pulley are is a variable, that is, the steady-state speed of the gravitational siphon lunar ladder It only matters its length.

[0158] It can be seen that the steady-state velocity and internal force of the ladder system decrease as the ladder length decreases, which is generally consistent with the results of the computational integration. The discrepancy between the numerical simulation results and the theoretical analysis results is mainly due to the neglect of the opening in the theoretical analysis. The opening is more complex, with the maximum opening at the ladder end when it is 70,000 to 80,000 kilometers from the Earth.

[0159] In addition, the simulation results show that even at a distance of 120,000 kilometers from the Earth (and the position of the movable pulley after dynamic elastic extension still reaches 119,000 kilometers), the ladder can still operate, although the running speed is very slow. That is, the end of the ladder is more than 110,000 kilometers away from the Earth, but it still does not fall to the moon. =125,000 km, the system fell onto the Moon. This indicates that the allowable length of a gravity-siphon lunar ladder is shorter. The main reason is that a siphon ladder requires a larger movable pulley at the end, which makes the Earth's gravitational pull on the entire system stronger, thus enhancing the overall stability of the system.

[0160] In summary, the embodiments of the present invention have the following advantages compared with the prior art:

[0161] 1) Using a bead-point simplification method, the continuous ladder structure is discretized into a series of nodes and elastic connecting segments, comprehensively considering factors such as the interaction forces between nodes, the gravitational forces of the Earth and the Moon, centrifugal force, Coriolis force, and material damping. A clever mechanical model for the coupling of the rope with the movable and fixed pulleys was devised, along with criteria for determining which nodes are coupled to the pulleys. Through continuous determination, the differential algebraic equation was transformed into a pure differential equation, enabling the uninterrupted, continuous, and practical process of integral solution of the differential equation.

[0162] 2) Provide an effective power system for the ladder's climber, enabling smooth movement on the cable. This invention proposes a power system utilizing gravitational siphoning as a power source. Orbital siphoning is an innovative physical mechanism designed to harness the rotational kinetic energy of an asteroid for propellant-free payload transfer. The core of this concept involves transferring material from the lunar surface to an orbiting collection spacecraft via a payload mass chain connected by a tether perpendicular to the asteroid's surface.

[0163] 3) A detailed sensitivity analysis was conducted on key operating parameters, such as the cargo-to-container mass ratio and ladder length. The results show that the cargo-to-container mass ratio has little impact on the ladder's performance indicators, including steady-state speed, internal forces, and stresses. The main performance indicators of a ladder's operation depend on its total length. This paper presents an analytical analysis of the relationship between steady-state speed and length based on a simplified model, which is validated by comparison with numerical simulation results. The results indicate that the longer the total length of the siphon ladder, the greater its final steady-state operating speed.

[0164] 4) The elevator designed in this embodiment of the present invention reaches a speed of approximately 1600 m / s, and cargo can be transported from the lunar surface to the ground in approximately 2.5 days. Although the linear speed is much lower than that of a rocket, the distance is much closer than most rocket lunar landing trajectories and is approximately a straight line, so the efficiency is not low. It must be noted that the gravity siphon lunar elevator was originally designed to mine lunar minerals and transport them to Earth. However, the uplink does not need to operate empty and can be loaded with lighter payloads for transportation toward the moon. Compared to using rockets for the entire journey, it can significantly save fuel, has a far greater total transport capacity, and is much easier to control during operation and landing and ascent. The travel time of approximately 2.5 days makes this system suitable for manned travel, well within the acceptable range of human interstellar travel.

[0165] Reference Figure 2 , an automatic lunar ladder modeling system based on the gravitational siphon effect, including:

[0166] The first module 201 is used to construct a gravity siphon lunar ladder model;

[0167] The second module 202 is used to perform bead point simplification processing on the gravity siphon lunar ladder model to obtain a simplified multi-body dynamics model of the gravity siphon lunar ladder;

[0168] The third module 203 is used to construct a coordinate system and perform dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain a dynamics model of the gravity siphon lunar ladder.

[0169] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0170] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. The automatic operation lunar ladder modeling method based on the gravitational siphon effect is characterized by: The following steps are involved: Construct a gravitational siphon lunar ladder model; The closed-loop rope in the gravity siphon lunar ladder model is divided into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; It is assumed that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravitational siphon lunar ladder model are both regarded as nodes; Set the fixed pulley node to be connected to the closed-loop rope node and the movable pulley node to be connected to the closed-loop rope node. Set the previous node of the fixed pulley in the gravity siphon lunar ladder model to P. mb The last node of the fixed pulley in the gravitational siphon lunar ladder model is P ma , the previous node of the movable pulley in the gravitational siphon lunar ladder model is P eb The last node of the movable pulley in the gravitational siphon lunar ladder model is P ea , we obtain the simplified multi-body dynamics model of the gravitational siphon lunar ladder; The coordinate system construction and dynamic analysis of the simplified multi-body dynamics model of the gravitational siphon lunar ladder are carried out to obtain the dynamics model of the gravitational siphon effect lunar ladder.

2. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 1 is characterized in that: The gravitational siphon lunar ladder model specifically includes a closed-loop rope, a fixed pulley, a movable pulley and a cargo box, wherein the fixed pulley is distributed on the near-Earth surface of the moon, and the movable pulley is distributed on the near-Earth surface of the earth. The closed-loop rope runs around both ends of the fixed pulley and the movable pulley respectively. The closed-loop rope running toward the moon is defined as the upward direction, and the closed-loop rope running toward the earth is defined as the downward direction. Cargo boxes are distributed at equal intervals on the upper surface of the closed-loop rope.

3. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 2 is characterized in that: The step of performing coordinate system construction and dynamic analysis on the simplified multi-body dynamics model of the gravity siphon lunar ladder to obtain the dynamics model of the gravity siphon lunar ladder specifically includes: Based on the Earth-Moon rotating coordinate system, a simplified multi-body dynamics model of the gravitational siphon lunar ladder with a coordinate system is constructed to obtain the position vectors of the model parameters; Based on the position vector of the model parameters, the dynamic equations of the node parameters are constructed by considering the interaction force factors, gravity factors, centrifugal force factors, Coriolis force factors and damping force factors; Characteristic node identification rules are introduced, and the dynamic equations of node parameters are transformed to obtain the dynamic model of the lunar ladder with gravitational siphon effect.

4. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 3 is characterized in that: The position vector of the model parameters specifically includes the closed-loop rope node P i The position vector is r i 、The Earth's position vector r e 、The moon's position vector r m , the position vector r of the fixed pulley pm , the position vector of the movable pulley is r pe , the position vector r of the previous node of the fixed pulley mb , the position vector r of the next node of the fixed pulley ma , the position vector r of the previous node of the movable pulley eb The position vector r of the next node of the movable pulley ea .

5. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 4 is characterized in that: The dynamic equations of the node parameters specifically include the closed-loop rope node P i The dynamic equation of the fixed pulley, the dynamic equation of the movable pulley, the dynamic equation of the previous node of the fixed pulley, the dynamic equation of the next node of the fixed pulley, the dynamic equation of the previous node of the movable pulley and the dynamic equation of the next node of the movable pulley, where: The closed-loop rope node P i The expression of the kinetic equation is: In the above formula, m i represents the i-th closed-loop rope node P i The concentrated mass, represents the i-th closed-loop rope node P i The second derivative of the position vector with respect to time, g ie represents the gravitational force of the earth on the nodes of the closed-loop rope, g im represents the gravitational force of the moon on the nodes of the closed-loop rope, f i+1 、f i represents the elastic force of the connecting rod between adjacent closed-loop rope nodes, fr i represents the centrifugal force on the closed-loop rope node, k i is the Coriolis force on the closed-loop rope node, c i represents the damping force on the closed-loop rope node; The dynamic equation of the movable pulley is expressed as: In the above formula, m pe represents the concentrated mass of the movable pulley, represents the second-order derivative of the position vector of the movable pulley with respect to time, g pee The gravitational force on the movable pulley is expressed as pem represents the gravitational force of the moon on the movable pulley, fr pe The centrifugal force on the movable pulley, k pe is the Coriolis force on the movable pulley, c pe represents the friction force on the movable pulley, f eb represents the elastic force of the connecting rod between the movable pulley and the node before the movable pulley, f ea It represents the elastic force of the connecting rod between the movable pulley and the next node after the movable pulley; The expression of the dynamic equation of the previous node of the fixed pulley is: In the above formula, m mb represents the concentrated mass of the previous rope node of the fixed pulley, The second derivative of the position vector of the previous rope node of the fixed pulley with respect to time, g mbe Indicates the gravitational force of the earth on the previous node of the fixed pulley, g mbm represents the lunar gravitational force on the previous node of the fixed pulley, fr mb represents the centrifugal force on the previous node of the fixed pulley, k mb represents the Coriolis force on the previous node of the fixed pulley, c mb represents the friction force on the previous node of the fixed pulley, f mb represents the elastic force of the connecting rod between the previous node of the fixed pulley and the adjacent node, f mbb represents the elastic force of the connecting rod between the adjacent node of the previous node of the fixed pulley and a node further away; The expression of the dynamic equation of the last node of the fixed pulley is: In the above formula, m ma represents the concentrated mass of the last rope node of the fixed pulley, The second derivative of the position vector of the next rope node of the fixed pulley with respect to time, g mae Indicates the gravitational force on the last node of the fixed pulley, g mam represents the lunar gravitational force on the last node of the fixed pulley, fr ma k represents the centrifugal force on the last node of the fixed pulley, ma represents the Coriolis force on the last node of the fixed pulley, c ma represents the friction force on the last node of the fixed pulley, f ma represents the elastic force of the connecting rod between the next node of the fixed pulley and the adjacent node, f maa represents the elastic force of the connecting rod between the adjacent node of the last node of the fixed pulley and the node further away; The expression of the dynamic equation of the previous node of the movable pulley is: In the above formula, m eb represents the concentrated mass of the previous rope node of the movable pulley, The second derivative of the position vector of the previous rope node of the movable pulley with respect to time, g ebe represents the gravitational force exerted on the previous node of the movable pulley, g ebm represents the gravitational force of the moon on the previous node of the movable pulley, fr eb represents the centrifugal force on the previous node of the movable pulley, k eb represents the Coriolis force on the previous node of the movable pulley, c eb represents the friction force on the previous node of the movable pulley, f eb represents the elastic force of the connecting rod between the previous node of the movable pulley and the adjacent node, f ebb represents the elastic force of the connecting rod between the adjacent node of the previous node of the movable pulley and the node further away; The expression of the dynamic equation of the last node of the movable pulley is: In the above formula, m ea represents the concentrated mass of the last rope node of the movable pulley, The second derivative of the position vector of the next rope node of the movable pulley with respect to time, g eae The gravitational force on the last node of the movable pulley is represented by eam represents the lunar gravitational force on the last node of the movable pulley, fr ea k represents the centrifugal force on the last node of the movable pulley. ea represents the Coriolis force on the last node of the movable pulley, c ea represents the friction force on the last node of the movable pulley, f eb represents the elastic force of the connecting rod between the next node of the movable pulley and the adjacent node, f eaa Represents the elastic force of the connecting rod between the adjacent node of the next node of the movable pulley and the node further away.

6. The method for modeling an automatically operated lunar ladder based on the gravitational siphon effect according to claim 5 is characterized in that: The introduced characteristic node identification rule is specifically as follows: Determine the closed-loop rope node closest to the pulley, number it, and determine the target node, wherein the pulley is a fixed pulley or a movable pulley; Determine the next node of the target node and the previous node of the target node, determine the distance between the next node of the target node and the pulley, and determine the distance between the previous node of the target node and the pulley; Determine the distance between the next node of the target node and the pulley, and the distance between the previous node of the target node and the pulley; If the distance between the next node of the target node and the pulley is less than the distance between the previous node of the target node and the pulley, then the next node of the target node is determined to be the previous node of the pulley and the target node is determined to be the next node of the pulley; If the distance between the next node of the target node and the pulley is greater than the distance between the previous node of the target node and the pulley, the target node is determined to be the previous node of the pulley and the previous node of the target node is the next node of the pulley.

7. The automatic operation lunar ladder modeling system based on the gravitational siphon effect is characterized by: Includes the following modules: The first module is used to construct a gravitational siphon lunar ladder model; The second module is used to divide the closed-loop rope in the gravitational siphon lunar ladder model into several segments with equal spacing, and each segment of the closed-loop rope is regarded as a node; It is assumed that adjacent nodes are connected by elastic straight rods, and the fixed pulley and movable pulley in the gravitational siphon lunar ladder model are both regarded as nodes; Set the fixed pulley node to be connected to the closed-loop rope node and the movable pulley node to be connected to the closed-loop rope node. Set the previous node of the fixed pulley in the gravity siphon lunar ladder model to P. mb The last node of the fixed pulley in the gravitational siphon lunar ladder model is P ma , the previous node of the movable pulley in the gravitational siphon lunar ladder model is P eb The last node of the movable pulley in the gravitational siphon lunar ladder model is P ea , we obtain the simplified multi-body dynamics model of the gravitational siphon lunar ladder; The third module is used to construct the coordinate system and conduct dynamic analysis on the simplified multi-body dynamics model of the gravitational siphon lunar ladder, and obtain the dynamics model of the gravitational siphon effect lunar ladder.

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