A method and apparatus for analyzing the coupling characteristics of asteroid impactors based on SPH

Abstract

This invention provides a method and apparatus for analyzing the coupling characteristics of asteroid impactors based on SPH (Smooth Particle Hydrodynamics), belonging to the field of spacecraft dynamics modeling. The method includes: establishing a liquid sloshing model described by the SPH method; SPH represents smooth particle hydrodynamics; calculating the liquid sloshing forces and moments in a non-inertial frame based on the liquid sloshing model; establishing a distributed parameter model of the flexible spacecraft; integrating the liquid sloshing forces and moments in the non-inertial frame into the distributed parameter model of the flexible spacecraft to establish a dynamic model of the liquid-filled flexible spacecraft; and, based on the dynamic model of the liquid-filled flexible spacecraft, analyzing the coupling characteristics of the central rigid body attitude and position, flexible appendage vibration, and liquid fuel sloshing as system states. This invention provides a new approach and reference for modeling liquid-filled flexible spacecraft.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft dynamics modeling, specifically involving a method and apparatus for analyzing the coupling characteristics of asteroid impactors based on SPH (Smooth Particle Hydrodynamics). Background Technology

[0002] Near-Earth asteroid impacts on Earth are a matter of vital importance to human survival and safety, representing a long-term common threat to humanity. Asteroid defense missions have become a crucial issue in the international space community. Their core objective is to mitigate asteroid impacts through early warning and effective intervention before they occur, while simultaneously exploring the potential for asteroid resource development and utilization. Compared to general deep-space exploration missions, asteroid impact missions are characterized by their instantaneous nature, non-repeatability, real-time nature, and autonomy. In this mission, the impactor's impact velocity is approximately 10 km / s, employing autonomous navigation, guidance, and control. Once the target is missed, recovery is difficult, thus requiring extremely high precision in guidance and control. Given that the asteroid impact mission's on-orbit flight period is approximately two years, liquid fuel will account for more than 50% of its total weight to meet its on-orbit operational lifespan. Furthermore, to ensure long-distance Earth communication and meet the power requirements of the communication antenna, the impactor needs to be equipped with large-area solar panels.

[0003] Spacecraft carrying a large proportion of liquid fuel and extensive flexible attachments exhibit rigid-flexible-fluid coupling characteristics. They are highly susceptible to vibrations in flexible attachments and sloshing of liquid fuel due to external space environment torque disturbances or instantaneous excitation during thruster activation and deactivation. Failure to address these issues can lead to spacecraft attitude instability and even fatigue fracture. This is particularly problematic for asteroid impact missions, which require high attitude control accuracy; the flexible solar panels and liquid fuel they carry could cause attitude instability and mission failure. Traditional rigid-body spacecraft modeling and control methods struggle to handle the vibrations and sloshing of flexible attachments. Therefore, research on modeling, coupling characteristic analysis, and control of liquid-filled flexible spacecraft has become crucial to the success of on-orbit missions involving these vehicles.

[0004] Existing research on liquid-filled flexible spacecraft generally employs the equivalent mechanical method to model liquid sloshing and the finite element method to model flexible attachments, establishing a rigid-flexible-fluid coupling model of the liquid-filled flexible spacecraft using the Hamiltonian method. However, these modeling methods have several unresolved issues. First, the equivalent mechanical method struggles to handle large-scale nonlinear sloshing. It also struggles to account for liquid surface tension, which is crucial for liquid fuels in microgravity environments. Second, the equivalent mechanical method cannot accurately represent the liquid surface or shape during sloshing, hindering research on tank management strategies and liquid sloshing control methods. Finally, the equivalent parameters are difficult to determine in the equivalent mechanical method. While the finite element method can accurately describe the vibration of flexible attachments and simplifies controller design, modal truncation of higher-order modes during modeling can lead to spillover effects, impacting control performance.

[0005] Chinese patent application CN 112364571 A proposes a modeling method for the dynamics of large and complex coupled spacecraft. It derives the standard equation for free vibration and solves for the natural frequencies by simplifying the solar panel as a cantilever beam; it uses a second-order spring-mass model to model liquid sloshing and supplements this model with CFD methods; finally, it establishes a rigid-flexible-fluid coupled dynamic model through the law of conservation of angular momentum. While this provides a modeling method for coupled spacecraft, several problems remain to be solved. First, the cantilever beam model is discretized using the assumed modal method, which inevitably introduces spillover effects. Second, although supplementing the equivalent mechanical model with CFD methods can accommodate large sloshing, the parameters of the equivalent mechanical model need to be determined experimentally or through CFD methods, and it is difficult to provide the liquid shape under microgravity conditions.

[0006] The journal article “Yu Qiang, Wang Tianshu. Dynamics Analysis of Large-Scale Liquid Sloshing in Spacecraft Tanks [J]. Science in China: Physics, Mechanics and Astronomy, 2019, 49(2):8.DOI:10.1360 / SSPMA2018-00109” proposes using the SPH method to calculate the forces and torques of large-scale liquid sloshing. Based on the SPH method, the momentum theorem, and the angular momentum theorem, the paper derives the forces and torques of liquid sloshing within the spacecraft's intrinsic system. Although it proposes a method for calculating the forces and torques of sloshing within this system, it does not combine the rigid body attitude and flexible accessory vibrations of the spacecraft with the liquid sloshing, and it does not establish coupled dynamic equations for a liquid-filled flexible spacecraft. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method and apparatus for analyzing the coupling characteristics of asteroid impactors based on Smooth Particle Hydrodynamics (SPH). It utilizes the Smooth Particle Hydrodynamics (SPH) method and the distributed parameter method, applicable to asteroid impactors, to establish a rigid-flexible-fluid coupling model for liquid-filled flexible spacecraft. This model accurately describes the nonlinear sloshing of liquids under microgravity conditions and provides the liquid shape during the sloshing process. Furthermore, the continuous system dynamics model established by the distributed parameter method fundamentally avoids spillage effects. This invention provides a new approach and reference for modeling liquid-filled flexible spacecraft.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for analyzing the coupling characteristics of asteroid impactors based on SPH includes the following steps:

[0010] Step 1: Establish a liquid sloshing model described by the SPH method; SPH stands for smooth particle hydrodynamics.

[0011] Step 2: Calculate the liquid sloshing forces and torques in a non-inertial frame based on the liquid sloshing model;

[0012] Step 3: Establish a distributed parameter model for the flexible spacecraft;

[0013] Step 4: Integrate the liquid sloshing forces and torques in the non-inertial frame into the distributed parameter model of the flexible spacecraft to establish a dynamic model of the liquid-filled flexible spacecraft;

[0014] Step 5: Based on the dynamic model of the liquid-filled flexible spacecraft established in Step 4, the attitude of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel are taken as the system states. Appropriate initial simulation conditions are set for the states to perform numerical simulation, and the coupling characteristics of the attitude and position of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel are analyzed.

[0015] This invention also provides an asteroid impactor coupling characteristic analysis device based on SPH, comprising the following modules:

[0016] The sloshing model building module establishes a liquid sloshing model described by the SPH method; SPH stands for smooth particle hydrodynamics.

[0017] The calculation module calculates the liquid sloshing forces and torques in a non-inertial frame based on the liquid sloshing model.

[0018] The parameter model building module is used to build a distributed parameter model for flexible spacecraft.

[0019] The dynamic model building module integrates the liquid sloshing forces and torques in a non-inertial frame into the distributed parameter model of the flexible spacecraft, thus establishing a dynamic model of the liquid-filled flexible spacecraft.

[0020] The analysis module, based on the dynamic model of the liquid-filled flexible spacecraft, takes the attitude of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel as the system states. It sets appropriate initial simulation conditions for the states and performs numerical simulation to analyze the coupling characteristics of the attitude and position of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel.

[0021] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for analyzing the coupling characteristics of an asteroid impactor based on SPH.

[0022] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for analyzing the coupling characteristics of an asteroid impactor based on SPH.

[0023] Beneficial effects:

[0024] This invention focuses on the field of liquid-filled flexible spacecraft and innovatively proposes a novel modeling method. This method integrates Smooth Particle Hydrodynamics (SPH) and distributed parameter methods to construct a dynamic model specifically applicable to the nonlinear sloshing of liquids in microgravity environments. This dynamic model possesses superior performance, accurately describing the nonlinear sloshing behavior of liquids in microgravity environments. Through precise algorithm and parameter settings, it accurately presents the dynamic shape changes of the liquid during the sloshing process, providing high-precision visualization evidence for related research. Crucially, this model, based on a continuous system dynamic model established by the distributed parameter method, effectively avoids the spillover effects that may occur in traditional models from a theoretical perspective, significantly improving the model's stability and reliability. The modeling method proposed in this invention not only provides a new perspective and powerful tool for the study of liquid sloshing in liquid-filled flexible spacecraft under microgravity environments but also opens up new ideas and directions for the accurate modeling and efficient control strategy formulation of subsequent liquid-filled flexible spacecraft, and is expected to promote technological progress and development in this field. Attached Figure Description

[0025] Figure 1 This is a flowchart of the SPH-based asteroid impactor coupling characteristic analysis method according to an embodiment of the present invention.

[0026] Figure 2 A flowchart illustrating the steps of numerical simulation of a liquid-filled flexible spacecraft based on the SPH method and the distributed parameter method;

[0027] Figure 3 This is a schematic diagram showing the location of the liquid storage tank and SPH particles;

[0028] Figure 4aA schematic diagram of the initial state of SPH particles in a liquid storage tank and fuel;

[0029] Figure 4b A schematic diagram of the pre-equilibrium state of liquid storage tanks and fuels under SPH particle microgravity environment.

[0030] Figure 5 This is a graph showing the change in the attitude angle of the central rigid body under symmetrical vibration conditions.

[0031] Figure 6 For a central rigid body under symmetrical vibration conditions Axial position change curve;

[0032] Figure 7 For a central rigid body under symmetrical vibration conditions Axial position change curve;

[0033] Figure 8 Under symmetrical vibration conditions Directional swaying force Line graph;

[0034] Figure 9 Under symmetrical vibration conditions Directional swaying force Line graph;

[0035] Figure 10 The torque of swaying motion under symmetrical vibration conditions Line graph.

[0036] The attached diagram is labeled as follows: central rigid body 1, flexible attachment 2, and liquid storage tank 3. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0038] like Figure 1 As shown, an embodiment of the present invention provides a method for analyzing the coupling characteristics of asteroid impactors based on SPH, comprising the following steps:

[0039] Step 1: Establish a liquid sloshing model described by the SPH method, including:

[0040] Step 1.1: Define the liquid domain and boundary conditions for the initial SPH particle distribution in Step 1.2, including:

[0041] Step 1.1.1: Determine the range of motion of the liquid sloshing based on the shape of the spacecraft tank, and set the boundary conditions.

[0042] Step 1.1.2: Define the initial state of the liquid based on its actual physical properties, including volume, height, density, and dynamic viscosity coefficient.

[0043] Step 1.2: Determine the initial SPH particle distribution based on the liquid domain and boundary conditions to provide initial parameters for subsequent SPH numerical simulations, including:

[0044] Step 1.2.1: Initialize the distribution of real particles in the liquid domain, and set the initial spacing and mass of the real particles.

[0045] Step 1.2.2: Initialize the distribution of virtual particles in the boundary domain, and set the initial spacing and mass of the virtual particles.

[0046] Step 1.3: Select the kernel function, including:

[0047] Select an appropriate kernel function based on the fluid properties and set a smooth length to control the range of inter-particle interactions.

[0048] Step 1.4: Based on the kernel function, establish the Navier-Stokes equations based on SPH, including:

[0049] The continuity equation is:

[0050] ;

[0051] The above formula uses dummy indices and Einstein's summation convention for representation. This represents the dummy index; N represents the total number of particles within the support domain of the particle. This represents the density of particle i; This represents the mass of particle j; Dumb Indicators The relative velocities of particles i and j in the direction; intermediate function , Represents a smooth kernel function; It represents the smooth length and controls the range of interactions between particles; This represents the position vector of particle i. Let t represent the position vector of particle j, and t represent time.

[0052] The momentum equation is:

[0053] ;

[0054] in, This represents the isotropic pressure of particle i; It also refers to a dummy indicator; It is the Kronecker symbol if and only if hour, In all other cases, the value is 0; These represent the dummy index of particle i. Velocity vector in direction, position vector; This represents the dynamic viscosity coefficient of particle i. This represents the dynamic viscosity coefficient of particle j; This represents the shear strain rate of particle i; Indicates that particle i is in The acceleration of physical force in a certain direction.

[0055] in, ;

[0056] in, , This represents the distance between particle i and particle j; Dumb Indicators The relative velocities of particles j and i in the direction; Indicates that particle i is in the dummy index Position vector in the direction.

[0057] Step 2: Based on the liquid sloshing model, calculate the liquid sloshing forces in a non-inertial frame of reference, including:

[0058] Step 2.1: Obtain the angular velocity and angular acceleration of the spacecraft in the inertial frame; obtain the position of particle i at the current moment in the non-inertial frame. and speed .

[0059] Step 2.2: Establish the SPH discrete equations in non-inertial frames.

[0060] ;

[0061] in, Indicates that particle i is in the dummy index The inertial force acting in the direction; Represents particles Position vector relative to the body coordinate system This represents the position vector of the center of the liquid tank in the body coordinate system; It represents the absolute derivative of a vector with respect to time; This represents the relative derivative with respect to time within this system; The translational acceleration of the spacecraft's center of mass. Indicates the velocity of the spacecraft's center of mass; Represents the angular acceleration of a spacecraft. Indicates the angular velocity of the spacecraft; Represents particles The interparticle forces acting upon it; Represents particles The physical force (including gravity) experienced. This represents the dynamic viscosity coefficient of particle j. This represents the shear strain rate of particle j.

[0062] Step 2.3: Calculate the force of liquid sloshing.

[0063] ;

[0064] in, This indicates the force exerted by the liquid sloshing on the tank; This indicates the contact force between the tank and the liquid; This represents the inertial force acting on a liquid in a non-inertial frame of reference. Indicates the body force acting on a liquid; This represents the mass of particle i (each particle has the same mass); This is the time step for SPH simulation; The difference symbol is used. This represents the inertial force exerted on particle i in the liquid in a non-inertial frame of reference.

[0065] Step 2.4: Calculate the liquid sloshing torque.

[0066] ;

[0067] in, This indicates the torque exerted by the liquid sloshing. This indicates the contact torque of the tank with the liquid.

[0068] Step 3: Establish a distributed parameter model for the flexible spacecraft, including:

[0069] Step 3.1: Define the structural characteristics of the flexible spacecraft.

[0070] Step 3.2: Establish a dynamic description of the flexible component.

[0071] Step 3.3: Establish a distributed parameter model for the flexible spacecraft using Hamilton's principle and variational method.

[0072] ;

[0073] in, State variables include rigid body position, velocity, attitude angle and attitude angular velocity, and flexible attachment deflection, etc. This represents the linear part of the equations of motion for a rigid body. This represents the nonlinear part of the equations of rigid body dynamics. This represents the linear part of the vibration equation for flexible attachment i. This represents the nonlinear part of the vibration equation for flexible attachment i; It refers to control torque, including control force and control torque.

[0074] Step 4: Establish a dynamic model of the liquid-filled flexible spacecraft using the distributed parameter model of the flexible spacecraft as the dynamic model for both the central rigid body and the flexible appendages, including:

[0075] The liquid sloshing force and torque calculated in step 3 are introduced as the resultant torque of the external disturbance force.

[0076] ;

[0077] in, The force and torque representing the liquid sloshing motion are obtained through step 2. Indicates the acceleration of the central rigid body; The rigid body attitude angle; This represents the position vector of particle i relative to the body coordinate system.

[0078] Step 5: Based on the dynamic model of the liquid-filled flexible spacecraft, perform coupling characteristic analysis, such as... Figure 2 As shown, it includes:

[0079] Step 5.1: Set the integration step size and simulation duration.

[0080] Step 5.1.1: Set the integration step size for the spacecraft attitude dynamics module This ensures the accuracy and stability of numerical integration.

[0081] Step 5.1.2: Set the time step for liquid sloshing integration in the SPH method. Based on the physical characteristics of liquid sloshing simulation, an appropriate time step is selected to ensure the accuracy of liquid particle motion and the computational stability of the SPH method.

[0082] Step 5.1.3: Set the simulation duration T.

[0083] Step 5.2: Initialization, obtain the initial state information of the spacecraft and the initial distribution information of liquid particles in the tank.

[0084] Step 5.2.1: Obtain the spacecraft state information at the initial time t=t0.

[0085] The attitude, position, velocity, and other state variables of the spacecraft at the initial time t0 are extracted to provide initial conditions for subsequent dynamic calculations.

[0086] Step 5.2.2: Initialize the liquid sloshing state.

[0087] Based on information such as the liquid distribution, velocity, and density within the liquid tank, the SPH particle configuration of the liquid is initialized. Considering the initial distribution of liquid particles under microgravity conditions, the liquid particles need to undergo pre-equilibrium (i.e.,...). Figure 2 Pre-equilibrium of liquid particles in a microgravity environment.

[0088] Step 5.3: Simulate the liquid sloshing using the SPH method to calculate the sloshing force and torque.

[0089] Step 5.3.1: Based on the initial spacecraft state extracted in Step 5.2.1, during t=t0~t0+ Within a given time period, the SPH method was used to simulate liquid sloshing.

[0090] Step 5.3.2: During the integration period Inside, based on the motion of liquid particles, the force and torque exerted by liquid sloshing on the spacecraft are calculated (i.e., Figure 2 (Calculation of liquid sloshing force and torque).

[0091] Step 5.4: Update spacecraft status information.

[0092] Based on the calculated swaying force and torque, it is considered that Within a step length, the spacecraft is subjected to external liquid sloshing forces and torques. Based on the dynamic model of the liquid-filled flexible spacecraft, t = t + ... Real-time spacecraft status information.

[0093] Step 5.5: Repeat the calculation until the simulation terminates.

[0094] Determine whether the simulation termination condition t>T is met at the current time. If it is met, end the calculation. If it is not met, use the current time t as the initial time and repeat steps 5.3 to 5.4 until the simulation termination time is reached.

[0095] Example:

[0096] A rigid-flexible-fluid coupled spacecraft system, consisting of a central rigid body 1, flexible attachments 2, and liquid fuel, is as follows: Figure 3 As shown. Wherein, the coordinate system... Indicates an inertial coordinate system; Indicates a coordinate system fixed to the central rigid body; and The coordinate systems for the right and left flexible attachments are shown, respectively. Liquid fuel is placed in liquid tank 3. For ease of modeling and simulation, only motion within a two-dimensional plane is considered. The flexible attachments 2 are symmetrically installed on both sides of the spacecraft, and the liquid tank 3 is spherical. Figure 3 The relevant parameter settings are shown in Table 1:

[0097] Table 1

[0098]

[0099] Based on the above parameters, this embodiment includes the following steps to establish a dynamic model of a liquid-filled flexible spacecraft based on the SPH method and the distributed parameter method:

[0100] Step 1: Establish a liquid sloshing model described by the SPH method.

[0101] ;

[0102] ;

[0103] Step 2: Calculate the force of liquid sloshing in a non-inertial frame.

[0104] ;

[0105] ;

[0106] Step 3: Establish a distributed parameter model for flexible spacecraft.

[0107] Based on Hamilton's principle and variational method, considering only the central rigid body and flexible attachments, the distributed parameter model of the flexible spacecraft is established as follows:

[0108] ;

[0109] The first formula represents the dynamic model of the central rigid body, while the remaining formulas represent the vibration equations of the flexible attachments.

[0110] Step 4: Among the central rigid body, flexible attachments, and liquid fuel, the central rigid body and flexible attachments interact directly, as do the central rigid body and liquid fuel. The flexible attachments and liquid fuel interact indirectly through the central rigid body. Therefore, after obtaining the distributed parameter model of the flexible spacecraft, by introducing liquid sloshing force and torque models into the central rigid body dynamics model, a direct interaction model between the central rigid body and liquid fuel is established, thereby establishing the dynamics model of the liquid-filled flexible spacecraft.

[0111] ;

[0112] The above expression can be written in integral form as follows:

[0113] (1)

[0114] (2)

[0115] (3)

[0116] (4)

[0117] (5)

[0118] (6)

[0119] ;

[0120] ;

[0121] ;

[0122] Formulas (1) to (3) correspond to matrix forms: , representing the dynamic model of rigid body rotation and translation; formulas (4) to (5) correspond to matrix forms: , represents the vibration dynamics model of the flexible attachment, where formula (5) represents the boundary conditions for the vibration of the flexible attachment; formula (6) corresponds to the last four rows of formulas in the matrix form, representing the liquid sloshing force and torque calculation model using the SPH method. The following symbols are defined in the above formulas:

[0123] If the function f(x,t) is a function of spatial coordinate x and time coordinate t, then the first and second partial derivatives with respect to t are represented by the following notation:

[0124] ;

[0125] The first, second, third, and fourth partial derivatives with respect to x are expressed in the following form:

[0126] ;

[0127] In addition, in the above formula These represent the moment of inertia, radius, and mass of the central rigid body, respectively. These represent the positions of the central rigid body in the inertial frame of reference, respectively. Indicates the rigid body attitude angle; These represent the linear density, length, elastic modulus, and deflection of the flexible attachment on the left, respectively. These represent the linear density, length, elastic modulus, and deflection of the flexible attachment on the right (assuming the flexible attachments on both sides have the same density). This indicates the mass of the end-load carried by the flexible attachments on both sides; These represent the control torque on the central rigid body, the control force on the central rigid body in the X direction, the control force on the central rigid body in the Y direction, and the control force on the flexible attachment, respectively. These represent the fourth-order partial derivatives of the left and right flexible attachments with respect to the spatial coordinate x, respectively.

[0128] Step 5: Based on the established dynamic model, perform coupling characteristic analysis.

[0129] Step 5.1: Simulation step size setting. The time interval for the liquid sloshing SPH simulation is... The spacecraft dynamics simulation time interval is This means that spacecraft dynamics integration is performed every 100 SPH simulation steps. Because simulation calculations are slow, the simulation time is set to T=30s in this example.

[0130] Step 5.2: Set the integration step size.

[0131] Step 5.2.1: Set the integration step size for the spacecraft attitude dynamics module This ensures the accuracy and stability of numerical integration. The spacecraft dynamics simulation time interval is... Since the simulation calculation is slow, the simulation time is set to T=30s in this example.

[0132] Step 5.2.2: Set the time step for liquid sloshing integration in the SPH method. The time interval for SPH simulation of liquid sloshing is... .

[0133] Step 5.3: Initialize spacecraft status information.

[0134] Step 5.3.1: Obtain the spacecraft state information at the initial time t0. Assume that at the initial time, only the flexible appendage of the spacecraft is subjected to external excitation and undergoes symmetrical vibration, with an initial amplitude of 0.2m.

[0135] Step 5.3.2: Initialize the liquid sloshing state, such as... Figure 4a , Figure 4b As shown.

[0136] Step 5.4: Simulate the liquid sloshing using the SPH method to calculate the sloshing force and torque.

[0137] Step 5.4.1: Based on the spacecraft initial state extracted in Step 5.3.1, t0-t0+ Simulations of liquid sloshing using the SPH method were performed within a specified time period.

[0138] Step 5.4.2: During the integration period Inside, based on the motion of liquid particles, the force and torque exerted by liquid sloshing on the spacecraft are calculated.

[0139] Step 5.5: Update spacecraft status information.

[0140] Based on the calculated swaying force and torque, it is considered that Within a step length, the spacecraft is subjected to external liquid sloshing forces and torques. Based on the dynamic model, t = t + t is updated. Real-time spacecraft status information.

[0141] Step 5.6: Repeat the calculation until the simulation terminates.

[0142] Using the current time t as the initial time, repeat steps 5.3 to 5.4 until the simulation ends.

[0143] The simulation results are as follows Figures 6-10 As shown, Figure 5 is a curve showing the change in the attitude angle of the central rigid body under symmetrical vibration conditions; Figure 6 is a curve showing the change in the attitude angle of the central rigid body under symmetrical vibration conditions. Figure 7 shows the position variation curve along the axial direction; Figure 7 shows the central rigid body under symmetrical vibration conditions. Figure 8 shows the position variation curve in the axial direction under symmetrical vibration conditions. Directional swaying force Curve graph; Figure 9 shows the symmetrical vibration condition. Directional swaying force Curve graph; Figure 10 shows the swaying torque under symmetrical vibration conditions. Line graph.

[0144] from Figure 5-10 As can be seen from the present invention, the coupling characteristic analysis method for liquid-filled flexible spacecraft based on the SPH method and distributed parameters can accurately describe the influence of liquid sloshing and flexible accessory vibration on spacecraft attitude, adapt to large nonlinear sloshing in microgravity environment, and has certain engineering value, providing a reference for subsequent modeling and controller design.

[0145] This invention also provides an asteroid impactor coupling characteristic analysis device based on SPH, comprising the following modules:

[0146] The sloshing model building module establishes a liquid sloshing model described by the SPH method; SPH stands for smooth particle hydrodynamics.

[0147] The calculation module calculates the liquid sloshing forces and torques in a non-inertial frame based on the liquid sloshing model.

[0148] The parameter model building module is used to build a distributed parameter model for flexible spacecraft.

[0149] The dynamic model building module integrates the liquid sloshing forces and torques in a non-inertial frame into the distributed parameter model of the flexible spacecraft, thus establishing a dynamic model of the liquid-filled flexible spacecraft.

[0150] The analysis module, based on the dynamic model of the liquid-filled flexible spacecraft, takes the attitude of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel as the system states. It sets appropriate initial simulation conditions for the states and performs numerical simulation to analyze the coupling characteristics of the attitude and position of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel.

[0151] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for analyzing the coupling characteristics of an asteroid impactor based on SPH.

[0152] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for analyzing the coupling characteristics of an asteroid impactor based on SPH.

[0153] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0154] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0155] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0156] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0157] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0158] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for analyzing the coupling characteristics of asteroid impactors based on SPH, characterized in that, Includes the following steps: Step 1: Establish a liquid sloshing model described by the SPH method; SPH stands for smooth particle hydrodynamics. Step 2: Calculate the liquid sloshing forces and torques in a non-inertial frame based on the liquid sloshing model; Step 3: Establish a distributed parameter model for the flexible spacecraft; Step 4: Integrate the liquid sloshing forces and torques in the non-inertial frame into the distributed parameter model of the flexible spacecraft to establish a dynamic model of the liquid-filled flexible spacecraft, including: Introducing the liquid sloshing force and torque as the resultant torque of external disturbance forces: ； in, State variables include rigid body position, velocity, attitude angle and attitude angular velocity, and flexible attachment deflection; This represents the linear part of the equations of motion for a rigid body. This represents the nonlinear part of the equations of rigid body dynamics. This represents the linear part of the vibration equation for flexible attachment i1. This represents the nonlinear part of the vibration equation for the flexible attachment i1; Indicates control torque. ; Indicates the force used in the sloshing of the liquid. and torque The vector is obtained through step 2; N represents the total number of particles; This represents the density of particle i; This represents the mass of particle j; Dumb Indicators The relative velocities of particles i and j in the direction; intermediate function , Represents a smooth kernel function; It represents the smooth length and controls the range of interactions between particles; This represents the position vector of particle i. Let t represent the position vector of particle j, and t represent time. This represents the isotropic pressure of particle i; It also refers to a dummy indicator; It is a Kronecker symbol if and only if hour, In all other cases, the value is 0; These represent the dummy index of particle i. Velocity vector in direction, position vector; This represents the dynamic viscosity coefficient of particle i. This represents the dynamic viscosity coefficient of particle j; This represents the shear strain rate of particle i; Indicates that particle i is in The acceleration due to force in the direction of movement; Indicates the acceleration of the central rigid body; The rigid body attitude angle; This represents the position vector of particle i relative to the body coordinate system; This represents the mass of particle i; all particles have the same mass. This represents the inertial force exerted on particle i in the liquid in a non-inertial frame of reference. Represents particles The physical exertion received; This is the time step for SPH simulation; The difference symbol is used. This represents the position of particle i at the current moment in a non-inertial frame of reference. This represents the velocity of particle i at the current moment in a non-inertial frame of reference. Step 5: Based on the dynamic model of the liquid-filled flexible spacecraft established in Step 4, the attitude of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel are taken as system states. Appropriate initial simulation conditions are set for the states, and numerical simulation is performed. The coupling characteristics of the central rigid body attitude and position, the vibration of the flexible appendages, and the sloshing of the liquid fuel are analyzed, including: Step 5.1: Set the integration step size; Step 5.1.1: Set the integration step size for the spacecraft attitude dynamics module This ensures the accuracy and stability of numerical integration. Step 5.1.2: Set the time step for liquid sloshing integration in the SPH method. ; Step 5.2: Initialize spacecraft status information; Step 5.2.1: Obtain the spacecraft state information at the initial time t0; Step 5.2.2: Initialize the liquid sloshing state; Step 5.3: Simulate the liquid sloshing using the SPH method to calculate the sloshing force and torque; Step 5.3.1: Based on the initial spacecraft state extracted in Step 5.2.1, t0 ~ (t0 + Simulation of liquid sloshing using the SPH method within a specified time period; Step 5.3.2: During the integration period Inside, based on the motion of liquid particles, the force and torque exerted by liquid sloshing on the spacecraft are calculated; Step 5.4: Update spacecraft status information; Step 5.5: Using the current time t as the initial time, repeat steps 5.3 to 5.4 until the simulation ends.

2. The method for analyzing the coupling characteristics of asteroid impactors based on SPH according to claim 1, characterized in that, Step 1 includes: Step 1.1: Define the liquid domain and boundary conditions, including: Step 1.1.1: Determine the range of motion of the liquid sloshing based on the shape of the spacecraft's storage tank, and set the boundary conditions; Step 1.1.2: Define the initial state of the liquid based on its actual physical properties, including volume, height, density, and dynamic viscosity coefficient; Step 1.2: Determine the initial SPH particle distribution based on the liquid domain and boundary conditions to provide initial parameters for subsequent SPH numerical simulations, including: Step 1.2.1: Initialize the distribution of real particles in the liquid domain, and set the initial spacing and mass of the real particles; Step 1.2.2: Initialize the distribution of virtual particles in the boundary domain, and set the initial spacing and mass of the virtual particles; Step 1.3: Select the kernel function, including: Select an appropriate kernel function based on the fluid properties and set a smoothing length to control the range of interparticle interactions; Step 1.4: Based on the kernel function, establish the Navier-Stokes equation based on SPH.

3. The method for analyzing the coupling characteristics of asteroid impactors based on SPH according to claim 1, characterized in that, Step 2 includes: Step 2.1: Obtain the angular velocity and angular acceleration of the spacecraft in the inertial frame; obtain the position of particle i at the current moment in the non-inertial frame. and speed ; Step 2.2: Establish the SPH discrete equations in non-inertial frames; Step 2.3: Calculate the force of liquid sloshing: ； in, This indicates the force exerted by the liquid sloshing on the tank; This indicates the contact force between the tank and the liquid; This represents the inertial force acting on a liquid in a non-inertial frame of reference. Indicates the body force acting on a liquid; Step 2.4: Calculate the liquid sloshing torque; ； in, This indicates the torque exerted by the liquid sloshing. This indicates the contact torque of the tank with the liquid.

4. The method for analyzing the coupling characteristics of asteroid impactors based on SPH according to claim 1, characterized in that, Step 3 includes: Step 3.1: Define the structural characteristics of the flexible spacecraft; Step 3.2: Establish a dynamic description of the flexible component; Step 3.3: Establish a distributed parameter model for the flexible spacecraft using Hamilton's principle and variational method: 。 5. A device for analyzing the coupling characteristics of asteroid impactors based on SPH, characterized in that, Includes the following modules: The sloshing model building module establishes a liquid sloshing model described by the SPH method; SPH stands for smooth particle hydrodynamics. The calculation module calculates the liquid sloshing forces and torques in a non-inertial frame based on the liquid sloshing model. The parameter model building module is used to build a distributed parameter model for flexible spacecraft. The dynamic model building module integrates the liquid sloshing forces and torques in a non-inertial frame into the distributed parameter model of the flexible spacecraft, establishing a dynamic model of the liquid-filled flexible spacecraft, including: Introducing the liquid sloshing force and torque as the resultant torque of external disturbance forces: ； in, State variables include rigid body position, velocity, attitude angle and attitude angular velocity, and flexible attachment deflection; This represents the linear part of the equations of motion for a rigid body. This represents the nonlinear part of the equations of rigid body dynamics. This represents the linear part of the vibration equation for flexible attachment i1. This represents the nonlinear part of the vibration equation for the flexible attachment i1; Indicates control torque. ; Indicates the force used in the sloshing of the liquid. and torque The vector is obtained through step 2; N represents the total number of particles; This represents the density of particle i; This represents the mass of particle j; Dumb Indicators The relative velocities of particles i and j in the direction; intermediate function , Represents a smooth kernel function; It represents the smooth length and controls the range of interactions between particles; This represents the position vector of particle i. Let t represent the position vector of particle j, and t represent time. This represents the isotropic pressure of particle i; It also refers to a dummy indicator; It is a Kronecker symbol if and only if hour, In all other cases, the value is 0; These represent the dummy index of particle i. Velocity vector in direction, position vector; This represents the dynamic viscosity coefficient of particle i. This represents the dynamic viscosity coefficient of particle j; This represents the shear strain rate of particle i; Indicates that particle i is in The acceleration due to force in the direction of movement; Indicates the acceleration of the central rigid body; The rigid body attitude angle; This represents the position vector of particle i relative to the body coordinate system; This represents the mass of particle i; all particles have the same mass. This represents the inertial force exerted on particle i in the liquid in a non-inertial frame of reference. Represents particles The physical exertion received; This is the time step for SPH simulation; The difference symbol is used. This represents the position of particle i at the current moment in a non-inertial frame of reference. This represents the velocity of particle i at the current moment in a non-inertial frame of reference. The analysis module, based on the dynamic model of a liquid-filled flexible spacecraft, takes the attitude of the central rigid body, the vibration of the flexible appendages, and the sloshing of the liquid fuel as system states. It sets appropriate initial simulation conditions for these states and performs numerical simulations. The module analyzes the coupling characteristics of the central rigid body attitude and position, the vibration of the flexible appendages, and the sloshing of the liquid fuel, including: Setting the integration step size includes: setting the integration step size of the spacecraft attitude dynamics module. To ensure the accuracy and stability of numerical integration; set the time step for liquid sloshing integration in the SPH method. ; Initialize spacecraft state information, including: acquiring spacecraft state information at initial time t0; initializing liquid sloshing state; The SPH method was used to simulate the liquid sloshing, and the sloshing forces and torques were calculated, including: based on the extracted initial state of the spacecraft, t0 ~ (t0 + ... Simulations of liquid sloshing using the SPH method were performed within a time interval; the integration time was... Inside, based on the motion of liquid particles, the force and torque exerted by liquid sloshing on the spacecraft are calculated; Update spacecraft status information; Using the current time t as the initial time, the SPH method is used to repeatedly simulate liquid sloshing, calculate the sloshing force and torque, and update the spacecraft state information until the simulation ends.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the SPH-based asteroid impactor coupling characteristic analysis method as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the SPH-based asteroid impactor coupling characteristic analysis method as described in any one of claims 1 to 4.

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