A three-node flexible probe and a method for modeling dynamics thereof

Abstract

The application provides a three-node flexible probe and a dynamic modeling method thereof, and belongs to the field of asteroid exploration. The three-node flexible probe comprises a flexible connecting structure and three prism-shaped rigid nodes with the same size which are embedded in the flexible connecting structure and are rotationally symmetrically distributed relative to the center of the probe; the height of the rigid node is equal to the distance between the upper and lower bottom surfaces of the flexible connecting structure; the flexible connecting structure is used for connecting the three rigid nodes and buffering during the process of the probe landing on an asteroid; and the rigid node is used for providing control force and control moment of the probe and protecting the equipment placed in the rigid node. The three-node flexible probe can improve the success rate of the asteroid landing exploration, the dynamic modeling method thereof can perform dynamic simulation and solving on the three-node flexible probe, and physical quantities such as displacement and speed of the three-node flexible probe in the process of landing on an asteroid are obtained, thereby providing technical support for the asteroid landing task.

Description

Technical Field

[0001] This invention belongs to the field of asteroid exploration, and specifically relates to a three-node flexible detector and its dynamic modeling method. Background Technology

[0002] The structure and composition of asteroids may contain information about the evolution of the solar system, and some asteroids also contain large amounts of rare metals such as platinum and iridium. Asteroid exploration and development have significant scientific and economic value.

[0003] Currently, landing on asteroids is the most direct and effective way to study them. However, in actual missions, due to the weak gravitational environment and irregular surface of asteroids, traditional rigid probes are prone to bounce, escape, and capsizing, leading to mission failure. Furthermore, the information we currently possess about asteroid surfaces is very limited, making it difficult for probes to determine a sufficiently flat landing site and to move extensively after landing, further contributing to mission failure. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a three-node flexible detector and its dynamic modeling method. The three-node flexible detector of this invention can improve the success rate of asteroid landing missions. The corresponding dynamic modeling method can perform dynamic simulation and solution of the three-node flexible detector, thereby obtaining physical quantities such as displacement and velocity of the three-node flexible detector during the asteroid landing process. This provides technical support for the control method of the three-node flexible detector and the research on asteroid landing missions.

[0005] A first aspect of the present invention provides a three-node flexible detector, comprising: a flexible connecting structure, and three identical prism-shaped rigid nodes embedded in the flexible connecting structure and distributed rotationally symmetrically with respect to the center of the detector; the height of each rigid node is equal to the distance between the upper and lower bottom surfaces of the flexible connecting structure; and the weight and moment of inertia of each rigid node are equal.

[0006] The flexible connection structure is used to connect the three rigid nodes and to provide cushioning during the probe's landing on the asteroid; the rigid nodes are used to provide control forces and control torques for the probe and to protect the equipment placed inside the rigid nodes.

[0007] In one specific embodiment of the present invention, the flexible connection structure consists of two disks of the same size and a ring with an inner diameter equal to that of the disks. The disks and the ring are both made of the same flexible material and have the same thickness. The two disks respectively form the upper and lower bottom surfaces of the semi-circular ring. The rigid nodes are hexagonal prisms, and the flexible connection structure is connected to the sides of the three rigid nodes by a rubber adhesive.

[0008] In one specific embodiment of the present invention, the rigid node includes: a rigid shell, a gas tank, and a jet duct; the gas tank is fixed to the center position inside the rigid node by a connecting frame inside the rigid shell; the gas tank is a hollow sphere; a section of the jet duct is connected to the upper and lower poles of the gas tank, and the two sections of the jet duct penetrate vertically through the upper and lower bottom surfaces of the rigid shell and are connected to the rigid shell by welding.

[0009] The gas tank is used to store high-pressure gas that provides control force and control torque during the landing process of the probe;

[0010] The jet duct is used to vent the high-pressure gas stored in the gas tank.

[0011] In one specific embodiment of the present invention, the rigid outer shell also houses a payload for the probe to conduct asteroid exploration.

[0012] A second aspect of this invention proposes a dynamic modeling method based on the above-described three-node flexible detector, comprising:

[0013] The surface of the flexible connection structure is discretized into several triangular units;

[0014] Based on the triangular element, the internal forces of the flexible structure when it deforms are calculated, including: the tensile internal forces at each vertex when the triangular element undergoes tensile deformation and the bending internal forces at each vertex when the triangular element undergoes bending deformation.

[0015] A dynamic model of the three-node flexible detector is established based on the internal forces when the flexible structure deforms.

[0016] In one specific embodiment of the present invention, the step of discretizing the surface of the flexible connection structure into a plurality of triangular units further includes:

[0017] The material mass of the flexible connection structure is equivalent to the area of ​​each triangular element at the vertices of each triangular element, as expressed below:

[0018]

[0019] Where, mi Let A represent the mass of the i-th vertex, N represent the number of triangle units connected to the i-th vertex, and A represent the mass of the i-th vertex. j Let ρ represent the area of ​​the j-th triangular unit connected to the i-th vertex, ρ be the density of the flexible material at the location of the triangular unit, and h be the thickness of the flexible material at the location of the triangular unit.

[0020] In a specific embodiment of the present invention, the method for calculating the tensile internal force at each vertex when the triangular element undergoes tensile deformation is as follows:

[0021] Let the three vertices of any triangular unit be denoted as x in a counterclockwise direction. i x j and x k When the triangular element undergoes stretching deformation, at vertex x... i The formula for calculating the resulting tensile internal force is as follows:

[0022]

[0023] in, It represents the vertex x i x j and x k When the triangular unit is stretched, at vertex x i The resulting tensile internal force, l i l j l k Representing the vertex x after the triangular unit is deformed i x j and x k Each of their opposite edges, i.e., edge x j x k x i x k x i x j The length of L i L j L k These represent the x-axis of the front side of the triangular unit after deformation. j x k x i x k x i x j The length, r xi Represents vertex x i Position vector, r xj Represents vertex x j Position vector; K ij K i and K j Let x represent the edges respectively. i x jangular stiffness, side x j x k Tensile stiffness, edge x i x k The tensile stiffness is calculated using the following expressions:

[0024]

[0025] Where E is the Young's modulus of the flexible structural material, μ is the Poisson's ratio of the flexible structural material, and α i The x-axis represents the front side of the triangular element after deformation. i x k and x i x j The included angle, α j The x-axis represents the front side of the triangular element after deformation. j x k and x i x j The included angle, α k The x-axis represents the front side of the triangular element after deformation. j x k and x i x k The included angle, where A represents the area of ​​the triangular element before deformation;

[0026] Calculate the tensile internal forces generated at each vertex when each triangular element undergoes tensile deformation, and sum the tensile internal forces generated at the same vertex to obtain the final tensile internal force at that vertex.

[0027] In a specific embodiment of the present invention, the method for calculating the bending internal force at each vertex when the triangular element undergoes bending deformation is as follows:

[0028] Let x0x1 be the common side of any two adjacent triangular elements. Let the vertices of one triangular element f0 be x0, x1, and x2, and the vertices of the other triangular element f1 be x0, x1, and x3. Then, the bending internal forces generated at each vertex when these two triangular elements undergo bending deformation are:

[0029]

[0030] in, Let x0, x1, x2, and x3 represent the bending internal forces generated at vertices x0, x1, x2, and x3 when triangular elements f0 and f1 undergo bending deformation, respectively. Let n0 and n1 represent the unit normal vectors of triangular elements f0 and f1, respectively. f0 and A f1 Let θ represent the areas of triangular units f0 and f1, respectively. e This represents the angle between n0 and n1 after deformation. This represents the angle between n0 and n1 before deformation. This represents the rate of change of the angle between n0 and n1 at the current moment, and e0 represents the length of the common side x0x1 after deformation. α represents the length of x0x1 before deformation. 01 Let α represent the angle between sides x0x1 and x0x2. 02 Let α represent the angle between sides x0x1 and x0x3. 03 Let α represent the angle between x0x1 and x1x2. 04 Represent edges x0x1 and x1x3; in Let f0 be the height of the triangular element relative to side x0x1. Let f1 be the height of the triangular element f1 relative to the side x0x1, and c be the damping coefficient of the flexible connection structure material.

[0031] Calculate the bending internal forces generated at each vertex when each adjacent triangular element undergoes bending deformation, and sum the bending internal forces generated at the same vertex to obtain the final bending internal force at that vertex.

[0032] In a specific embodiment of the present invention, establishing a dynamic model of the three-node flexible detector based on the internal forces when the flexible structure deforms includes:

[0033] 1) Construct the nodal dynamics equations of the three-node flexible detector:

[0034]

[0035] Where, m ci Let r represent the quality of the i-th node. ci F represents the centroid position vector of the i-th node. ci I represents the control force acting on the i-th node. i Let ω represent the inertia matrix of the i-th node. i M represents the rotational angular velocity of the i-th node. ci This represents the control torque acting on the i-th node;

[0036] 2) Construct the dynamic equations for the flexible connection structure of the three-node flexible detector:

[0037]

[0038] Where Np represents the number of vertices after the flexible connection structure is discretized into triangular units, m i Let r represent the mass of the i-th vertex. i This represents the position vector of the i-th vertex; This represents the sum of all tensile internal forces acting at the i-th vertex. This represents the sum of all bending internal forces acting at the i-th vertex;

[0039] 3-3) Apply rigid constraints to the vertices at the locations occupied by nodes on the surface of the flexible connection structure:

[0040] φ i =R c (r φi -r c )+C i =0 i=1,…N φ (7)

[0041] Where, N φ φ represents the total number of vertices occupying positions at the nodes on the surface of the flexible connection structure. i Let r represent the rigid constraint equation corresponding to the i-th vertex at the location of a node on the surface of the flexible connection structure. φi r represents the position vector of the i-th vertex at the node's location on the surface of the flexible connection structure. c R represents the centroid position vector of the node connected to the i-th vertex at the position occupied by the node on the surface of the flexible connection structure. c C represents the attitude transformation matrix from the inertial frame to the body coordinate system of that node. i This represents the vector from the i-th vertex of the node at the surface of the flexible connection structure, to the centroid of the corresponding node, when the structure is undeformed.

[0042] In one specific embodiment of the present invention, the method further includes:

[0043] Solving the dynamic model yields the displacement and velocity vectors of each triangular unit vertex, as well as the angular velocity, center-of-mass displacement, and velocity vectors of the three rigid nodes.

[0044] The features and beneficial effects of this invention are as follows:

[0045] This invention proposes a three-node flexible probe suitable for asteroid landing exploration. During the landing process, the three-node flexible probe can dissipate energy through the deformation and collision of flexible materials, reducing the collision rebound velocity and avoiding the rebound escape phenomenon.

[0046] The symmetrical structural design of the three-node flexible detector of this invention ensures that the detector can still operate normally in a flipped state, avoiding tipping and loss of control. Each of the three nodes of the three-node flexible detector can carry different detection instruments, preventing the failure of the entire mission due to damage to a single node and improving the success rate of the detection mission.

[0047] This invention introduces a discrete curvature model to establish an internal force solution model for the flexible material of a three-node flexible detector. By introducing the constrained default stability method, the coupling relationship between the flexible material and the three nodes in the three-node flexible detector is established, thereby establishing and solving the dynamic model of the three-node flexible detector, providing a new solution for asteroid landing exploration.

[0048] This invention can be used in future asteroid exploration missions such as asteroid landing and asteroid surface exploration, and has high application value. Attached Figure Description

[0049] Figure 1 This is a structural diagram of a three-node flexible detector in a specific embodiment of the present invention.

[0050] Figure 2 This is a cross-sectional view of a three-node flexible detector and its nodes in a specific embodiment of the present invention.

[0051] Figure 3 This is an overall flowchart of a dynamic modeling method for a three-node flexible detector in a specific embodiment of the present invention.

[0052] Figure 4 This is a schematic diagram of triangular unit segmentation in a specific embodiment of the present invention.

[0053] Figure 5 This is a schematic diagram of adjacent triangular units in a specific embodiment of the present invention. Detailed Implementation

[0054] This invention proposes a three-node flexible detector and its dynamic modeling method. The invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] A first aspect of this invention provides a three-node flexible probe, comprising: a flexible connecting structure, and three rigid nodes of identical size embedded in the flexible connecting structure and rotationally symmetrical with respect to the probe's center; the height of each rigid node is equal to the distance between the upper and lower bottom surfaces of the flexible connecting structure. The flexible connecting structure connects the three rigid nodes and acts as a buffer during the probe's landing on an asteroid to prevent it from bouncing off. The rigid nodes house easily damaged equipment such as payloads, gas tanks, and jet ducts, providing control forces and control torques to the probe and protecting the equipment used for exploration.

[0056] It should be noted that each node can carry different payloads or detection devices. To ensure the overall symmetry of the detector, the weight and moment of inertia of the three nodes must be the same.

[0057] In one specific embodiment of the present invention, the overall structure of the three-node flexible detector is as follows: Figure 1 As shown, the flexible connection structure specifically consists of two disks with a diameter of 2m and a thickness of 5mm, and a semi-circular ring with an inner diameter of 2m, an outer diameter of 2.8m, and a thickness of 5mm. The disks respectively form the upper and lower bottom surfaces of the semi-circular ring, and the distance between the upper and lower surfaces is 0.4m. The flexible connection structure connects three rigid nodes that are rotationally symmetrical with respect to the center of the detector, denoted as node ①, node ②, and node ③. It should be noted that the shape and size of the flexible connection structure can be modified according to the specific detection task, such as proportionally enlarging or changing to a cube shape. The material of the flexible connection structure can be selected from materials with low Young's modulus, such as vulcanized rubber and silicone rubber. In this embodiment, silicone rubber is used as the flexible connection material. In this embodiment, the three rigid nodes are all rigid hexagonal prisms with a height of 0.4m and a side length of 0.2m, distributed rotationally symmetrically with respect to the center of the detector, and each rigid node is 0.6m away from the center of the detector. The flexible connection structure is connected to the sides of the three rigid nodes by rubber adhesive. The shape and size of the rigid nodes can be modified according to the specific detection mission, but they must be prism-shaped, such as a quadrangular prism or a pentagonal prism, and the three nodes must have the same shape.

[0058] In one specific embodiment of the present invention, the three-node flexible detector and its node cross-sectional view are as follows: Figure 2 As shown, each node has the same structure, including a rigid shell, a gas tank, and a jet duct. In this embodiment, the rigid shell is a hexagonal prism shell with a wall thickness of more than 2 mm. A connecting frame is embedded in the middle of the rigid shell to fix the gas tank at the center of the rigid node. The connecting frame is integral with the rigid shell, and the gas tank and the connecting frame are fixed by welding. The gas tank is a hollow sphere, and its specific size and volume can be adjusted according to the control requirements of the deep space exploration mission. A jet duct is connected to the upper and lower poles of the gas tank, and the two jet ducts penetrate vertically through the upper and lower bottom surfaces of the rigid shell, respectively. The gas tank and the jet duct are connected by welding, and the rigid shell and the jet duct are connected by welding.

[0059] In one specific embodiment of the present invention, the rigid outer shell material of each node is an impact-resistant alloy material, such as any one of steel alloy, aluminum alloy, or magnesium alloy. In this embodiment, 16Mn steel alloy is used to protect the payload, gas tank, and jet duct. The gas tank material inside the node is a lightweight alloy material, such as any one of steel alloy, aluminum alloy, or magnesium alloy. In this embodiment, 1A95 aluminum alloy is used to store high-pressure gas, such as 10MPa high-pressure nitrogen, which provides control force and control torque during the landing of the three-node flexible probe. The jet duct material of the node can be any one of steel alloy, aluminum alloy, or magnesium alloy. In this embodiment, 16Mn steel alloy is used. The jet duct is used to exhaust the high-pressure gas stored in the gas tank. Furthermore, the remaining space in the node can also be used to install payloads such as radar, communication equipment, and sampling devices for asteroid exploration.

[0060] A second aspect of this invention also proposes a dynamic modeling method based on the above-described three-node flexible detector, the overall process of which is as follows: Figure 3 As shown, it includes the following steps:

[0061] 1) Mesh generation for flexible connection structures:

[0062] The surface of the flexible connection structure is discretized into several triangular elements, where the positions of the nodes on the surface of the flexible connection structure also participate in the discretization. The areas of the triangular elements can be different, and the discretization process can be completed using commercial finite element software. A schematic diagram of the flexible connection structure after triangular element division is shown in a specific embodiment of the present invention. Figure 4 As shown.

[0063] The material mass of the flexible connection structure is equivalent to the area of ​​each triangular element after division, and is expressed as follows:

[0064]

[0065] Where, m i Let A represent the mass of the i-th vertex, N represent the number of triangle units connected to the i-th vertex, and A represent the mass of the i-th vertex. j Let ρ represent the area of ​​the j-th triangular unit connected to the i-th vertex, ρ be the density of the flexible material at the location of the triangular unit, and h be the thickness of the flexible material at the location of the triangular unit.

[0066] It should be noted that ρ and h can take different values ​​in different elements. For elements located at nodes, ρ and h can be taken as a large fixed value.

[0067] 2) Solve for the internal forces when the flexible connection structure deforms, including the following specific steps:

[0068] 2-1) Obtain the Young's modulus E, Poisson's ratio μ, density ρ, and damping coefficient c of the material (vulcanized rubber in this example) of the flexible connection structure through experimental verification or literature review.

[0069] 2-2) Calculate the tensile internal forces at each vertex when the triangular element undergoes tensile deformation;

[0070] Figure 5 This is a schematic diagram of two adjacent discretized triangular units f0 and f1 in a specific embodiment of the present invention. The three vertices of each triangular unit are denoted as x in a counter-clockwise direction. i x j and x k .

[0071] In this embodiment, taking the basic triangular unit f0 as an example, Figure 5 The three vertices of the triangular element are denoted as x0, x1, and x2. The tensile internal force generated at any vertex when the triangular element undergoes tensile deformation is:

[0072]

[0073] in, It represents the vertex x i x j and x k When the triangular unit is stretched, at vertex x i The resulting tensile internal force, l i l j l k Representing the vertex x after the triangular unit is deformed i x j and x k Each of their opposite edges, i.e., edge x j x k x i x k x i x j The length of L i L j L k These represent the x-axis of the front side of the triangular unit after deformation. j x k x i x k x i x j The length, r xi Represents vertex x i Position vector, r xj Represents vertex x j Position vector; K ij K i and K jLet x represent the edges respectively. i x j angular stiffness, side x j x k Tensile stiffness, edge x i x k The tensile stiffness is calculated using the following expression:

[0074]

[0075] Where, α i The x-axis represents the front side of the triangular element after deformation. i x k and x i x j The included angle, α j The x-axis represents the front side of the triangular element after deformation. j x k and x i x j The included angle, α k The x-axis represents the front side of the triangular element after deformation. j x k and x i x k The included angle, A represents the area of ​​the triangular unit (f0 in this embodiment) before deformation;

[0076] Calculate the tensile internal forces generated at each vertex when each triangular element undergoes tensile deformation, and sum the tensile internal forces generated at the same vertex to obtain the final tensile internal force at that vertex.

[0077] 2-2) Calculate the bending internal forces at each vertex when the triangular element undergoes bending deformation;

[0078] In this embodiment, as Figure 5 As shown, let the common side of any two adjacent triangular elements be x0x1, and let the vertices of one triangular element f0 be x0, x1, and x2, and the vertices of the other triangular element f1 be x0, x1, and x3. Then, the bending internal forces generated at each vertex when these two triangular elements undergo bending deformation are:

[0079]

[0080] in, Let x0, x1, x2, and x3 represent the bending internal forces generated at vertices x0, x1, x2, and x3 when triangular elements f0 and f1 undergo bending deformation, respectively. Let n0 and n1 represent the unit normal vectors of triangular elements f0 and f1, respectively. f0 and A f1 Let θ represent the areas of triangular units f0 and f1, respectively. e This represents the angle between n0 and n1 after deformation. This represents the angle between n0 and n1 before deformation. This represents the rate of change of the angle between n0 and n1 at the current moment, and e0 represents the length of the common side x0x1 after deformation. α represents the length of x0x1 before deformation. 01 Let α represent the angle between sides x0x1 and x0x2. 02 Let α represent the angle between sides x0x1 and x0x3. 03 Let α represent the angle between x0x1 and x1x2. 04 Let x0x1 and x1x3 be the edges. in Let f0 be the height of the triangular element relative to side x0x1. Let f1 be the height of the triangular unit relative to the side x0x1.

[0081] Calculate the bending internal forces generated at each vertex when each adjacent triangular element undergoes bending deformation, and sum the bending internal forces generated at the same vertex to obtain the final bending internal force at that vertex.

[0082] 3) Establish a dynamic model for the three-node flexible detector;

[0083] 3-1) Construct the nodal dynamics equations of the three-node flexible detector;

[0084] In this embodiment, the dynamic equations for each node of the three-node flexible detector are as follows:

[0085]

[0086] Where, m ci Let r represent the quality of the i-th node. ci F represents the centroid position vector of the i-th node. ci I represents the control force acting on the i-th node. i Let ω represent the inertia matrix of the i-th node. i M represents the rotational angular velocity of the i-th node. ci This represents the control torque acting on the i-th node.

[0087] 3-2) Construct the dynamic equations of the flexible connection structure of the three-node flexible detector;

[0088] In this embodiment, the dynamic equations for the flexible connection structure are as follows:

[0089]

[0090] Where Np represents the number of vertices after the flexible connection structure is discretized into triangular units, m i Let r represent the mass of the i-th vertex. iThis represents the position vector of the i-th vertex. This represents the sum of all tensile internal forces acting at the i-th vertex. This represents the sum of all bending internal forces at the i-th vertex, which is obtained through step 2).

[0091] 3-3) Apply rigid constraints to the vertices at the locations occupied by nodes on the surface of the flexible connection structure;

[0092] In this embodiment, the rigid constraint equation is:

[0093] φ i =R c (r φi -r c )+C i =0 i=1,…N φ (7)

[0094] Where, N φ φ represents the total number of vertices occupying positions at the nodes on the surface of the flexible connection structure. i Let r represent the rigid constraint equation corresponding to the i-th vertex at the location of a node on the surface of the flexible connection structure. φi r represents the position vector of the i-th vertex at the node's location on the surface of the flexible connection structure. c R represents the centroid position vector of the node connected to the i-th vertex at the position occupied by the node on the surface of the flexible connection structure. c (This value is independent of i and is determined by the nodal dynamics equations) represents the attitude transformation matrix from the inertial frame to the body coordinate system of that node, C i This represents the vector from the i-th vertex of the node at the surface of the flexible connection structure, to the centroid of the corresponding node, when the structure is undeformed.

[0095] 4) Solve the dynamic model three of the three-node flexible detector.

[0096] In this embodiment of the invention, the fourth-order Runge-Kutta method and the constrained default stability method are used to solve equations (5), (6), and (7), which can calculate the displacement vector and velocity vector of each triangle unit vertex obtained after the flexible connection structure in the three-node flexible detector is discretized at each time, as well as the angular velocity, centroid displacement vector, and velocity vector of the three rigid nodes, thus realizing the dynamic simulation of the three-node flexible detector.

Claims

1. A dynamic modeling method for a three-node flexible detector, characterized in that, The three-node flexible probe includes: a flexible connecting structure, and three identical prismatic rigid nodes embedded in the flexible connecting structure and distributed rotationally symmetrically with respect to the center of the probe; the height of each rigid node is equal to the distance between the upper and lower bottom surfaces of the flexible connecting structure; the weight and moment of inertia of each rigid node are equal; the flexible connecting structure connects the three rigid nodes and provides cushioning during the probe's landing on the asteroid; the rigid nodes provide control forces and control torques for the probe and protect the equipment placed inside the rigid nodes. The method includes: The surface of the flexible connection structure is discretized into several triangular units; Based on the triangular element, the internal forces of the flexible connection structure when it deforms are calculated, including: the tensile internal forces at each vertex when the triangular element undergoes tensile deformation and the bending internal forces at each vertex when the triangular element undergoes bending deformation. Based on the internal forces when the flexible connection structure deforms, a dynamic model of the three-node flexible detector is established. The method for calculating the tensile internal force at each vertex when the triangular element undergoes tensile deformation is as follows: Let the three vertices of any triangular unit be denoted as follows, in a counterclockwise direction: and When the triangular element undergoes tensile deformation, at the vertex... The formula for calculating the resulting tensile internal force is as follows: （1） in, Indicates the origin of the vertex and When the triangular unit is stretched, at the vertex The resulting tensile internal force, These represent the vertices of the triangular unit after deformation. and Each of their opposite edges Length, These represent the front sides of the triangular unit after deformation. Length, Represents vertices position vector, Represents vertices Position vector; and Representing edges respectively The included angle stiffness, edge Tensile stiffness, edge The tensile stiffness is calculated using the following expressions: （2） in, The Young's modulus of the flexible connection structure material. Poisson's ratio for flexible connection structural materials. Indicates the front side of the triangular unit deformation and The included angle, Indicates the front side of the triangular unit deformation and The included angle, Indicates the front side of the triangular unit deformation and The included angle, This represents the area of ​​the triangular element before deformation; The thickness of the flexible material at the location of the triangular unit; Calculate the tensile internal forces generated at each vertex when each triangular element undergoes tensile deformation, and sum the tensile internal forces generated at the same vertex to obtain the final tensile internal force at that vertex.

2. The method according to claim 1, characterized in that, Discretizing the surface of the flexible connection structure into a plurality of triangular units further includes: The material mass of the flexible connection structure is equivalent to the area of ​​each triangular element at the vertices of each triangular element, as expressed below: （3） in, Indicates the first The mass of each vertex Representing the The number of triangle units connected to each vertex, Indicates the first The vertex connection of the first vertex The area of ​​each triangular unit The density of the flexible material at the location of the triangular unit.

3. The method according to claim 1, characterized in that, The method for calculating the bending internal force at each vertex when the triangular element undergoes bending deformation is as follows: Let the common side of any two adjacent triangular units be denoted as . One of the triangular units The vertex is and Another triangular unit The vertex is and Then, the bending internal forces generated at each vertex when the two triangular elements undergo bending deformation are: （4） in, , Representing triangular units and At the apex when bending deformation occurs , , , The resulting bending internal force, , Representing triangular units and triangular unit The unit normal vector, and Representing triangular units and area, Indicates after deformation and The included angle, Indicates before deformation and The included angle, Indicates the current time and The rate of change of the included angle Indicates the common edge after deformation Length, Indicates before deformation Length, Representing an edge and The included angle, Representing an edge and The included angle, express and The included angle, Representing an edge and ; ,in Triangular unit Relative to the edge of high, Triangular unit Relative to the edge of high, The damping coefficient of the flexible connection structure material; Calculate the bending internal forces generated at each vertex when each adjacent triangular element undergoes bending deformation, and sum the bending internal forces generated at the same vertex to obtain the final bending internal force at that vertex.

4. The method according to claim 3, characterized in that, The step of establishing a dynamic model of the three-node flexible detector based on the internal forces when the flexible connection structure deforms includes: 1) Construct the nodal dynamics equations of the three-node flexible detector: （5） in, Indicates the first The quality of each node Indicates the first The centroid position vector of each node, Indicates the action in the Control at each node Indicates the first The inertia matrix of each node. Indicates the first The rotational angular velocity of each node, Indicates the action in the Control torque at each node; 2) Construct the dynamic equations for the flexible connection structure of the three-node flexible detector: （6） in, This represents the number of vertices after the flexible connection structure is discretized into triangular units. Indicates the first The mass of each vertex Indicates the first The position vectors of the vertices; Indicates the action in the The sum of all tensile internal forces at each vertex, Indicates the action in the The sum of all bending internal forces at each vertex; 3) Apply rigid constraints to the vertices at the locations of nodes on the surface of the flexible connection structure: （7） in, This represents the total number of vertices occupying positions at the nodes on the surface of the flexible connection structure. The position of the node on the surface of the flexible connection structure is indicated by the number of nodes. The rigid constraint equations corresponding to each vertex The position of the node on the surface of the flexible connection structure is indicated by the number of nodes. The position vectors of the vertices, The position of the node on the surface of the flexible connection structure is indicated by the number of nodes. The centroid position vectors of the corresponding nodes connected by each vertex. This represents the attitude transformation matrix from the inertial frame to the body coordinate system of this node. This indicates the position of the node at the surface of the flexible connection structure when it is not deformed. The vector from each vertex to the centroid of the corresponding node.

5. The method according to claim 4, characterized in that, The method further includes: Solving the dynamic model yields the displacement and velocity vectors of each triangular unit vertex, as well as the angular velocity, center-of-mass displacement, and velocity vectors of the three rigid nodes.

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