Gravitational wave detection satellite ground microgravity simulation platform dynamics modeling method

Abstract

The invention discloses a gravitational wave detection satellite ground microgravity simulation platform dynamics modeling method, system, device, medium and program, and belongs to the technical field of spaceflight. The method comprises the following steps: acquiring a spacecraft simulation platform coordinate system and a reference mass torsional pendulum coordinate system in a ground simulation platform; determining the position of each component according to the spacecraft simulation platform coordinate system and the reference mass torsional pendulum coordinate system; determining kinetic energy and potential energy of each component of the spacecraft simulation platform according to the position of each component, and establishing a kinetic model of the spacecraft simulation platform; kinetic energy and potential energy of the torsional pendulum are determined according to the position of each component, and a Lagrange kinetic model of the torsional pendulum is established; and constructing a satellite ground microgravity simulation platform dynamic model based on the dynamic model of the spacecraft simulation platform and the torsional pendulum Lagrange dynamic model. According to the method, the satellite ground microgravity simulation platform dynamic model is constructed, so that the microgravity level required by gravitational wave detection can be achieved in the gravitational wave detection satellite ground test process.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and particularly relates to a method, a system, a device, a medium and a program for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite. Background Art

[0002] The perturbation of the gravitational field propagates in the universe to form gravitational waves. The propagation of gravitational waves in the universe contains a lot of information about the evolution of celestial bodies, and this information will help humans better understand the evolution history of the universe. Gravitational wave detectors can be deployed on the ground or in space. The gravitational wave detector in space has an unrestricted arm length of the interferometer arm, can better detect lower-frequency gravitational waves, and can greatly improve the detection frequency band of the detector. Therefore, many countries and institutions in the world have proposed various space gravitational wave detection implementation plans, such as the LISA plan in the United States, the TianQin plan and the Taiji plan in China. The gravitational wave detection satellite consists of a reference mass and a spacecraft platform that encloses the reference mass. The spacecraft platform will provide a pure mechanical environment for the reference mass to detect the tiny perturbations caused by gravitational waves.

[0003] Before the gravitational wave satellite is put into orbit, it needs to undergo strict ground tests. The current ground microgravity test methods, such as drop tower experiments and neutral buoyancy pool experiments, and other existing ground test equipment are difficult to provide the microgravity environment required for the ground test of the gravitational wave detection satellite. Therefore, it is necessary to propose a new ground experimental equipment to seek to provide the high-level microgravity environment required for the test of the gravitational wave detection satellite in the ground environment. This system needs to simulate the motions of the spacecraft platform and the reference mass respectively according to the structural characteristics of the gravitational wave detection satellite. At the same time, the motions of the two are controlled by the actuators mounted on them to generate control forces and control torques. These actuators have the same principle as the actuators actually mounted on the space gravitational wave detection satellite. Therefore, the actual operation of the control system can be tested in the ground environment. Summary of the Invention

[0004] Aiming at the problem that the microgravity level required for the ground test of the gravitational wave detection satellite cannot be achieved in the prior art. The present invention provides a method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite. According to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system in the ground simulation platform, a dynamic model of the ground microgravity simulation platform for the satellite is constructed, so that the microgravity level required for the ground test of the gravitational wave detection satellite can be achieved.

[0005] To achieve the above object, the present invention provides the following technical solutions.

[0006] In a first aspect, the present invention provides a method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite, including: Obtain the coordinate system of the spacecraft simulation platform and the coordinate system of the reference mass pendulum in the ground simulation platform; Determine the positions of each component according to the coordinate system of the spacecraft simulation platform and the coordinate system of the reference mass pendulum; Determine the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establish the dynamic model of the spacecraft simulation platform; Determine the kinetic energy and potential energy of the pendulum according to the positions of each component, and establish the Lagrangian dynamic model of the pendulum; Construct the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the pendulum.

[0007] As a further improvement of the present invention, the obtaining of the coordinate system of the spacecraft simulation platform and the reference mass coordinate system in the ground simulation platform includes: For the spacecraft simulation platform in the ground simulation platform, define that the rotation angle of the pivot arranged along the O I y I axis of the translation part around the O I y I positive direction of the axis is the generalized coordinate θ 1, and the rotation angle of the pivot arranged along the O I x I axis of the translation part around the O I x I negative direction of the axis is the generalized coordinate θ 2; the rotation angle of the pivot connecting the outer frame and the upper plate along the O I y I axis, and its rotation angle along the O I y I positive direction of the axis is the generalized coordinate θ 4; the rotation angle of the pivot connecting the middle frame and the outer frame along the O I x I axis, and its rotation angle along the O I x I positive direction of the axis is the generalized coordinate θ 3; the rotation angle of the pivot connecting the inner frame and the middle frame along the O I z I axis, and its rotation angle along theO I z I The rotation angle in the positive direction of the axis is the generalized coordinate θ 5; form the spacecraft simulation platform coordinate system in the ground simulation platform; For the reference mass torsion pendulum in the ground simulation platform, it is stipulated that when transforming from the torsion pendulum coordinate system to the reference mass coordinate system, first rotate by the generalized coordinate around the x-axis α , then rotate by the generalized coordinate around the y-axis β , and finally rotate by the generalized coordinate around the z-axis φ ; record the change in the length of the wire of the pendulum as the generalized coordinate δ ( t ), and make the generalized coordinate φ positive when the suspension wire of the torsion pendulum increases; form the reference mass torsion pendulum coordinate system in the ground simulation platform.

[0008] As a further improvement of the present invention, the positions of each component are determined according to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system; According to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system, it is stipulated that the rod length of the support rod is l ,( x 1, y 1, z 1) T is the position vector of the outer frame centroid in the moving platform coordinate system,( x 2, y 2, z 2) T is the position vector of the middle frame centroid in the moving platform coordinate system,( x 3, y 3, z 3) T is the position vector of the inner frame centroid in the moving platform coordinate system,( x 4, y 4, z 4) T is the position vector of the upper plate centroid in the moving platform coordinate system, the arm length of the cross support structure below the torsion pendulum is d , the upper suspension point of the torsion pendulum is O TP , its position vector in the inertial coordinate system is , the centroid position vector of the whole torsion pendulum in the nominal state is in the torsion pendulum coordinate system, where is the z-direction component of the torsion pendulum centroid in the torsion pendulum coordinate system; Determine the position vectors of the centroids of each component of the spacecraft simulation platform in the inertial coordinate system according to the relative relationship; the expression of the upper plate centroid position vector is ; Position vector of the centroid of the outer frame is represented as ; Position vector of the centroid of the middle frame is represented as ; Position vector of the centroid of the inner frame is represented as ; Determine the position vector of the centroid of the reference mass of the torsion pendulum suspension in the inertial coordinate system according to the relative relationship; the position vector of the centroid of the reference mass is in the torsion pendulum coordinate system, then it is in the inertial coordinate system.

[0009] As a further improvement of the present invention, determining the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of the components, and establishing a dynamic model of the spacecraft simulation platform includes: Determine the translational kinetic energy and rotational kinetic energy of each component of the spacecraft simulation platform according to the positions of the components: The translational kinetic energy is ; The rotational kinetic energy is ; In the formula, I O is the inertia matrix of the outer frame; I M is the inertia matrix of the middle frame; I N is the inertia matrix of the inner frame; m P is the mass of the upper plate; m O is the mass of the outer frame; m M is the mass of the middle frame; m N is the mass of the inner frame; Determine the potential energy of each component of the spacecraft simulation platform according to the positions of the components;

[0010] In the formula, is the z-direction component of the position vector of the center of gravity of the upper plate, is the z-direction component of the position vector of the center of gravity of the outer frame, is the z-direction component of the position vector of the center of gravity of the middle frame, is the z-direction component of the position vector of the center of gravity of the inner frame; k1 is the stiffness coefficient of the pivot of the translational part, and k2 is the stiffness coefficient of the pivot of the rotational part; Determine the translational kinetic energy, rotational kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of the components, and establish a dynamic model of the spacecraft simulation platform .

[0011] As a further improvement of the present invention, determining the kinetic energy and potential energy of the torsion pendulum according to the positions of the components and establishing the Lagrangian dynamics model of the torsion pendulum includes: The kinetic energy of the torsion pendulum determined by the positions of the components is ; In the formula, m TP is the mass of the torsion pendulum system, and I TP is the inertia matrix of the torsion pendulum system; The potential energy of the torsion pendulum determined by the positions of the components is ; In the formula, is the z-direction component of the position vector of the centroid of the torsion pendulum; is the telescopic stiffness of the torsion wire of the torsion pendulum; is the torsional stiffness of the torsion wire of the torsion pendulum; Determining the kinetic energy and potential energy of the torsion pendulum according to the positions of the components and establishing the Lagrangian dynamics model of the torsion pendulum L TP = T TP - U。

[0012] As a further improvement of the present invention, constructing the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum includes: Constructing the dynamic model of the spacecraft simulation platform in the translational direction according to the centroid kinematic model of the spacecraft simulation platform and the dynamic model of the spacecraft simulation platform; Constructing the dynamic model of the reference mass in the translational direction according to the centroid kinematic equation model of the reference mass and the Lagrangian dynamic model of the torsion pendulum.

[0013] In the second aspect, the present invention provides a dynamic modeling system for a satellite ground microgravity simulation platform, including: A coordinate system acquisition module: used to acquire the coordinate system of the spacecraft simulation platform and the reference mass torsion pendulum coordinate system in the ground simulation platform; A component position module: used to clarify the positions of the components according to the coordinate system of the spacecraft simulation platform and the reference mass torsion pendulum coordinate system; A platform dynamics module: used to determine the kinetic energy and potential energy of the components of the spacecraft simulation platform according to the positions of the components and establish the dynamic model of the spacecraft simulation platform; A torsion pendulum dynamics module: used to determine the kinetic energy and potential energy of the torsion pendulum according to the positions of the components and establish the Lagrangian dynamics model of the torsion pendulum; A microgravity simulation platform dynamics module: used to construct the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum.

[0014] In a third aspect, the present invention 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 computer program, the steps of the dynamic modeling method for the ground microgravity simulation platform of a gravitational wave detection satellite are implemented.

[0015] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the dynamic modeling method for the ground microgravity simulation platform of a gravitational wave detection satellite are implemented.

[0016] In a fifth aspect, the present invention provides a computer program product including computer instructions, and when the computer instructions are executed by a processor, the steps of the dynamic modeling method for the ground microgravity simulation platform of a gravitational wave detection satellite are implemented.

[0017] Compared with the prior art, the present invention has the following beneficial effects: By defining the coordinate systems of the spacecraft simulation platform and the reference mass pendulum, the present invention lays a foundation for subsequent modeling. By determining the positions of the components within these coordinate systems, the relative motion between the components of the platform can be clearly understood, thus providing key data for establishing an accurate dynamic model. On this basis, the present invention further considers the kinetic energy and potential energy of the spacecraft simulation platform and establishes a dynamic model of the platform. This model can comprehensively describe the dynamic behavior of the platform under various external forces and provides a theoretical basis for the accurate simulation of the microgravity environment. In addition, the present invention further considers the dynamic characteristics of the reference mass pendulum and establishes a Lagrangian dynamic model of the pendulum. As an important dynamic component in the ground microgravity simulation platform, the accurate calculation of the energy state of the pendulum is crucial for the microgravity control of the platform. Through the Lagrangian equation, an accurate equation describing the motion of the pendulum can be obtained, providing a scientific basis for the simulation of the microgravity environment. By combining the dynamic model of the spacecraft simulation platform with the Lagrangian dynamic model of the pendulum, the present invention constructs a comprehensive dynamic model of the satellite ground microgravity simulation platform. This model can comprehensively consider the interaction and dynamic changes between different components, enabling a more accurate simulation of the microgravity level in the space environment during ground testing, thus providing a reliable technical guarantee for the ground testing of gravitational wave detection satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the disclosure of the present invention in any way. In the drawings: Figure 1 is a schematic flowchart of a method for dynamic modeling of a ground microgravity simulation platform of a gravitational wave detection satellite according to the present invention; Figure 2 Schematic diagram of the specific method flow for the dynamic modeling method of the ground microgravity simulation platform of a gravitational wave detection satellite according to the present invention; Figure 3 Schematic diagram of the structure of the ground microgravity simulation platform of a gravitational wave detection satellite according to the present invention; Figure 4 Schematic diagram of the relationship between the coordinate system and the generalized coordinates of the ground microgravity simulation platform of a gravitational wave detection satellite according to the present invention; Figure 5 Graph of the displacement of the spacecraft simulation platform in the x - direction over time in a specific embodiment; Figure 6 Graph of the displacement of the spacecraft simulation platform in the y - direction over time in a specific embodiment; Figure 7 Graph of the rotation angle of the spacecraft simulation platform about the x - axis over time in a specific embodiment; Figure 8 Graph of the rotation angle of the spacecraft simulation platform about the y - axis over time in a specific embodiment; Figure 9 Graph of the rotation angle of the spacecraft simulation platform about the z - axis over time in a specific embodiment; Figure 10 Graph of the displacement of the reference mass in the x - direction over time in a specific embodiment; Figure 11 Graph of the displacement of the reference mass in the y - direction over time in a specific embodiment; Figure 12 Schematic diagram of the structure of the dynamic modeling system of the ground microgravity simulation platform of a gravitational wave detection satellite according to the present invention; Figure 13 Schematic diagram of the electronic device in an embodiment of the present invention. Detailed implementation manners

[0019] In order to enable those skilled in the art of the present technology to better understand the technical solutions in the present invention, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the accompanying drawings in the present invention. The described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs. The terms used in the description of the present invention in this specification are only for the purpose of describing specific embodiments, and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0021] Aiming at the problem that the microgravity level required for gravitational wave detection cannot be achieved during the ground test of a gravitational wave detection satellite in the existing technology, the present invention provides a method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite. As Figure 1 shown, the method includes: S100: Obtain the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system in the ground simulation platform; S200: Define the positions of each component according to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system; S300: Determine the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establish a dynamic model of the spacecraft simulation platform; S400: Determine the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establish a Lagrangian dynamic model of the torsion pendulum; S500: Construct a dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum.

[0022] According to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system in the ground simulation platform, the present invention constructs a dynamic model of the satellite ground microgravity simulation platform, enabling the microgravity level required for gravitational wave detection to be achieved during the ground test of the gravitational wave detection satellite.

[0023] The following further explains and illustrates the present invention with specific drawings.

[0024] As Figure 2 shown, a method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite according to the present invention specifically includes the following steps: S1: Define the coordinate systems required for dynamic derivation of the ground simulation platform: As Figure 3 shown, the ground simulation platform is divided into two parts: a spacecraft simulation platform and a reference mass torsion pendulum. Therefore, coordinate systems need to be determined for the two respectively.

[0025] The base of the spacecraft simulation platform is fixed on a foundation with vibration isolation ability. The translation mechanism and the base are connected by 4 support rods and 16 identical pivot shafts; the rotation mechanism consists of an outer frame, a middle frame, and an inner frame. The inner frame is fixedly connected to the scaled-down satellite platform, and the outer frame is connected to the translation mechanism. The translation mechanism and the outer frame, as well as the three parts inside the rotation mechanism, are all connected by two pivot shafts. The reference mass is suspended by the torsion pendulum, and the arc swept by the torsion pendulum is used to approximate the translational motion of the reference mass in space.

[0026] 1) Inertial coordinate system O I -xI y I z I 。The origin is at the center of the moving stage base. O I x I The axis passes through the origin and is in the same direction as the bisector of the angle between the double telescopes in the horizontal plane; O I z I The axis is opposite to the direction of the local gravity.

[0027] 2) Moving stage coordinate system O R -x R y R z R 。Its origin is at the intersection of the three pivot connections of the rotating mechanism; in the nominal state, the other axes point in the same direction as the axes of the inertial system.

[0028] 3) Reference mass coordinate system O TM -x TM y TM z TM 。Its origin is at the center of mass of the reference mass; in the nominal state O TM x TM the axis is in the same direction as the sensitive axis, O TM z TM the axis is opposite to the direction of the local gravity.

[0029] 4) Electrode cage coordinate system O E -x E y E z E 。Its origin is at the center of the electrode cage and is formed by rotating the moving stage coordinate system around its z axis by -30°.

[0030] 5) Torsional pendulum coordinate system O TP -x TP y TP zTP Its origin is located at the suspension point of the torsion pendulum; in the nominal state, the directions of other axes are consistent with those of the coordinate axes of the reference mass system.

[0031] S2: Define the positions of all components: S21: Determine the generalized coordinates of the system; The ground simulation platform is divided into two parts: the spacecraft simulation platform and the reference mass torsion pendulum. Therefore, the generalized coordinates need to be determined for each of them separately.

[0032] For the spacecraft simulation platform, determine the generalized coordinates. Define the rotation angle of the pivot arranged along the O I y I axis around the O I y I positive direction of the axis as the generalized coordinate θ 1, and the rotation angle of the pivot arranged along the O I x I axis around the O I x I negative direction of the axis as the generalized coordinate θ 2. The rotation angle of the pivot connecting the outer frame and the upper plate along the O I y I axis, and its rotation angle along the O I y I positive direction of the axis is the generalized coordinate θ 4. The rotation angle of the pivot connecting the middle frame and the outer frame along the O I x I axis, and its rotation angle along the O I x I positive direction of the axis is the generalized coordinate θ 3. The rotation angle of the pivot connecting the inner frame and the middle frame along the O I z I axis, and its rotation angle along the O I z I positive direction of the axis is the generalized coordinate θ 5.

[0033] Determine the generalized coordinates for the reference mass torsion pendulum. The reference mass is suspended below the torsion pendulum, and there is a relative motion relationship between the reference mass coordinate system and the torsion pendulum coordinate system. Therefore, it is stipulated that when transforming from the torsion pendulum coordinate system to the reference mass coordinate system, the (1-2-3) transformation sequence is adopted, that is, first rotate by the generalized coordinate α around the x-axis, then rotate by the generalized coordinate β around the y-axis, and finally rotate by the generalized coordinate φ around the z-axis. In addition, the extensional elasticity of the torsion pendulum wire needs to be considered. During the movement of the torsion pendulum, the length of the wire changes with time. Therefore, the change in the length of the wire of the pendulum is recorded as the generalized coordinate δ ( t ), and the value of this generalized coordinate is positive when the torsion pendulum suspension wire lengthens.

[0034] S22: Determine the positions of each component according to the generalized coordinates of the system.

[0035] To determine the positions of each component in the inertial coordinate system, some design parameters of each component also need to be determined. It is stipulated that the rod length of the support rod is l ( x 1, y 1, z 1) T is the position vector of the centroid of the outer frame in the moving platform coordinate system, ( x 2, y 2, z 2) T is the position vector of the centroid of the middle frame in the moving platform coordinate system, ( x 3, y 3, z 3) T is the position vector of the centroid of the inner frame in the moving platform coordinate system, ( x 4, y 4, z 4) T is the position vector of the centroid of the upper plate in the moving platform coordinate system. The arm length of the cross support structure below the torsion pendulum is d , the upper suspension point of the torsion pendulum is O TP , its position vector in the inertial coordinate system is , and the centroid position vector of the entire torsion pendulum in the nominal state is in the torsion pendulum coordinate system. Here, is the z-direction component of the centroid of the torsion pendulum in the torsion pendulum coordinate system.

[0036] Subsequently, determine the position vectors of the centroids of each component of the spacecraft simulation platform in the inertial coordinate system according to the relative relationship. The expression of the centroid position vector of the upper plate is ; the expression of the centroid position vector of the outer frame is ; Position vector of the centroid of the middle frame is expressed as ; Position vector of the centroid of the inner frame is expressed as ; Among them, the expressions of each rotation matrix are

[0037] Subsequently, according to the relative relationship, determine the position vector of the centroid of the reference mass of the torsion pendulum suspension in the inertial coordinate system. The position vector of the centroid of the reference mass in the torsion pendulum coordinate system is , then its value in the inertial coordinate system is ; Among them, the expressions of each rotation matrix are

[0038] S3: Establish the Lagrangian dynamics equation of the spacecraft platform S31: Determine the kinetic energy of each component of the spacecraft simulation platform; The kinetic energy of the moving platform system is divided into translational kinetic energy and rotational kinetic energy. It is stipulated that m P is the mass of the upper plate; m O is the mass of the outer frame; m M is the mass of the middle frame; m N is the mass of the inner frame.

[0039] The expression of translational kinetic energy is .

[0040] The expression of rotational kinetic energy is , where I O is the inertia matrix of the outer frame; I M is the inertia matrix of the middle frame; I N is the inertia matrix of the inner frame. The inertia matrices of each part of the parts during processing satisfy the following equations

[0041] The angular velocities of each part are

[0042] S32: Determine the potential energy of each component of the spacecraft simulation platform; The potential energy of the moving platform includes gravitational potential energy and elastic potential energy of two different stiffness pivots. It is stipulated that is the z direction component of the position vector of the center of gravity of the upper plate, is the z direction component of the position vector of the center of gravity of the outer frame, is the direction component of the position vector of the center of gravity of the middle frame z ; is the direction component of the position vector of the center of gravity of the inner frame z ; k 1 is the stiffness coefficient of the pivot of the translational part k 2 is the stiffness coefficient of the pivot of the rotational part. The total potential energy is calculated as follows

[0043] S33: Establish the Lagrangian dynamics equation of the spacecraft simulation platform; The Lagrangian of the moving platform can be written as , and the Euler-Lagrange equation can be expressed as . In the formula, is is the generalized torque.

[0044] S34: Determine reasonable assumptions and simplify the Lagrangian dynamics equation of the spacecraft simulation platform.

[0045] In order to eliminate the adverse effects caused by mass eccentricity, during the machining process of the moving platform parts, mass balance can be carried out through design and precision machining, and the center of mass of each component will satisfy the equation

[0046] For the spacecraft simulation platform, its actuation amplitude is within a very small range. Therefore, the trigonometric function operation of the generalized coordinates can be simplified through the small angle assumption. For the generalized coordinates representing rotational motion θ 3, θ 4 and θ 5, to describe more precise dynamic behavior, the second-order terms will be retained at the left end of the Lagrangian equation, and higher-order terms will not be considered. Higher-order terms refer to the product of three or more generalized coordinates and their derivatives. For the generalized coordinates representing translational motion θ 1 and θ 2, only the first-order terms are retained. The specific expression of the Euler-Lagrange equation of S3.3 is

[0047] The expressions of other terms in the formula are

[0048] S4: Establish the Lagrangian dynamics equation of the reference mass S41: Determine the kinetic energy of the torsion pendulum; Denote the unit vectors of the reference mass coordinate system as i TM , j TM and k TM , then they can be respectively expressed in the inertial system as

[0049] According to the Poisson formula for the time derivative of the unit vector in the reference mass coordinate system, the angular velocity of the reference mass in the inertial system can be obtained as

[0050] where m TP is the mass of the torsion pendulum system, I TP is the inertia matrix of the torsion pendulum system, and the kinetic energy of the torsion pendulum system is . Where

[0051] S42: Determine the potential energy of the torsion pendulum; It is stipulated that is the z direction component of the position vector of the centroid of the torsion pendulum; is the telescopic stiffness of the torsion wire of the torsion pendulum; is the torsional stiffness of the torsion wire of the torsion pendulum, then the potential energy of the torsion pendulum system is

[0052] S43: Establish the Lagrangian dynamics equation of the torsion pendulum; The Lagrangian of the torsion pendulum can be written as L TP = T TP - U , and the Euler - Lagrange equation can be expressed as . Where is is the generalized torque.

[0053] S44: Determine reasonable assumptions and simplify the Lagrangian dynamics equation of the torsion pendulum.

[0054] For the torsion pendulum system, its three generalized coordinates α , β and φ that characterize the rotational motion are first simplified through the small - angle assumption; subsequently, only the first - order terms are retained in the obtained dynamic expression, and the Lagrangian dynamics obtained is

[0055] S5: Establish the translational kinematic equation and simplify the translational - related terms in the Lagrangian dynamics equation S51: Determine the kinematic equation of the centroid of the spacecraft simulation platform in the inertial coordinate system; Among the 5 generalized coordinates related to the spacecraft simulation platform, only the generalized coordinates θ 1 and θ2 has an impact on the translational motion. According to the position vector of the centroid of the inner frame of the spacecraft simulation platform and reasonable assumptions, the first-order approximate solution of the centroid of the spacecraft simulation platform in the inertial coordinate system is

[0056] S52: Rewrite the dynamic equation of the spacecraft simulation platform in the translational direction; Combining the kinematic equation of the centroid of the spacecraft simulation platform and the first two terms of the Lagrangian dynamic equation of the spacecraft simulation platform, the dynamic equation of the spacecraft simulation platform in the translational direction is

[0057] The dynamic model of the spacecraft simulation platform in the translational direction is obtained.

[0058] S53: Determine the kinematic equation of the centroid of the reference mass in the inertial coordinate system; Combining the position vector of the centroid of the reference mass and reasonable assumptions, the first-order approximate solution of the kinematic equation of the reference mass in the inertial coordinate system is

[0059] S54: Rewrite the dynamic equation of the reference mass in the translational direction.

[0060] Combining the kinematic equation of the centroid of the reference mass and the first two terms of the Lagrangian dynamic equation of the torsion pendulum, the dynamic equation of the reference mass in the translational direction is

[0061] The dynamic model of the reference mass in the translational direction is obtained.

[0062] S6: Construct the dynamic model of the satellite ground microgravity simulation platform according to the dynamic model of the spacecraft simulation platform in the translational direction and the dynamic model of the reference mass in the translational direction.

[0063] The following further illustrates the present invention with specific embodiments: The parameters of the spacecraft simulation platform in the satellite ground microgravity simulation platform considered in the present invention are , and the mass of the reference mass is . The initial deviation of the ground microgravity simulation platform is . The initial deviation of the reference mass is . The entire system initially remains stationary, and each component has no velocity and acceleration. Subsequently, it is freely released, and the simulation results are as shown in Figures 5 - 11 , where Figure 5It is the graph of the x-direction displacement of the spacecraft simulation platform in a specific embodiment changing with time. The x-direction displacement shows an oscillating trend and does not decay, which conforms to the kinematic and dynamic equation characteristics of the translational degree of freedom of the center of mass of the spacecraft simulation platform in an inertial coordinate system; Figure 6 It is the graph of the y-direction displacement of the spacecraft simulation platform in a specific embodiment changing with time. The y-direction displacement shows an oscillating trend and does not decay, which conforms to the kinematic and dynamic equation characteristics of the translational degree of freedom of the center of mass of the spacecraft simulation platform in an inertial coordinate system; Figure 7 It is the graph of the rotation angle of the spacecraft simulation platform around the x-axis changing with time in a specific embodiment. The rotation angle around the x-axis shows an oscillating trend and does not decay, which conforms to the kinematic and dynamic equation characteristics of the rotational degree of freedom of the spacecraft simulation platform in an inertial coordinate system; Figure 8 It is the graph of the rotation angle of the spacecraft simulation platform around the y-axis changing with time in a specific embodiment. The rotation angle around the y-axis shows an oscillating trend and does not decay, which conforms to the kinematic and dynamic equation characteristics of the rotational degree of freedom of the spacecraft simulation platform in an inertial coordinate system; Figure 9 It is the graph of the rotation angle of the spacecraft simulation platform around the z-axis changing with time in a specific embodiment. The rotation angle around the z-axis shows an oscillating trend and does not decay, which conforms to the kinematic and dynamic equation characteristics of the rotational degree of freedom of the spacecraft simulation platform in an inertial coordinate system; Figure 10 It is the graph of the x-direction displacement of the reference mass in a specific embodiment changing with time. The x-direction displacement does not change with time, which conforms to the kinematic and dynamic equation characteristics of the translational degree of freedom of the center of mass of the reference mass in an inertial coordinate system; Figure 11 It is the graph of the y-direction displacement of the reference mass in a specific embodiment changing with time. The y-direction displacement does not change with time, which conforms to the kinematic and dynamic equation characteristics of the translational degree of freedom of the center of mass of the reference mass in an inertial coordinate system. In the absence of external force interference, the two translational degrees of freedom and three rotational degrees of freedom of the spacecraft platform present a spring second-order system oscillation mode, and the reference mass is in a static state in inertial space, all of which are consistent with the theoretical analysis, indicating the effectiveness of the dynamic modeling method proposed by the present invention.

[0064] In summary, compared with traditional microgravity simulation methods, the advantages of the present invention are that it takes into account more actual factors. In particular, it has carefully modeled the dynamic behaviors of the spacecraft platform and the torsion pendulum, enabling higher-precision microgravity control during ground tests. This is of great significance for the ground tests of gravitational wave detection satellites because gravitational wave detection satellites have extremely stringent requirements for microgravity and must be tested in an environment close to zero gravity to minimize the interference and errors brought by the ground environment. Through the microgravity simulation platform dynamics modeling method provided by the present invention, a microgravity level close to the space environment can be achieved during ground tests, thereby providing more reliable data support for the performance verification and optimization of the satellite. In addition, the microgravity simulation platform established based on this model can be applied to the ground tests of other space missions, including but not limited to the dynamic performance tests of space devices such as satellites and detectors. By accurately simulating the microgravity environment, the interference of the ground environment on the test results can be effectively reduced, providing a more scientific and accurate basis for the design and optimization of space devices. In short, by establishing the dynamics model of the ground microgravity simulation platform for gravitational wave detection satellites, the present invention solves the problem of unable to achieve accurate microgravity simulation in the prior art and has significant technical advantages.

[0065] The second object of the present invention is to propose a dynamics modeling system for a ground microgravity simulation platform of a gravitational wave detection satellite, as Figure 11 shown, including: A coordinate system acquisition module 100: used to acquire the coordinate system of the spacecraft simulation platform and the coordinate system of the reference mass torsion pendulum in the ground simulation platform; A component position module 200: used to clarify the positions of each component according to the coordinate system of the spacecraft simulation platform and the coordinate system of the reference mass torsion pendulum; A platform dynamics module 300: used to determine the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establish a dynamics model of the spacecraft simulation platform; A torsion pendulum dynamics module 400: used to determine the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establish a Lagrangian dynamics model of the torsion pendulum; A microgravity simulation platform dynamics module 500: used to construct a dynamics model of the satellite ground microgravity simulation platform based on the dynamics model of the spacecraft simulation platform and the Lagrangian dynamics model of the torsion pendulum.

[0066] As Figure 12As shown, the third object of the present invention is to provide an electronic device, which includes: a processor 601, a memory 602, and a display screen 603. Among them, the memory 602 and the display screen 603 are both connected to the processor 601, such as through a bus 604. Optionally, the electronic device may further include a transceiver 605. It should be noted that in practical applications, the transceiver 605 is not limited to one, and the structure of the electronic device does not constitute a limitation to the embodiments of the present application.

[0067] The processor 601 may be a CPU (Central Processing Unit, central processor), a general-purpose processor, a DSP (Digital Signal Processor, data signal processor), an ASIC (Application Specific Integrated Circuit, application-specific integrated circuit), an FPGA (Field Programmable Gate Array, field programmable gate array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute various exemplary logical blocks, modules, and circuits described in combination with the disclosure of the present application. The processor 601 may also be a combination that implements a computing function, such as a combination including one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0068] The bus 604 may include a path for transmitting information between the above components. The bus 604 may be a PCI (Peripheral Component Interconnect, peripheral component interconnect standard) bus or an EISA (Extended Industry Standard Architecture, extended industry standard architecture) bus, etc. The bus 604 may be divided into an address bus, a data bus, a control bus, etc.

[0069] The memory 602 can be a ROM (Read Only Memory), or other types of static storage devices that can store static information and instructions, a RAM (Random Access Memory), or other types of dynamic storage devices that can store information and instructions. It can also be an EEPROM (Electrically Erasable Programmable Read Only Memory), a CD-ROM (Compact Disc Read Only Memory), or other optical disc storage, optical disc storage (including compact discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic disk storage media, or other magnetic storage devices, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto.

[0070] The memory 602 is used to store the application program code for executing the solution of this application and is controlled by the processor 601 for execution. The processor 601 is used to execute the application program code stored in the memory 602 to implement the content shown in the foregoing method embodiments.

[0071] Figure 12 The illustrated electronic device is only an example and should not impose any limitations on the functions and usage scope of the embodiments of this application.

[0072] The fourth object of the present invention is to provide a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the program is executed by a processor, it implements the processes of the method embodiments as described above Figure 1 and Figure 2 shown. For example, a memory including instructions, and the above instructions can be executed by the processor of the electronic device to complete the above method.

[0073] A computer-readable storage medium can be a tangible device that holds and stores instructions used by an instruction execution device. A computer-readable storage medium can be, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination of the above. Specifically, a computer-readable storage medium can be a portable computer disk, a hard disk, a USB flash drive, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, an optical disc, a magnetic disk, a mechanical coding device, and any combination of the above.

[0074] The fifth objective of the present invention is to provide a computer program product, including computer instructions, which implement the various processes of the method embodiments described above when executed by a processor, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here. Figure 1 and Figure 2 shown in the method embodiments, and can achieve the same technical effects. To avoid repetition, it will not be elaborated here.

[0075] Upon reading the above description, many embodiments and many applications beyond the provided examples will be obvious to those skilled in the art. Therefore, the scope of this teaching should not be determined with reference to the above description, but rather should be determined with reference to the full scope of the foregoing claims and the equivalents thereof. For the sake of completeness, all articles and references, including patent applications and publications, are incorporated herein by reference. The omission of any aspect of the subject matter disclosed herein in the foregoing claims is not intended to abandon such subject matter, nor should it be considered that the applicant has not considered such subject matter to be part of the disclosed inventive subject matter.

[0076] The above content is a further detailed description of the present invention. It cannot be determined that the specific implementation of the present invention is limited to this. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should all be regarded as belonging to the protection scope determined by the claims submitted for the present invention.

Claims

1. A dynamic modeling method for a ground microgravity simulation platform of a gravitational wave detection satellite, characterized in that Including: Obtain the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system in the ground simulation platform; Determine the positions of each component according to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system; Determine the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establish the dynamic model of the spacecraft simulation platform; Determine the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establish the Lagrangian dynamic model of the torsion pendulum; Construct the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum.

2. A dynamic modeling method for a ground microgravity simulation platform of a gravitational wave detection satellite according to claim 1, characterized in that The obtaining of the spacecraft simulation platform coordinate system and the reference mass coordinate system in the ground simulation platform includes: For the spacecraft simulation platform in the ground simulation platform, it is defined that the rotation angle of the pivot arranged along the O I y I axis of the translational part around the O I y I positive direction of the axis is the generalized coordinate θ 1, and the rotation angle of the pivot arranged along the O I x I axis of the translational part around the O I x I negative direction of the axis is the generalized coordinate θ 2; the pivot connecting the outer frame and the upper plate is arranged along the O I y I axis, and its rotation angle along the O I y I positive direction of the axis is the generalized coordinate θ 4; the pivot connecting the middle frame and the outer frame is arranged along the O I x I axis, and its rotation angle along the O I x I positive direction of the axis is the generalized coordinate θ 3; the pivot connecting the inner frame and the middle frame is arranged along the O I z I axis, and its rotation angle along the O I z I positive direction of the axis is the generalized coordinate θ 5; a coordinate system of the spacecraft simulation platform in the ground simulation platform is formed; For the reference mass torsion pendulum in the ground simulation platform, it is stipulated that when transforming the torsion pendulum coordinate system to the reference mass coordinate system, the generalized coordinates are first rotated around the x-axis α , then the generalized coordinates are rotated around the y-axis β , and finally the generalized coordinates are rotated around the z-axis φ ; Denote the change in the length of the wire of the pendulum as the generalized coordinate δ ( t ), and make the value of the generalized coordinate φ positive when the suspension wire of the torsion pendulum increases; thus forming the reference mass torsion pendulum coordinate system in the ground simulation platform.

3. A dynamic modeling method for a ground microgravity simulation platform of a gravitational wave detection satellite according to claim 1, characterized in that The determining of the positions of each component according to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system; According to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system, it is stipulated that the rod length of the support rod is l , ( x 1, y 1, z 1) T is the position vector of the outer frame centroid in the moving platform coordinate system, ( x 2, y 2, z 2) T is the position vector of the middle frame centroid in the moving platform coordinate system, ( x 3, y 3, z 3) T is the position vector of the inner frame centroid in the moving platform coordinate system, ( x 4, y 4, z 4) T is the position vector of the upper plate centroid in the moving platform coordinate system. The arm length of the cross support structure below the torsion pendulum is d , and the upper suspension point of the torsion pendulum is O TP , and its position vector in the inertial coordinate system is . In the nominal state, the centroid position vector of the whole torsion pendulum in the torsion pendulum coordinate system is . In the formula, is the z-direction component of the torsion pendulum centroid in the torsion pendulum coordinate system; Determine the position vectors of the centroids of the components of the spacecraft simulation platform in the inertial coordinate system according to the relative relationship; the position vector of the centroid of the upper plate is expressed as ; the position vector of the centroid of the outer frame is expressed as ; the position vector of the centroid of the middle frame is expressed as ; the position vector of the centroid of the inner frame is expressed as ; Determine the position vector of the centroid of the reference mass of the torsion pendulum suspension in the inertial coordinate system according to the relative relationship; the position vector of the centroid of the reference mass is in the torsion pendulum coordinate system, and its position vector in the inertial coordinate system is .

4. A dynamic modeling method for a ground microgravity simulation platform of a gravitational wave detection satellite according to claim 1, characterized in that, The determining of the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establishing the dynamic model of the spacecraft simulation platform includes: Determine the translational kinetic energy and rotational kinetic energy of each component of the spacecraft simulation platform according to the positions of each component: The translational kinetic energy is ; The rotational kinetic energy is ; In the formula, I O is the outer frame inertia matrix; I M is the middle frame inertia matrix; I N is the inner frame inertia matrix; m P is the mass of the upper plate; m O is the mass of the outer frame; m M is the mass of the middle frame; m N is the mass of the inner frame; Determine the potential energy of each component of the spacecraft simulation platform according to the positions of each component; In the formula, is the z-direction component of the position vector of the center of gravity of the upper plate, is the z-direction component of the position vector of the center of gravity of the outer frame, is the z-direction component of the position vector of the center of gravity of the middle frame, is the z-direction component of the position vector of the center of gravity of the inner frame; k1 is the stiffness coefficient of the pivot of the translational part, and k2 is the stiffness coefficient of the pivot of the rotational part; Determine the translational kinetic energy, rotational kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of the components, and establish the dynamic model of the spacecraft simulation platform .

5. A dynamic modeling method for a ground microgravity simulation platform of a gravitational wave detection satellite according to claim 1, characterized in that The determining of the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establishing the Lagrangian dynamic model of the torsion pendulum includes: The kinetic energy of the torsion pendulum with the positions of each component determined is ; where m TP is the mass of the torsion pendulum system, and I TP is the inertia matrix of the torsion pendulum system; The potential energy of the torsion pendulum with the positions of each component determined is ; wherein, is the z-direction component of the position vector of the centroid of the torsion pendulum; is the telescopic stiffness of the torsion wire of the torsion pendulum; is the torsional stiffness of the torsion wire of the torsion pendulum; Determine the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establish the Lagrangian dynamics model of the torsion pendulum L TP = T TP - U 。 6. A method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite according to claim 1, characterized in that The constructing of the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum includes: Construct the dynamic model of the spacecraft simulation platform in the translational direction according to the centroid kinematic model of the spacecraft simulation platform and the dynamic model of the spacecraft simulation platform; Construct the dynamic model of the reference mass in the translational direction according to the centroid kinematic equation model of the reference mass and the Lagrangian dynamic model of the torsion pendulum.

7. A dynamic modeling system for a ground microgravity simulation platform of a gravitational wave detection satellite, characterized in that, Including: Coordinate system acquisition module: used to obtain the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system in the ground simulation platform; Component position module: used to determine the positions of each component according to the spacecraft simulation platform coordinate system and the reference mass torsion pendulum coordinate system; Platform dynamics module: used to determine the kinetic energy and potential energy of each component of the spacecraft simulation platform according to the positions of each component, and establish the dynamic model of the spacecraft simulation platform; Torsion pendulum dynamics module: used to determine the kinetic energy and potential energy of the torsion pendulum according to the positions of each component, and establish the Lagrangian dynamic model of the torsion pendulum; Microgravity simulation platform dynamics module: used to construct the dynamic model of the satellite ground microgravity simulation platform based on the dynamic model of the spacecraft simulation platform and the Lagrangian dynamic model of the torsion pendulum.

8. An electronic device, characterized in that, Including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the method for dynamically modeling a satellite ground microgravity simulation platform according to any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program. When the computer program is executed by the processor, it implements the steps of the method for dynamically modeling a satellite ground microgravity simulation platform according to any one of claims 1-6.

10. A computer program product, characterized in that, Including computer instructions, when the computer instructions are executed by a processor, the steps of a method for dynamic modeling of a ground microgravity simulation platform for a gravitational wave detection satellite as described in any one of claims 1-6 are implemented.

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