Tethered satellite system dynamics modeling method considering perturbation factor

Abstract

The invention discloses a tethered satellite system dynamics modeling method considering perturbation factors. The tethered satellite system dynamics modeling method comprises the steps that a geocentric coordinate system, an orbital coordinate system of a Kepler orbit where a tethered satellite system is located and a body coordinate system of a unit satellite are established; according to the movement of the centroid of the tethered satellite system on the orbit, the generalized coordinates are the distance from the centroid of the system to the earth center and the true anomaly of the orbit, the Lagrange function of the centroid of the system is obtained; according to the movement of the unit star relative to the centroid, the generalized coordinates are the distance between the unit star and the centroid, the relative first rotation angle and the relative second rotation angle, the relative Lagrange function of the unit star is obtained; comprehensively considering perturbation factors to obtain non-spherical earth, third gravitational force and solar pressure perturbation potential energy; establishing a system kinetic equation considering comprehensive perturbation factors; and obtaining a complete Lagrange equation of the tethered satellite system. The error problem caused by the fact that the master satellite directly serves as the mass point of the system and the influence of comprehensive perturbation on system motion is not considered is solved, and the number of the slave satellites is not limited.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology, specifically relating to a dynamic modeling method for tethered satellite systems that considers perturbation factors. Background Technology

[0002] A tethered satellite system refers to a space multi-body spacecraft that connects a primary satellite and a secondary satellite using several tethers. The tethers can self-deploy using the gravitational gradient effect or spin. With its advantages of high spatial flexibility, structural flexibility, and self-balancing, it can accomplish tasks that ordinary spacecraft cannot, covering many important space applications including space solar sails, space solar stations, and space debris removal. In traditional master-slave satellite modeling methods, the system's center of mass is usually assumed to be at the location of the primary satellite. However, there is actually a mass difference between the primary and secondary satellites (i.e., the mass of the secondary satellite is not infinitesimal), which can lead to errors in dynamic modeling. In high-precision control scenarios, such as precise formation flying and gravity field measurement, neglecting the influence of the secondary satellite's mass on the system's center of mass will cause the actual orbit of the center of mass to deviate from the theoretical model, thus affecting the accuracy of relative state determination and control performance. Furthermore, traditional master-slave star modeling methods are generally only applicable to the case of a single slave star. When there are multiple slave stars (i.e., a "one master, multiple slaves" formation), this method is difficult to describe the mutual coupling between slave stars. The motion of each slave star is not only affected by the master star, but also by other gravitational perturbations. The traditional one master and one slave model cannot naturally reflect the multi-body coupling effect, which leads to a sharp increase in model complexity and inaccuracy.

[0003] As spacecraft, tethered satellite systems are subject to perturbations from Earth's non-spherical shape, the third gravitational force, and solar radiation pressure during their orbits. Although these perturbations are approximately one ten-thousandth of Earth's gravitational pull, their prolonged effects can still cause the system to deviate from its mission requirements and impact the spacecraft's lifespan. With the advancement of my country's manned spaceflight, lunar exploration, and space energy development, accurate on-orbit motion prediction is crucial for completing a series of complex tasks related to the design, manufacturing, and flight of tethered satellite systems. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention aims to provide a dynamic modeling method for tethered satellite systems that considers perturbation factors. This method solves the error problem caused by directly using the primary satellite as the system's point mass and not considering the influence of comprehensive perturbation on the system's motion, and does not limit the number of slave satellites.

[0005] This invention is achieved through the following technical solution: A dynamic modeling method for tethered satellite systems considering perturbation factors includes the following steps: Step 1: Establish the geocentric coordinate system, the orbital coordinate system of the Keplerian orbit in which the tethered satellite system is located, and the volume coordinate system of the unit satellite; Step 2: Based on Step 1, and considering that the center of mass of the tethered satellite system moves in orbit, the generalized coordinates are the distance from the system's center of mass to the Earth's center. Angle of true anterior to orbit We obtain the Lagrange function of the system's centroid; Step 3: Based on Step 1, according to the motion of the unit star relative to the center of mass, the generalized coordinates are the distance between the unit star and the center of mass. Relative to the first rotation angle Second rotation angle The relative Lagrangian function of the unit star is obtained; Step 4: The perturbation factors include the Earth's non-spherical perturbation, the gravitational perturbation potential energy of the third body, and the solar radiation pressure perturbation potential energy. Based on the coordinate system of Step 1, the Earth's non-spherical perturbation potential energy, the third gravitational perturbation potential energy, and the solar radiation pressure perturbation potential energy of the system's center of mass and the unit star are obtained. Step 5: Establish the system dynamic equations considering the perturbation factors described in Step 4; Step 6: Substitute the Lagrangian function of the system's centroid obtained in Step 2, the relative Lagrangian function of the unit star obtained in Step 3, and the perturbation factor obtained in Step 4 into the system dynamics equations in Step 5 to establish the complete Lagrangian equations for the tethered satellite system.

[0006] Furthermore, step 1 involves establishing a geocentric coordinate system. The origin is the Earth's center. , The axis points to the vernal equinox in the equatorial plane. The axis is perpendicular to the equatorial plane and aligns with the direction of the Earth's rotational angular velocity. The axis satisfies the right-hand rule; quality is The tethered satellite system, whose orbital coordinate system is Kepler orbit, is... With the system's center of mass as the origin With the Earth's core The distance between them is , Pointing towards the Earth's center, The axis lies in the orbital plane along the velocity direction. The axis is determined by the right-hand rule; The mass of the tethered satellite system is Unit Star The body coordinate system is Set the origin of the orbital coordinate system Translation Obtain the origin of the unit star coordinate system , and then around Rotation get , then go around Rotation get , The axis is determined by the right-hand rule.

[0007] Furthermore, the Lagrangian function of the system's centroid in step 2 is: (2-1) in, Let Lagrangian function be the mass center of the system. The gravitational constant of Earth, The non-spherical perturbation potential energy of the Earth acting on its center of mass. The gravitational perturbation potential energy of the third body acting on the center of mass. Let be the rate of change of the distance from the system's center of mass to the Earth's center. This represents the rate of change of the true anomaly angle of the orbit.

[0008] Furthermore, the relative Lagrangian function of the unit star in step 3 is: (2-2) in, The non-spherical perturbation potential energy of Earth acting on a unit star. This refers to the gravitational perturbation potential energy of a third body acting on a monoplanet. For a single star, the Lagrangian function is... The instantaneous rate of change of the distance between the unit star and its center of mass. The rate of change of the first rotation angle of the unit star. This represents the rate of change of the second rotation angle of the unit star.

[0009] Furthermore, the Earth-like non-spherical perturbation potential energy of the system's center of mass and the unit star in step 4 is expressed as: (2-3) in, This is the Earth's oblateness coefficient. For the Earth's radius, The geocentric latitude of the center of mass. The geocentric latitude of the unit star. This represents the distance from the unit star to the Earth's center. The non-spherical perturbation potential energy of the Earth at the system's center of mass. The non-spherical perturbation potential energy of the Earth for a single star; (2-4) in, Let be the angle between the unit star and the line connecting the system's center of mass and the Earth's center, at a small angle. ; The third gravitational perturbation potential energy of the system's center of mass and the unit star is expressed as: (2-5) in, It is the third gravitational constant, determined by the third celestial body. The position of the third celestial body is such that the angle between the line connecting the system's center of mass to the Earth's center and the line connecting the third celestial body to the Earth's center is . , The third gravitational perturbation potential energy is the center of mass of the system. This represents the third gravitational perturbation potential energy of the monoplanet; The solar radiation pressure perturbation potential energy can be expressed as: (2-6) in, For generalized coordinates, the system centroid is and For a single star , and ; Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force.

[0010] Furthermore, the system dynamic equation considering perturbation factors in step 5 is as follows: (2-7) in, Lagrangian functions of the system's centroid, respectively Lagrange function of a single star , This represents the derivative with respect to generalized coordinates, where the centroid of the system is... and For a single star , and .

[0011] Furthermore, in step 6, applying the Lagrange equation to the center of mass of the tethered satellite system, we get: (2-8) in, The acceleration representing the change in distance between the system's center of mass and the Earth's center. Represents the acceleration due to the change of the true anomaly angle of the orbit; For a single satellite in a tethered satellite system, applying the Lagrange equations, we get: (2-9) in, The acceleration representing the change in distance between the unit star and the system's center of mass. Represents the acceleration due to the change in the first rotation angle of the unit star. This represents the acceleration due to the change in the second rotation angle of the unit star.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: In modeling the motion of a tethered satellite system, this invention treats the system as a combination of a center of mass and unit stars, rather than the traditional master-slave model, thus eliminating model errors caused by erroneous assumptions. Furthermore, it introduces the concept of unit stars, where all slave stars (or multiple unit bodies) are considered as unit stars moving relative to the same center of mass of the system, and the relative motion of each unit star is... , and The descriptions are all independently and parallelly established in the center-of-mass orbital coordinate system. To expand the model, only new unit stars and their relative coordinates need to be added. All unit stars are naturally coupled together through their shared orbital motion. Regardless of the number of unit stars in the system, their relative motion equations have the same form, greatly simplifying the complexity of the model and the design of the controller. At the same time, the influence of perturbation factors on the motion of the tethered satellite system is fully considered. The non-spherical perturbation of the Earth and the gravitational perturbation of the third body are explicitly included in the Lagrangian function, and the solar radiation pressure perturbation is considered in the Lagrangian equation through generalized forces, which improves the accuracy of the system motion description. It can reproduce the motion behavior of the spacecraft in the real space environment and construct a model that can not only fully describe the overall system but also accurately analyze the system motion characteristics. This lays a solid foundation for in-depth research on tethered satellite systems and is suitable for long-life, high-precision missions. Attached Figure Description

[0013] Figure 1 This is a schematic diagram of the coordinate system of the tethered satellite system of the present invention; Figure 2(a) shows the operation of the unperturbed two-body tethered satellite system in an elliptical orbit; Figure 2(b) shows the distance between the unit satellite and the center of mass; and Figure 2(c) shows the distance between the center of mass and the Earth's center. Figure 3(a) is a comparison of the orbits of the two-body tethered satellite system before and after the perturbation, and Figure 3(b) is a magnified view of the orbits in Figure 3(a). Figure 4(a) shows the distance between unit satellite 1 and the center of mass in the two-body tethered satellite system before and after the perturbation. Figure 4(b) shows the distance difference caused by the perturbation. Figure 5(a) shows the distance between unit satellite 2 and the center of mass in the two-body tethered satellite system before and after the perturbation. Figure 5(b) shows the distance difference caused by the perturbation. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to specific embodiments. These descriptions are for explanation purposes only and are not intended to limit the scope of the invention.

[0015] This invention provides a dynamic modeling method for tethered satellite systems that considers perturbation factors, comprising the following steps: Step 1: Setting up the coordinate system: A tethered satellite system generally consists of two or more unit satellites connected by a tether; in this invention, the system's centroid is not assumed during modeling, and each satellite is treated as a unit satellite. The following will be used... Figure 1 The coordinate system of the tethered satellite system shown: (1) It is a geocentric coordinate system, with the origin at the Earth's center. , The axis points to the vernal equinox in the equatorial plane. The axis is perpendicular to the equatorial plane and aligns with the direction of the Earth's rotational angular velocity. The axis satisfies the right-hand rule.

[0016] (2) It is quality The orbital coordinate system of the tethered satellite system in Kepler orbit, with the system's center of mass as the origin. With the Earth's core The distance between them is , Pointing towards the Earth's center, The axis lies in the orbital plane along the velocity direction. The axis is determined by the right-hand rule.

[0017] (3) It is a tethered satellite system with a mass of Unit Star The body coordinate system, with the origin of the orbital coordinate system... Translation Obtain the origin of the unit coordinate system , and then around Rotation get , then go around Rotation get , The axis is determined by the right-hand rule.

[0018] Step 2: Lagrangian function of the system's center of mass: The center of mass of the tethered satellite system moves in its space orbit, and the generalized coordinates represent the distance from the system's center of mass to the Earth's center. Angle of true anterior to orbit Its Lagrange function is: (2-1) in, is the Earth's gravitational constant. This refers to the non-spherical perturbation potential energy of the Earth acting on its center of mass (e.g., term J2). The gravitational perturbation potential energy of a third body acting on the center of mass (such as the sun or moon). Let be the rate of change of the distance from the system's center of mass to the Earth's center. This represents the rate of change of the true anomaly angle of the orbit.

[0019] Step 3: Lagrangian function of the unit star: The generalized coordinates of the unit star's motion relative to the center of mass are the distance between the unit star and the center of mass. Relative to the first rotation angle Second rotation angle The relative Lagrangian function of a single star is: (2-2) in, This refers to the non-spherical perturbation potential energy of Earth acting on the unit star (such as term J2). This refers to the gravitational perturbation potential energy of a third body (such as the Sun or Moon) acting on a unit star. For a single star, the Lagrangian function is... The instantaneous rate of change of the distance between the unit star and its center of mass. The rate of change of the first rotation angle of the unit star. This represents the rate of change of the second rotation angle of the unit star.

[0020] Step 4: Perturbation Factors ① Earth's non-spherical perturbations Earth's non-spherical perturbation, caused by the Earth's shape deviating from a perfect sphere and its uneven mass distribution, generates gravitational disturbances that can affect the motion of tethered satellite systems. Based on the general form of Earth's non-spherical perturbation potential energy, the Earth's non-spherical perturbation potential energy for the system's center of mass and the unit star is expressed as follows: (2-3) in, The Earth's oblateness coefficient (approximately) ), It is the Earth's radius (approximately 6378 km). The geocentric latitude of the center of mass. The geocentric latitude of the unit star. This represents the distance from the unit star to the Earth's center. For system The non-spherical perturbation potential energy of the Earth's center of mass. The non-spherical perturbation potential energy of the Earth for a single star; (2-4) in, The angle between the unit star and the line connecting its center of mass and the Earth's center, at small angles. .

[0021] ②Third gravitational perturbation The third gravitational perturbation refers to the disturbance of the orbit of a tethered satellite system by the gravity of celestial bodies other than the host celestial body. Based on the general form of the third gravitational perturbation potential energy, the third gravitational perturbation potential energy of the system's center of mass and the unit star is expressed as follows: (2-5) in, It is the third gravitational constant, determined by the third celestial body. The position of the third celestial body is such that the angle between the line connecting the center of mass to the Earth's center and the line connecting the third celestial body to the Earth's center is . , The third gravitational perturbation potential energy is the center of mass of the system. This is the third gravitational perturbation potential energy of the monoplanet.

[0022] ③Solar radiation pressure perturbation Solar radiation pressure perturbation is the minute pressure generated by solar photons impacting a tethered satellite system, causing a shift in the system's motion. Solar radiation pressure is a non-conservative force, and therefore a generalized force in the Lagrange equations. Its magnitude depends on the sun's direction, the spacecraft's attitude, and the area exposed to sunlight.

[0023] (2-6) in, For generalized coordinates, with the centroid as and For a single star , and , Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force.

[0024] Step 5: System dynamics equations considering perturbation factors: Applying the Lagrange equations to tethered satellite systems, i.e.: (2-7) in, Lagrangian functions of the centroid Lagrange function of a single star , This represents the derivative with respect to generalized coordinates, where the centroid of the system is... and For a single star , and ; Step Six: Substitute the formulas obtained in Steps Two, Three, and Four into Step Five. The complete dynamic equations for the tethered satellite are as follows: Applying the Lagrange equation to the center of mass of a tethered satellite system: (2-8) in, The acceleration representing the change in distance between the system's center of mass and the Earth's center. Represents the acceleration due to the change of the true anomaly angle of the orbit; For the unit satellites of a tethered satellite system, the Lagrange equations are applied.

[0025] (2-9) in, The acceleration representing the change in distance between the unit star and the system's center of mass. Represents the acceleration due to the change in the first rotation angle of the unit star. This represents the acceleration due to the change in the second rotation angle of the unit star.

[0026] In summary, the complete dynamic equations of the tethered satellite system considering perturbation factors are equations (2-8) and (2-9).

[0027] Simulation Examples With the continuous advancement of space exploration, based on theoretical analysis, a simulation example of a two-body tethered satellite system can be established. This can serve as a reference for the design of system flight missions, improve the design reliability of tethered satellite systems, provide a basis for orbit control, extend the service life of spacecraft, and meet the development needs of various fields.

[0028] Basic experimental conditions for simulation In the simulation experiment, the total mass of the tethered satellite system was chosen to be 16000 kg, with unit satellite 1 having a mass of 15000 kg and unit satellite 2 having a mass of 1000 kg. The initial distance between the two unit satellites was 1000 m. The orbital parameters of the tethered satellite system are as follows: Perigee radius: 6486.533km apogee radius: 34054.303km Eccentricity: 0.68 Inclination angle: 50° Right ascension of the ascending node: 0° Argument of perigee: 60° Horizontal near point angle: 0.12 rad Angle of approach: 0.18 rad True closest angle: 79.92° In the complete dynamic equations 2-8 and 2-9 of the tethered satellite system considering perturbations, removing the influence of the perturbation terms yields the equations of motion for a two-body tethered satellite system without considering perturbations: The motion of the center of mass of the tethered satellite system is as follows: (2-10) The motion of the unit satellite in a tethered satellite system is as follows: (2-11) Taking the basic simulation conditions from the simulation example, and following equations (2-10) and (2-11), we can obtain the results shown in Figure 2: As can be seen, Figure 2(a) shows the overall operation of the two-body tethered satellite system under no perturbation influence, demonstrating that the system's center of mass operates normally in the predetermined elliptical orbit. Figures 2(b) and 2(c) show the motion of the center of mass and the relative motion of the unit star. Within one elliptical orbit cycle, the distance between the unit star and the system's center of mass remains constant after reaching the set value. Furthermore, the distance between the center of mass and the Earth's center further illustrates that the system can maintain its normal orbit. Therefore, the correctness of the dynamic modeling method obtained by the present invention is verified.

[0029] Simulation results of this invention Taking the basic simulation conditions in the simulation example, the dynamic equations of the tethered satellite considering perturbation factors obtained from equations (2-8) and (2-9) are used to conduct the simulation, and the results are compared with those without perturbation factors: Figure 3(a) shows a comparison of the orbits of the two-body tethered satellite systems before and after the perturbation, while Figure 3(b) shows a magnified view of the area with the greatest orbital difference. It is clear from the figures that the perturbation significantly affected the system's motion in its elliptical orbit, and this effect was most pronounced near the apogee. The apogee is the point farthest from Earth; at this location, the system's velocity is relatively slow, the perturbation force acts for a relatively long time, and the orbital curvature is small, making it easier for the perturbation force to cause changes in the orbit's shape and position. Therefore, the orbital difference is most pronounced in this region.

[0030] Figure 4(a) shows a comparison of the distance changes between Unit Satellite 1 and the system's center of mass before and after the perturbation, while Figure 4(b) shows the distance changes caused by the perturbation. It is clear from the figures that the perturbation has a certain impact on the distance between Unit Satellite 1 and the system's center of mass, with a maximum difference of 0.0022 meters, which also occurs near the apogee of the system. Since it is a tethered satellite system, the unit satellites are generally connected by elastic tethers; therefore, such distance fluctuations are effectively absorbed and buffered by the elastic properties of the tethers.

[0031] Figure 5(a) visually compares the changes in distance between Unit Star 2 and the system's center of mass before and after the perturbation, while Figure 5(b) precisely depicts the specific distance changes caused by the perturbation. It is clear from the figures that the perturbation significantly affected the distance between Unit Star 2 and the system's center of mass, with a trend similar to that of Unit Star 1, but the maximum difference was only 0.0002 meters, significantly smaller than that of Unit Star 1. This is mainly because Unit Star 2 has a relatively smaller mass and a smaller moment of inertia, thus its change is relatively smaller.

[0032] Simulation results show that, taking a traditional two-body tethered system as an example, when perturbation factors are considered, the perturbation causes the center of mass to deviate from its predetermined elliptical orbit, resulting in a certain offset. Simultaneously, the perturbation causes fluctuations in the distance between the unit satellites and the center of mass in the tethered satellite system.

[0033] In summary, this invention elevates the modeling perspective from a reference frame centered on the primary star to a more fundamental inertial / orbital reference frame centered on the system's center of mass. Traditional methods forcibly fix the center of mass on the primary star. When the mass of the secondary star is not negligible, the true center of mass of the system is actually a point on the line connecting the primary and secondary stars, shifting slightly with their relative motion. Forcibly fixing the position of the center of mass introduces an inherent, theoretical error into the dynamic equations. This invention, however, models the system's center of mass as an independent, clearly defined dynamic entity, using generalized coordinates. and This describes the orbital motion of the true center of mass of the tethered satellite system, rather than the position of the primary star. Thus, regardless of the mass ratio of the primary and secondary stars, the motion of the center of mass is rigorously and accurately described, eliminating model errors caused by erroneous assumptions at their source. Furthermore, traditional methods using a one-primary-one-secondary model cannot describe the interactions between multiple secondary stars. Further expansion requires establishing a one-primary-multiple-secondary star configuration, but in this model, each secondary star is only coupled to the primary star, with no direct dynamic link between them, resulting in an incomplete model. This invention introduces the concept of a unit star, where all secondary stars (or multiple unit bodies) are considered as unit stars moving relative to the same center of mass of the system. The relative motion of each unit star... , and The descriptions are all independently and parallelly established in the center-of-mass orbit coordinate system. Multiple unit satellites are supported simultaneously; to expand the model, only new unit satellites and their relative coordinates need to be added. All unit satellites are naturally coupled together through their shared, dependent center-of-mass orbital motion. Regardless of the number of unit satellites in the system, their relative motion equations have the same form, greatly simplifying the model's complexity and controller design. The sequentially established model more realistically reflects the physical nature of the system, especially crucial in high-precision missions (such as gravity gradient stabilization and measurement, active space debris removal, and tethered rendezvous and docking), where the accuracy of the center-of-mass orbit is paramount. Furthermore, it can seamlessly expand from a master-slave configuration to a master-multiple-slave tethered satellite system, providing a unified modeling tool for complex distributed spacecraft systems and laying the foundation for precise control.

[0034] Traditional methods often rely on simplified analyses or only consider the Earth's central gravitational field in the preliminary design phase, which is far from sufficient for modern high-precision space missions. Ignoring perturbations leads to significant deviations between theoretical and actual trajectories. This invention explicitly incorporates Earth's non-spherical perturbations and third-body gravitational perturbations into the Lagrangian function, and considers solar radiation pressure perturbations through generalized forces in the Lagrangian equations. This enables the reproduction of spacecraft motion behavior in real space environments. For example, the J2 perturbation causes orbital plane rotation and elliptical orbit rotation within the orbital plane, which is a decisive factor for maintaining long-term formation configuration; third-body perturbations have a significant impact on the orbits of high-orbit missions (such as GEO and lunar orbits); solar radiation pressure has a huge impact on tethered satellite systems with large area-to-mass ratios (such as tethered solar sails), and is a factor that must be considered for orbit and attitude control. Only by fully considering these long-term effects can the established model be used for accurate prediction, simulation, and control throughout the mission's entire lifecycle, ensuring mission success.

[0035] This invention is more rigorous in theory, more precise in application, and more versatile in function. It can directly serve as a full-chain dynamic modeling solution for modern complex and high-precision spacecraft formation missions, and provides a theoretical basis for subsequent controller design, mission simulation analysis, and fault diagnosis.

Claims

1. A dynamic modeling method for tethered satellite systems considering perturbation factors, characterized in that, Includes the following steps: Step 1: Establish the geocentric coordinate system, the orbital coordinate system of the Keplerian orbit in which the tethered satellite system is located, and the volume coordinate system of the unit satellite; Step 2: Based on Step 1, and considering that the center of mass of the tethered satellite system moves in its orbit, the generalized coordinates represent the distance from the system's center of mass to the Earth's center. Angle of true anterior to orbit We obtain the Lagrange function of the system's centroid; Step 3: Based on Step 1, according to the motion of the unit star relative to the center of mass, the generalized coordinates are the distance between the unit star and the center of mass. Relative to the first rotation angle Second rotation angle The relative Lagrangian function of the unit star is obtained; Step 4: The perturbation factors include the Earth's non-spherical perturbation, the gravitational perturbation potential energy of the third body, and the solar radiation pressure perturbation potential energy. Based on the coordinate system of Step 1, the Earth's non-spherical perturbation potential energy, the third gravitational perturbation potential energy, and the solar radiation pressure perturbation potential energy of the system's center of mass and the unit star are obtained. Step 5: Establish the system dynamic equations considering the perturbation factors described in Step 4; Step 6: Substitute the Lagrangian function of the system's centroid obtained in Step 2, the relative Lagrangian function of the unit star obtained in Step 3, and the perturbation factor obtained in Step 4 into the system dynamics equations in Step 5 to establish the complete Lagrangian equations for the tethered satellite system.

2. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, Step 1 is to establish a geocentric coordinate system. The origin is the Earth's center. , The axis points to the vernal equinox in the equatorial plane. The axis is perpendicular to the equatorial plane and aligns with the direction of the Earth's rotational angular velocity. The axis satisfies the right-hand rule; quality is The tethered satellite system, whose orbital coordinate system is Kepler orbit, is... With the system's center of mass as the origin With the Earth's core The distance between them is , Pointing towards the Earth's center, The axis lies in the orbital plane along the velocity direction. The axis is determined by the right-hand rule; The mass of the tethered satellite system is Unit Star The body coordinate system is Set the origin of the orbital coordinate system Translation Obtain the origin of the unit star coordinate system , and then around Rotation get , then go around Rotation get , The axis is determined by the right-hand rule.

3. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, The Lagrangian function of the system's centroid in step 2 is: (2-1) in, Let Lagrangian function be the mass center of the system. The gravitational constant of Earth, The non-spherical perturbation potential energy of the Earth acting on its center of mass. The gravitational perturbation potential energy of the third body acting on the center of mass. Let be the rate of change of the distance from the system's center of mass to the Earth's center. This represents the rate of change of the true anomaly angle of the orbit.

4. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, The relative Lagrange function of the unit star in step 3 is: (2-2) in, The non-spherical perturbation potential energy of Earth acting on a unit star. This refers to the gravitational perturbation potential energy of a third body acting on a monoplanet. For a single star, the Lagrangian function is... The instantaneous rate of change of the distance between the unit star and its center of mass. The rate of change of the first rotation angle of the unit star. This represents the rate of change of the second rotation angle of the unit star.

5. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, In step 4, the non-spherical perturbation potential energy of the system's center of mass and the unit star is expressed as follows: (2-3) in, This is the Earth's oblateness coefficient. For the Earth's radius, The geocentric latitude of the center of mass. The geocentric latitude of the unit star. This represents the distance from the unit star to the Earth's center. The non-spherical perturbation potential energy of the Earth at the system's center of mass. The non-spherical perturbation potential energy of the Earth for a single star; (2-4) in, Let be the angle between the unit star and the line connecting the system's center of mass and the Earth's center, at a small angle. ; The third gravitational perturbation potential energy of the system's center of mass and the unit star is expressed as: (2-5) in, It is the third gravitational constant, determined by the third celestial body. The position of the third celestial body is such that the angle between the line connecting the system's center of mass to the Earth's center and the line connecting the third celestial body to the Earth's center is . , The third gravitational perturbation potential energy is the center of mass of the system. This represents the third gravitational perturbation potential energy of the monoplanet; The solar radiation pressure perturbation potential energy can be expressed as: (2-6) in, For generalized coordinates, the system centroid is and For a single star , and ; Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force, Generalized coordinates The corresponding generalized force.

6. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, The system dynamics equation considering perturbation factors in step 5 is: (2-7) in, Lagrangian functions of the system's centroid, respectively Lagrange function of a single star , This represents the derivative with respect to generalized coordinates, where the centroid of the system is... and For a single star , and .

7. The method for dynamic modeling of a tethered satellite system considering perturbation factors according to claim 1, characterized in that, In step 6, applying the Lagrange equation to the center of mass of the tethered satellite system yields: (2-8) in, The acceleration representing the change in distance between the system's center of mass and the Earth's center. Represents the acceleration due to the change of the true anomaly angle of the orbit; For a single satellite in a tethered satellite system, applying the Lagrange equations, we get: (2-9) in, The acceleration representing the change in distance between the unit star and the system's center of mass. Represents the acceleration due to the change in the first rotation angle of the unit star. This represents the acceleration due to the change in the second rotation angle of the unit star.

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