Method for suppressing out-of-plane chaos of rope-load system induced by periodic perturbation

Abstract

The present invention discloses a method for suppressing the out-of-plane chaos of a rope-load system induced by periodic perturbation, which relates to the field of spacecraft flight technology, and specifically proposes a method for identifying and suppressing the chaos of the out-of-plane rolling motion of the system induced by periodic perturbation excitation for a space rope-load system. First, a periodically changing environmental perturbation factor is introduced, and then the out-of-plane motion dynamics equation of the system is converted into a dimensionless form, and then the unstable equilibrium point and heteroclinic orbit of the system are calculated by the unperturbed Hamiltonian system, and then the Menekov function is used to study whether the system will have a transverse intersection of heteroclinic orbits near the heteroclinic point under periodic excitation, thereby identifying the phenomenon of out-of-plane chaos of the system, and finally the parameters of the space rope-load system are adjusted to avoid the occurrence of chaos.

Description

Technical Field

[0001] The invention relates to the field of spacecraft flight technology, and in particular to a space rope-load system, and proposes a method for identifying chaos caused by the out-of-plane rolling motion of the system induced by periodic perturbation excitation. Background Art

[0002] Due to the strong nonlinear structure of the space tether system itself, there will inevitably be a large number of nonlinear phenomena during its on-orbit flight, such as internal resonance, bifurcation, quasi-periodic motion, chaos, etc. In particular, the chaotic phenomenon has attracted close attention from a large number of scientific researchers. For example, Steiner numerically studied the transient chaotic motion of a type of undisturbed tether-load system in the orbital plane, and pointed out that transient chaotic phenomena may occur when the initial state of the system is near the unstable equilibrium point [1]. Nakanishi et al. discussed the relationship between the chaotic motion of the tether-load system and the orbital eccentricity, and found that as long as the orbital eccentricity is greater than 0.3138, the system's in-plane pitch motion will be chaotic [2]. Kojima et al. simulated the orbital motion and earth gravity of a two-dimensional tether-load system through a rotating platform and a table with an inclination, respectively, and experimentally verified that a large orbital eccentricity will cause chaos in the tether-load system [3]. Pang et al. studied an asymmetric tethered spacecraft rigid body and found that irregular rigid body loads can also cause the system to have in-plane chaotic motion [4]. Aslanov et al. used the Menekov function and Poincare cross section to deeply explore the in-plane chaotic motion of a low-thrust space rope-debris towing system[5,6]. Lian et al. studied an in-plane rope-tethered solar sail system and found that chaotic phenomena would occur when it orbited a highly irregular planet[7].

[0003] Previous studies have shown that orbital eccentricity and irregular rigid bodies can cause chaotic motion in the in-plane rope-load system. However, whether the out-of-plane motion of the rope-load system and periodic perturbation excitation will cause chaotic behavior in the system has never been studied, and whether chaos will be caused cannot be identified.

[0004] [1]Steiner W.Transient chaotic oscillations of a tethered satellitesystem.Acta Mechanica,1998,127(1-4):155-163.

[0005] [2]Nakanishi K.,Fujii H.A.Periodic motion of multi-compound-tethersatellite system.Proceedings of 56th International Astronautical Congress ofthe International Astronautical Federation,the International Academy ofAstronautics,and the International Institute of Space Law,Fukuoka,Japan,2005.

[0006] [3]Kojima H.,Furukawa Y.,Trivailo P.M.Experimental verification ofperiodic libration of tethered satellite system in elliptic orbit.Journal ofGuidance,Control,and Dynamics,2011, 34(2):614-618.

[0007] [4]Pang Z.J.,Yu B.S.,Jin D.P.Chaotic motion analysis of a rigidspacecraft dragging a satellite by elastic tether.Acta Mechanica,2015,226(8):2761-2771.

[0008] [5]Aslanov V.S.Chaos behavior of space debris during tetheredtow.Journal of Guidance,Control,and Dynamics,2016,39(10):1-7.

[0009] [6]Aslanov VS, Misra AK, Yudintsev VVChaotic attitude motion of alow-thrust tug-debris tethered system in a Keplerian orbit. Acta Astronautica, 2017, 139(1): 419-427.

[0010] [7] Lian XB, Liu JF, Zhang JX, Wang C. Chaotic motion and control of a tethered-sailcraft system orbiting an asteroid. Communications in NonlinearScience and Numerical Simulation, 2019,77(1):203-224. Summary of the invention

[0011] The technical problem to be solved by the present invention is to construct an identification method for the external rope-load system under periodic perturbation excitation. By studying whether the cross-sectional intersection of heteroclinic orbits will occur near the unstable equilibrium point of the system, it is possible to identify whether such excitation will cause the system to produce out-of-plane chaotic motion, effectively predict the occurrence of chaos, and avoid the damage of periodic perturbation excitation to the external rope-load system.

[0012] In order to solve the above technical problems, the present invention proposes a method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation, which comprises the following steps:

[0013] Step 1: Study the space rope-load system composed of the main load, sub-load and the connecting adiabatic tether. Based on the second-kind Lagrangian equation, establish the rope-load system dynamics model, form the system out-of-plane motion dynamics equation, and describe the out-of-plane motion of the space rope-load system with a constant in-plane pitch angle.

[0014] Step 2: Introduce the periodically changing environmental perturbation factor and transform the system's out-of-plane motion dynamics equation into a dimensionless form to complete the construction of the external rolling rope-load model under periodic perturbation excitation.

[0015] Step 3: Calculate the unstable equilibrium point and heteroclinic orbit of the system by the undisturbed Hamiltonian system, and then use the Menekov function to study whether the system will have a transverse intersection of heteroclinic orbits near the heteroclinic point under periodic excitation, so as to provide an identification method for the system's out-of-plane chaos.

[0016] Step 4: Adjust the parameters of the space rope-load system to avoid the occurrence of chaos.

[0017] like Figure 1 As shown, the space rope-load system in step 1 is set as:

[0018] The main load and sub-load are both cylinders with masses m M and m S ; Considering that the tether is always in a taut state during the state-keeping phase, the simplified linear density is ρ t , length l, diameter d t The rigid rod has its two ends extended and the axes of the two load cylinders coincident; assuming that the earth is a homogeneous sphere, the center of mass o of the system is located at a height of H o The circular orbit around the earth is ν, the true anomaly angle around the earth is ν, and the angle between the orbital plane and the equatorial plane is i; the motion of the system in the orbital plane Π and the non-orbital plane Σ can be expressed by the in-plane pitch angle θ and the out-plane roll angle φ respectively; a control force orthogonal to the plane Σ is applied to keep the system at a constant in-plane pitch angle to study the out-of-plane roll motion of the system; an orbital coordinate system o-xyz fixed to the system's center of mass o is constructed, with its x-axis pointing to the direction of system motion, the y-axis orthogonal to the orbital plane, and the z-axis pointing to the earth's center of mass.

[0019] In step 1, based on the second kind of Lagrangian equation, the rope-load system dynamics model is established to form the system out-of-plane motion dynamics equation. The specific process is:

[0020] First, the kinetic energy generated by the rotation of the system's center of mass around the earth and itself can be expressed as

[0021]

[0022] In the formula, the symbol ' represents the derivative of the variable with respect to time t, R o The scalar indicating the distance of the system's center of mass from the Earth's center of mass, m t =ρ t l is the mass of the tether, and To derive the mass parameters; at the same time, taking infinity as the potential energy zero point, the system potential energy expression can be listed:

[0023]

[0024] Here, μ E represents the earth's gravitational parameters;

[0025] Select the out-of-plane rolling angle φ as the generalized coordinate and transform the system kinetic energy T = T t +T r Substituting the potential energy expression (2) into the second kind Laplace equation, we can obtain

[0026]

[0027] In the formula, Q φ represents the generalized force corresponding to the out-of-plane roll angle φ; the following dimensionless transformation is introduced

[0028]

[0029] Here, the true anomaly ν is chosen as the dimensionless time, L r represents the reference length. The system dynamics equation (3) can be transformed into the following dimensionless form:

[0030]

[0031] The dynamic model of the system constructed above can describe the out-of-plane motion of the system with a constant in-plane pitch angle.

[0032] The specific process of step 2 is:

[0033] The perturbation effects of atmospheric damping and solar pressure on the out-of-plane motion of the system are investigated to obtain the generalized force Q corresponding to the out-of-plane roll angle caused by them. φ , which is the perturbation torque. Introducing the virtual work equation

[0034]

[0035] The virtual displacement of the tether segment ds caused by the virtual external rolling angle δφ can be expressed as

[0036] δd φ (s)=(-sinθsinφe x -cosφe y -cosθsinφe z )(s-χ l )·δφ (7)

[0037] In the formula, e x 、e y 、e z They represent the unit vectors of the x, y, and z axes respectively. s represents a local length coordinate measuring the subload pointing to the main load. The parameters is the out-of-plane perturbation force acting on the tether microelement segment ds;

[0038] The atmospheric damping acting on the main load rigid body, sub-load rigid body and tether infinitesimal segment ds can be written as

[0039]

[0040] In the formula, C d,M , C d,S , C d,trepresents the atmospheric damping coefficient of the main load rigid body, sub-load rigid body and tether, ρ a,M , a,S , a,t represents the atmospheric density at the orbital altitude of the main load rigid body, sub-load rigid body and tether, A represents the relative velocity of the system relative to the atmosphere in the direction of the out-of-plane roll angle. M and A S Represents the windward area of ​​the main load rigid body and the sub-load rigid body; taking into account the relative velocity vector The unit vector e with respect to the coordinate axis of the orbital coordinate system x 、e z Always keep orthogonal, substitute equation (8) into the virtual work equation (6), and we can get the generalized force of atmospheric damping acting on the main load rigid body, sub-load rigid body and tether in the direction of out-of-plane roll angle φ:

[0041]

[0042] in

[0043]

[0044] Therefore, the generalized force corresponding to the out-of-plane roll angle caused by atmospheric damping is for

[0045]

[0046] In addition, the solar pressure acting on the main load rigid body, sub-load rigid body and tether microelement segment ds can be expressed as

[0047]

[0048] Among them, I s =1372w·m -2 represents the incident radiation energy flux density of the sun on the earth's surface, v lc represents the speed of light, β is the angle between the sun's rays and the main load rigid body, sub-load rigid body, and tether axis, C sr and C dr represents the specular reflection coefficient and diffuse reflection coefficient of the main load rigid body, sub-load rigid body, and tether. n and u t represents the unit vector of the surface normal and light projection direction of the main load rigid body, sub-load rigid body, and tether; similarly, substituting equation (12) into the virtual work equation (6) yields the generalized force of the sunlight pressure acting on the main load rigid body, sub-load rigid body, and tether in the direction of the out-of-plane roll angle φ:

[0049]

[0050] Therefore, the generalized force corresponding to the out-of-plane roll angle caused by the solar pressure is for

[0051] Substituting expressions (11) and (14) into the system generalized force expression The dimensionless dynamics equation (5) of the system can be further written as

[0052]

[0053] In the formula

[0054]

[0055] So far, the construction of the external rolling rope-load model under periodic perturbation excitation has been completed.

[0056] The specific process of step 3 is:

[0057] make The dimensionless dynamics equation (15) of the system can be rewritten into the following state equation form:

[0058]

[0059] The specific expressions of the vector field and perturbation term are:

[0060]

[0061] It can be seen that the period of the perturbation term g(φ,ν) is P=π, that is, g(φ,ν)=g(φ,ν+π); when the system does not consider the perturbation factor, that is, g(φ,ν)=0, it is a Hamiltonian system, and it can be calculated that the system has an unstable equilibrium point and heteroclinic orbits

[0062]

[0063] Substitute the above heteroclinic trajectory into the following Menekov function

[0064]

[0065] Then in the periodic dimensionless time ν0∈[0,P], we have

[0066]

[0067] When the following conditions are met

[0068]

[0069] The Menekov function has simple zeros. At this time, the stable manifold and the unstable manifold of the system intersect crosswise near the heteroclinic point, which will produce chaotic phenomena.

[0070] In step 4, the parameter adjustment of the space tether-load system includes adjusting at least one parameter of the in-plane pitch angle, main load mass, sub-load mass, tether length, orbit height or orbit inclination so that it does not satisfy the establishment condition of equation 22, thereby avoiding the occurrence of chaos.

[0071] Based on the chaos discriminant (22), the present invention can identify the out-of-plane chaotic motion of the rope-load system induced by periodic perturbation excitation.

[0072] In order to verify the effectiveness of the present invention, the following system parameters are taken for numerical simulation to verify the correctness of the chaos identification method proposed in the present invention. The masses of the main load rigid body and the sub-load rigid body are m M =50kg and m S =10kg, the density, length and diameter of the tether are ρ t =5×10 -3 kg / m, l = 1km, d t =0.5×10 -3 m. The atmospheric damping coefficients of the main load rigid body, sub-load rigid body, and tether are all C d,M(S)(t) =2.2, the windward areas of the main load rigid body and the sub-load rigid body are A M =1.0m 2 and A S =0.3m 2 The specular reflection coefficient and diffuse reflection coefficient of the main load rigid body, sub-load rigid body and tether surface are C sr =0.8 and C dr =0.2.

[0073] Based on the above parameters, according to the chaos discriminant (22), we can first obtain the system parameters (θ,i,H o ) of the chaotic domain, such as Figure 2 shown. Figure 2 (a) is the global chaotic domain. As long as the system parameters are within this chaotic domain, chaos may occur. Figure 2 (b) shows the influence of the in-plane pitch angle θ on the chaotic domain. It can be seen that the larger the in-plane pitch angle, the smaller the chaotic domain. Figure 2 (c) is the orbit height H o From the impact on the chaotic domain, it can be seen that the higher the center of mass orbit height, the larger the chaotic domain. Figure 2 (d) shows the influence of orbital inclination i on the chaotic domain. It can be seen that the larger the orbital inclination, the smaller the chaotic domain.

[0074] Now, let the system's in-plane pitch angle, orbit inclination, and orbit altitude be θ = π / 4, i = π / 8, and H o= 350 km for dynamic simulation. At this time, the system parameters satisfy the chaos discriminant (22), that is, |γ / 2| = 1.1321×10 -6 <2.8554×10 -6 The system's orbital out-of-plane rolling chaotic motion is as follows Figure 3 shown. Figure 3 (a) Represents the irregular motion of the system’s out-of-plane roll angle. Figure 3 (b) is the Poincare section of the out-of-plane rolling motion. It can be clearly seen that there are a large number of heteroclinic points near the unstable equilibrium point, so the system undergoes chaotic motion at this time. Figure 3 (c) is the power spectral density of the system, which has a dense power spectrum in the range of (0, 0.25 Hz). Figure 3 (d) is the dimensionless time history of the system’s maximum Lyapunov exponent, which is always greater than 0 as the dimensionless time changes. Figure 3 The results of (c) and 3(d) further verify that the system does have chaotic motion. Therefore, the numerical simulation results shown in Figure 3 verify the correctness of the chaos identification method proposed in the present invention.

[0075] Keep the parameters unchanged and only change the orbit height of the system's center of mass to H o = 250 km, the system parameters no longer satisfy the chaos discriminant (22), that is, |γ / 2| = 9.1034×10 -6 >6.4413×10 -6 At this time, the system's out-of-plane quasi-periodic motion is as follows Figure 4 As shown. Figure 4 In (a), the out-of-plane roll angle of the system varies periodically. Figure 4 (b) is the Poincare section of the out-of-plane rolling motion. This closed orbit line shows that the system is in quasi-periodic motion. Figure 4 (c) is the power spectrum density of the system. Several isolated peaks further verify that this is a quasi-periodic motion. Figure 4 (d) is the dimensionless time history of the maximum Lyapunov exponent of the system, which eventually tends to 0 with dimensionless time change, also indicating the quasi-periodic motion of the system. At this time, chaotic motion no longer occurs, which is consistent with the identification result of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 is a schematic diagram of the rope-load system of the present invention with out-of-plane rolling;

[0077] Figure 2 is the system parameter (θ,i,H o )'s chaotic domain;

[0078] Figure 3 It is the rolling chaotic motion outside the orbital plane of the system in the present invention;

[0079] Figure 4 It is a nearly periodic motion outside the orbital plane of the present invention. DETAILED DESCRIPTION

[0080] The present invention is further described clearly and completely below in conjunction with specific embodiments and drawings. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0081] The space rope-load system consisting of the main load M, the sub-load S and the connecting adiabatic tether is studied. Figure 1 As shown. Both the main load and the sub-load are cylinders with masses m M and m S Considering that the tether is always in a taut state during the state-holding stage, the linear density is simplified to ρ t , length l, diameter d t The rigid rod has its two ends extended to coincide with the axes of the two load cylinders. Assume that the earth is a homogeneous sphere and the center of mass o of the system is located at a height of H above the ground. o is a circular orbit around the Earth, ν is the true anomaly angle around the Earth, and the angle between the orbital plane and the equatorial plane is i. The motion of the system in the orbital plane Π and the non-orbital plane Σ can be expressed by the in-plane pitch angle θ and the out-plane roll angle φ, respectively. A control force orthogonal to the plane Σ is applied to keep the system at a constant in-plane pitch angle to study the out-of-plane roll motion of the system. An orbital coordinate system o-xyz fixed to the system's center of mass o is constructed, with its x-axis pointing in the direction of system motion, the y-axis orthogonal to the orbital plane, and the z-axis pointing to the Earth's center of mass.

[0082] Based on the second kind of Lagrange equation, the dynamic model of the rope-load system is established. First, the kinetic energy generated by the rotation of the system center of mass around the ground and itself can be expressed as

[0083]

[0084] In the formula, the symbol ' represents the derivative of the variable with respect to time t, R o The distance between the center of mass of the system and the center of mass of the earth, m t =ρ t l is the mass of the tether, and To derive the mass parameters. At the same time, taking infinity as the potential energy zero point, the system potential energy expression can be listed

[0085]

[0086] Here, μ E Represents the Earth's gravitational parameters.

[0087] Select the out-of-plane rolling angle φ as the generalized coordinate and transform the system kinetic energy T = T t +Tr Substituting the potential energy expression (2) into the second kind Laplace equation, we can obtain

[0088]

[0089] In the formula, Q φ represents the generalized force corresponding to the out-of-plane roll angle φ. The following dimensionless transformation is introduced:

[0090]

[0091] Here, the true anomaly ν is chosen as the dimensionless time, L r represents the reference length. The system dynamics equation (3) can be transformed into the following dimensionless form:

[0092]

[0093] The dynamic model of the system constructed above can describe the out-of-plane motion of the system with a constant in-plane pitch angle.

[0094] The perturbation effects of atmospheric damping and solar pressure on the out-of-plane motion of the system are investigated to obtain the generalized force Q corresponding to the out-of-plane roll angle caused by them. φ , which is the perturbation torque. Introducing the virtual work equation

[0095]

[0096] The virtual displacement of the tether segment ds caused by the virtual external rolling angle δφ can be expressed as

[0097] δd φ (s)=(-sinθsinφe x -cosφe y -cosθsinφe z )(s-χ l )·δφ (7)

[0098] In the formula, e x 、e y 、e z They represent the unit vectors of the x, y, and z axes respectively. s represents a local length coordinate measuring the subload pointing to the main load. The parameters is the out-of-plane perturbation force acting on the tether segment ds.

[0099] The atmospheric damping acting on the main load rigid body, sub-load rigid body and tether infinitesimal segment ds can be written as

[0100]

[0101] In the formula, C d,M , C d,S , Cd,t represents the atmospheric damping coefficient of the main load rigid body, sub-load rigid body and tether, ρ a,M , a,S , a,t represents the atmospheric density at the orbital altitude of the main load rigid body, sub-load rigid body and tether, A represents the relative velocity of the system relative to the atmosphere in the direction of the out-of-plane roll angle. M and A S Represents the windward area of ​​the main load rigid body and the sub-load rigid body. Considering the relative velocity vector The unit vector e with respect to the coordinate axis of the orbital coordinate system x 、e z Always keep orthogonal, substitute equation (8) into the virtual work equation (6), and we can get the generalized force of atmospheric damping acting on the main load rigid body, sub-load rigid body and tether in the direction of out-of-plane roll angle φ:

[0102]

[0103] in

[0104]

[0105] Therefore, the generalized force corresponding to the out-of-plane roll angle caused by atmospheric damping is for

[0106]

[0107] In addition, the solar pressure acting on the main load rigid body, sub-load rigid body and tether microelement segment ds can be expressed as

[0108]

[0109] Among them, I s =1372w·m -2 represents the incident radiation energy flux density of the sun on the earth's surface, v lc represents the speed of light, β is the angle between the sun's rays and the main load rigid body, sub-load rigid body, and tether axis, C sr and C dr represents the specular reflection coefficient and diffuse reflection coefficient of the main load rigid body, sub-load rigid body, and tether. n and u t Represents the unit vector of the surface normal and light projection direction of the main load rigid body, sub-load rigid body, and tether. Similarly, substituting equation (12) into the virtual work equation (6) yields the generalized force of the sunlight pressure acting on the main load rigid body, sub-load rigid body, and tether in the direction of the out-of-plane roll angle φ:

[0110]

[0111] Therefore, the generalized force corresponding to the out-of-plane roll angle caused by the solar pressure is for

[0112] Substituting expressions (11) and (14) into the system generalized force expression The dimensionless dynamics equation (5) of the system can be further written as

[0113]

[0114] In the formula

[0115]

[0116] So far, the construction of the external rolling rope-load model under periodic perturbation excitation has been completed. Obviously, this is a two-dimensional non-autonomous nonlinear system.

[0117] make The dimensionless dynamics equation (15) of the system can be rewritten into the following state equation form:

[0118]

[0119] The specific expressions of the vector field and perturbation term are:

[0120]

[0121] It is not difficult to see that the period of the perturbation term g(φ,ν) is P=π, that is, g(φ,ν)=g(φν+π). It is worth noting that when the system does not consider the perturbation factor, that is, g(φ,ν)=0, it is a Hamiltonian system, and it can be calculated that the system has an unstable equilibrium point and heteroclinic orbits

[0122]

[0123] Substitute the above heteroclinic trajectory into the following Menekov function

[0124]

[0125] Then in the periodic dimensionless time ν0∈[0,P], we have

[0126]

[0127] When the following conditions are met

[0128]

[0129] The Menekov function has simple zeros. At this time, the stable manifold and the unstable manifold of the system intersect crosswise near the heteroclinic point, which will produce chaotic phenomena.

[0130] Parameter adjustment of the space tether-load system includes adjusting at least one parameter of the in-plane pitch angle, main load mass, sub-load mass, tether length, orbit height or orbit inclination, so that it does not satisfy the establishment condition of equation 22, thereby avoiding the occurrence of chaos.

[0131] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation, characterized in that The following steps are involved: Step 1: Study the space rope-load system composed of the main load, sub-load and the connecting adiabatic tether. Based on the second kind of Lagrangian equation, establish the rope-load system dynamics model, form the system out-of-plane motion dynamics equation, and describe the out-of-plane motion of the space rope-load system with a constant in-plane pitch angle; The space rope-load system is set as follows: the main load and the sub-load are both cylinders with masses m M and m S ; Considering that the tether is always in a taut state during the state-keeping phase, the simplified linear density is ρ t , length l, diameter d t The rigid rod has its two ends extended and the axes of the two load cylinders coincident; assuming that the earth is a homogeneous sphere, the center of mass o of the system is located at a height of H o The circular orbit around the earth is ν, the true anomaly around the earth is i, and the angle between the orbital plane and the equatorial plane is i; the motion of the system in the orbital plane Π and the non-orbital plane Σ can be expressed by the in-plane pitch angle θ and the out-plane roll angle φ respectively; a control force orthogonal to the plane Σ is applied to keep the system at a constant in-plane pitch angle to study the out-of-plane roll motion of the system; an orbital coordinate system o-xyz fixed to the center of mass o of the system is constructed, with its x-axis pointing to the direction of system motion, the y-axis orthogonal to the orbital plane, and the z-axis pointing to the center of mass of the earth; Step 2: Introduce the periodic environmental perturbation factor and transform the system's out-of-plane motion dynamics equation into a dimensionless form to complete the construction of the external rolling rope-load model under periodic perturbation excitation; Step 3: Calculate the unstable equilibrium point and heteroclinic orbit of the system by the unperturbed Hamiltonian system, and then use the Menekov function to study whether the system will have a transverse intersection of heteroclinic orbits near the heteroclinic point under periodic excitation, so as to provide an identification method for the system's out-of-plane chaos; Step 4: Adjust the parameters of the space rope-load system to avoid the occurrence of chaos.

2. The method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation according to claim 1, characterized in that: In step 1, based on the second kind of Lagrangian equation, the rope-load system dynamics model is established to form the system out-of-plane motion dynamics equation. The specific process is: First, the kinetic energy generated by the rotation of the system's center of mass around the earth and itself can be expressed as In the formula, the symbol ' represents the derivative of the variable with respect to time t, R o The scalar indicating the distance of the system's center of mass from the Earth's center of mass, m t =ρ t l is the mass of the tether, and To derive the mass parameters; at the same time, taking infinity as the potential energy zero point, the system potential energy expression can be listed: Here, μ E represents the earth's gravitational parameters; Select the out-of-plane rolling angle φ as the generalized coordinate and transform the system kinetic energy T = T t +T r Substituting the potential energy expression (2) into the second kind Laplace equation, we can obtain In the formula, Q φ represents the generalized force corresponding to the out-of-plane roll angle φ; Introduce the following dimensionless transformation Here, the true anomaly ν is chosen as the dimensionless time, L r represents the reference length; the system dynamics equation (3) can be transformed into the following dimensionless form The dynamic model of the system constructed above can describe the out-of-plane motion of the system with a constant in-plane pitch angle.

3. The method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation according to claim 2, characterized in that: The specific process of step 2 is: The perturbation effects of atmospheric damping and solar pressure on the out-of-plane motion of the system are investigated to obtain the generalized force Q corresponding to the out-of-plane roll angle caused by them. φ , that is, the perturbation torque; introduce the virtual work equation The virtual displacement of the tether segment ds caused by the virtual external rolling angle δφ can be expressed as δd φ (s)=(-sinθsinφe x -cosφe y -cosθsinφe z )(s-χl)·δφ (7) In the formula, e x 、e y 、e z They represent the unit vectors of the x, y, and z axes respectively. s represents a local length coordinate measuring the subload pointing to the main load. The parameters is the out-of-plane perturbation force acting on the tether microelement segment ds; The atmospheric damping acting on the main load rigid body, sub-load rigid body and tether infinitesimal segment ds can be written as In the formula, C d,M , C d,S , C d,t represents the atmospheric damping coefficient of the main load rigid body, sub-load rigid body and tether, ρ a,M , a,S , a,t represents the atmospheric density at the orbital altitude of the main load rigid body, sub-load rigid body and tether, A represents the relative velocity of the system relative to the atmosphere in the direction of the out-of-plane roll angle. M and A S Represents the windward area of ​​the main load rigid body and the sub-load rigid body; taking into account the relative velocity vector The unit vector e with respect to the coordinate axis of the orbital coordinate system x 、e z Always keep orthogonal, substitute equation (8) into the virtual work equation (6), and we can get the generalized force of atmospheric damping acting on the main load rigid body, sub-load rigid body and tether in the direction of out-of-plane roll angle φ: in Therefore, the generalized force corresponding to the out-of-plane roll angle caused by atmospheric damping is for In addition, the solar pressure acting on the main load rigid body, sub-load rigid body and tether microelement segment ds can be expressed as Among them, I s =1372w·m -2 represents the incident radiation energy flux density of the sun on the earth's surface, v lc represents the speed of light, β is the angle between the sun's rays and the main load rigid body, sub-load rigid body, and tether axis, C sr and C dr represents the specular reflection coefficient and diffuse reflection coefficient of the main load rigid body, sub-load rigid body, and tether. n and u t represents the unit vector of the surface normal and light projection direction of the main load rigid body, sub-load rigid body, and tether; similarly, substituting equation (12) into the virtual work equation (6) yields the generalized force of the sunlight pressure acting on the main load rigid body, sub-load rigid body, and tether in the direction of the out-of-plane roll angle φ: Therefore, the generalized force corresponding to the out-of-plane roll angle caused by the solar pressure is for Substituting expressions (11) and (14) into the system generalized force expression The dimensionless dynamics equation (5) of the system can be further written as In the formula So far, the construction of the external rolling rope-load model under periodic perturbation excitation has been completed.

4. The method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation according to claim 3 is characterized in that: The specific process of step 3 is: make The dimensionless dynamics equation (15) of the system can be rewritten into the following state equation form: The specific expressions of the vector field and perturbation term are: It can be seen that the period of the perturbation term g(φ,ν) is P=π, that is, g(φ,ν)=g(φ,ν+π); when the system does not consider the perturbation factor, that is, g(φ,ν)=0, it is a Hamiltonian system, and it can be calculated that the system has an unstable equilibrium point and heteroclinic orbits Substitute the above heteroclinic trajectory into the following Menekov function Then in the periodic dimensionless time ν0∈[0,P], we have When the following conditions are met The Menekov function has simple zeros. At this time, the stable manifold and the unstable manifold of the system intersect crosswise near the heteroclinic point, which will produce chaotic phenomena.

5. The method for suppressing out-of-plane chaos of a rope-load system induced by periodic perturbation according to claim 4, characterized in that: The step 4 adjusts the parameters of the space tether-load system, including adjusting at least one parameter of the in-plane pitch angle, main load mass, sub-load mass, tether length, orbit height or orbit inclination, so that it does not satisfy the establishment condition of equation 22, thereby avoiding the occurrence of chaos.

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