Quaternion-based spatial rotation tether system dynamics modeling method

Abstract

The invention discloses a quaternion-based dynamic modeling method for a spatial rotation tether system, and the method comprises the steps: introducing a quaternion to replace a conventional Euler angle, and enabling the quaternion to be used for representing a conversion relation between coordinate systems; on the basis of dumbbell rod hypothesis, the whole space rotation tether system is regarded as a rigid body, and a corresponding constraint equation is provided; the quaternion is used for describing the motion characteristics of the spatial rotation tether system to replace a traditional in-plane angle and a traditional out-of-plane angle; deriving an incomplete constraint Lagrange equation in a quaternion form on the basis of the quaternion; solving a quaternion-based spatial rotation tether system dynamic model, and completing modeling; according to the method, the singular point problem in a traditional Lagrange model is effectively avoided, model basis and reference are provided for researching on-orbit three-dimensional motion of the space rotation tether system, and the method is already applied to mathematical simulation verification of the space rotation tether system.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft, and in particular relates to a quaternion-based dynamic modeling method for a space rotating tether system. Background Art

[0002] The space rotating tether system is a space combination vehicle that connects two spacecraft together through a tether to jointly complete on-orbit flight missions. The system can be applied to various space missions such as payload jettisoning and capture missions, earth observation missions, and artificial gravity. Therefore, it has attracted widespread attention and research, showing a very broad development prospect. Scholars have proposed a variety of dynamic models for the application of space rotating tether systems in different scenarios. For example, the Chinese patent with application number CN202110161862.2 proposes a modeling method for a bare electric power rope system based on the absolute node coordinate method for the bending and large deformation scenarios of flexible tethers; and the Chinese patent with application number 202310957524.9 proposes a modeling method for a space tether system in a restricted three-body problem for deep space exploration based on a restricted three-body scenario based on the L1 libration point.

[0003] However, there are few inventions of modeling methods for the three-dimensional motion of a space rotating tether system. Traditional modeling methods based on in-plane angles and out-of-plane angles will produce singularity problems, so they are not suitable for studying the three-dimensional motion of a space rotating tether system. In the paper "Angular velocity observer for space tetherexploiting non-singular dynamics and vector measurements" in the journal Nonlinear Dynamics, based on the tether dumbbell bar assumption, angular velocity is used instead of the traditional in-plane angles and out-of-plane angles to derive the six-degree-of-freedom dynamic equations of the space rotating tether system, thereby avoiding the singularity problem; in the paper "Saturated Control of Space Tether System for Maneuvering Between ArbitrarySpinning Orientations" in the journal Journal of Guidance Control and Dynamics, based on the bead-point tether assumption, a new non-inertial coordinate system is used to cleverly set the singularity at a position that the space rotating tether system cannot reach. These modeling methods provide effective technical solutions for the three-dimensional motion of a space rotating tether system. However, since the quaternion expression can fully express the rotation operation in three dimensions, it not only avoids the singularity problem of Euler angles, but also reduces the complex calculation of the rotation matrix. Therefore, using quaternions to model the dynamics of the space rotation tether system is a better modeling method. However, there are few dynamics modeling methods for the space rotation tether system based on quaternions in the existing technology. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a quaternion-based dynamic modeling method for a space rotation tether system, introduces quaternions to replace traditional Euler angles, and is used to represent the conversion relationship between coordinate systems; based on the dumbbell bar hypothesis, the space rotation tether system is regarded as a rigid body as a whole, and the corresponding constraint equations are proposed; and quaternions are used to describe the motion characteristics of the space rotation tether system, replacing the traditional in-plane angles and out-of-plane angles; based on quaternions, the Lagrange equations of non-holonomic constraints in quaternion form are derived; the dynamic model of the space rotation tether system based on quaternions is solved to complete the modeling; the method of the present invention effectively avoids the singularity problem in the traditional Lagrangian model, provides a model basis and reference for studying the on-orbit three-dimensional motion of the space rotation tether system, and has been applied to the mathematical simulation verification of the space rotation tether system.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] Step 1: Introduce quaternions instead of Euler angles to represent the conversion relationship between coordinate systems;

[0007] Based on the space rotating tether system, the geocentric orbital coordinate system OXYZ and the geocentric orbital motion coordinate system OX are established. o Y o Z o , orbital motion coordinate system Cx0y0z0, tether coordinate system Cx t y t z t , end-body satellite tether coordinate system Kx t y t z t ;

[0008] The transformation relationship between these coordinate systems is as follows:

[0009] The transformation quaternion Q from the geocentric orbital coordinate system OXYZ to the orbital motion coordinate system Cx0y0z0 D :

[0010]

[0011] Where f is the true anomaly of the space rotating tether system, and Represents the three imaginary units in quaternions;

[0012] From the orbital motion coordinate system Cx0y0z0 to the tether coordinate system Cx t y t z t The transformation quaternion Q T :

[0013]

[0014] Among them, β represents the out-of-plane angle of the space rotating tether system, and θ represents the in-plane angle of the space rotating tether system;

[0015] From orbital motion coordinate system Cx0y0z0 to end-body satellite tether coordinate system Kx t y t z t Transformation quaternion

[0016]

[0017] in, Represents a transformation quaternion The four components of represents the torsion angle of the formal system of rotating tethers in space;

[0018] The direct conversion relationship between quaternion and Euler angle is:

[0019]

[0020] From the geocentric orbital coordinate system OXYZ to the end-body satellite tether coordinate system Kx t y t z t The transformed quaternion is Q:

[0021]

[0022] From the geocentric orbital coordinate system OXYZ to the end-body satellite tether coordinate system Kx t y t z t The rotation matrix L q The quaternion Q is expressed in the form of:

[0023]

[0024] Step 2: Based on the dumbbell bar hypothesis, the spatial rotating tether system is regarded as a rigid body and the corresponding constraint equations are proposed;

[0025] The spatial rotating tether system is considered as a rigid body, and the dumbbell bar hypothesis is proposed as follows:

[0026] Assumption 1: The quaternions used are all unit quaternions, that is, the modulus of the quaternion is the unit modulus;

[0027] Assumption 2: The tether is regarded as a rigid rod with uniform density, and the flexibility, torsion and elastic properties of the tether are ignored;

[0028] Assumption 3: Since the size of the two satellites is much smaller than the length of the tether, the two satellites are simplified to mass points;

[0029] Assumption 4: The space tether system is only affected by the earth's gravity, active control thrust and uncertain disturbances, and J2 perturbation, atmospheric drag, solar pressure and other celestial gravitational effects are ignored;

[0030] Based on the dumbbell bar assumption, two constraints are proposed:

[0031] Constraint 1: Select quaternion Q = [q0, q1, q2, q3] T Satisfy the unit constraint:

[0032]

[0033] Constraint 2: Ignore the torsion characteristics of the tether, so the torsion angular velocity of the tether is 0:

[0034]

[0035] Constraints (7) and (8) can be written as constraint equations as follows:

[0036]

[0037] Among them, the matrix Σ is the constraint matrix, r is the orbit vector length when the center of mass of the space tether system is running on the orbit; l is the length of the released tether;

[0038] Step 3: Use quaternions to describe the motion characteristics of the space rotation tether system, replacing the in-plane angle and out-of-plane angle;

[0039] The quaternion, rope length, semi-major axis and true anomaly angle are used to describe the center of mass position and rotation state of the space tether system. The generalized coordinate P is shown in formula (10):

[0040] P=[r,f,l,q0,q1,q2,q3] T (10)

[0041] Step 4: Derive the Lagrange equation of nonholonomic constraints in quaternion form based on quaternions;

[0042] The generalized force is a pair of equal and opposite control input thrusts F and -F applied at the center of mass A of the parent star and the center of mass B of the daughter star, F = [0, F y ,F z ] T , its quaternion form is:

[0043]

[0044] Among them, S represents the quaternion The conversion matrix M is the conversion matrix of the derivative to angular velocity. sum It represents the thrust torque generated by the control input thrusts F and -F of equal magnitude and opposite direction;

[0045] The total kinetic energy T of the space rotating tether system tot is the kinetic energy T of the center of mass of the space tether system in orbit C , the kinetic energy of the space tether system relative to the center of mass T r The sum of , its quaternion form is:

[0046]

[0047] Among them, m A represents the mass of the parent star A in the space rotating tether system, m B represents the mass of neutron star B in the space rotating tether system, m t represents the mass of the tether in the space rotating tether system, and m represents the total mass of the space rotating tether system, that is, m = mA +m B +m t ; Equivalent mass m of the space tether system rotation * :

[0048]

[0049] The potential energy in quaternion form is:

[0050]

[0051] Among them, μ is the gravitational constant;

[0052] Subtracting the kinetic energy from the potential energy, we get the Lagrange function:

[0053]

[0054] Step 5: Solve the quaternion-based dynamic model;

[0055] The specific form of the Lagrange equation with nonholonomic constraints is as follows:

[0056]

[0057] Where λ is the Lagrange multiplier matrix; τ is the generalized force corresponding to the generalized coordinate P in the quaternion dynamics model of the space rotation tether system;

[0058] The matrix γ is used to eliminate the Lagrange multiplier terms:

[0059]

[0060] γ satisfies the following conditions:

[0061]

[0062] The specific form of the Lagrange equation that eliminates the nonholonomic constraints of the Lagrange multiplier term is as follows:

[0063]

[0064] Step 6: Solve the dynamic model of the spatial rotation tether system based on quaternion and complete the modeling;

[0065] Substituting formula (11)-formula (14) into the Lagrange equation (18) with the nonholonomic constraints of the Lagrange multiplier term eliminated, after simplification, the dynamic model of the spatial rotation tether system based on quaternion is obtained as follows:

[0066]

[0067]

[0068] u=[0,0,-F z l,F y l] T

[0069] J(q)|=-1

[0070]

[0071] The beneficial effects of the present invention are as follows:

[0072] The present invention can fully express the rotation operation in three dimensions, which not only avoids the singularity problem of Euler angles, but also reduces the complex calculation of the rotation matrix. The present invention provides a model basis and reference for studying various problems of on-orbit three-dimensional motion of space rotating tether systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 The figure is a flow chart of the method of the present invention.

[0074] Figure 2 These are the geocentric orbital coordinate system, the orbital motion coordinate system and the orbital motion coordinate system of the embodiments of the present invention.

[0075] Figure 3 This is the orbital motion coordinate system and the tether coordinate system of the embodiment of the present invention.

[0076] Figure 4 It is the tether coordinate system of the embodiment of the present invention and the tether coordinate system of the end-body satellite.

[0077] Figure 5 This is the coordinate system transformation relationship under the assumption of the dumbbell bar model in the embodiment of the present invention.

[0078] Figure 6 This is a quaternion change curve from state 1 to state 3 under uncontrolled conditions in an embodiment of the present invention.

[0079] Figure 7 1 is a trajectory diagram of a quaternion and a determinant |J(q)| with an out-of-plane angle of 90° in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0081] like Figure 1 Shown is a flow chart of the method of the present invention.

[0082] like Figure 2As shown, the geocentric orbital coordinate system OXYZ is established, with its origin O located at the center of the earth, the OX axis pointing to the orbital perigee, the OZ axis along the direction of the orbital momentum torque vector, and the OY axis is determined according to the right-hand rule; establish the geocentric orbital motion coordinate system OX o Y o Z o , with its origin O at the center of the earth, OX o The axis is along the radial direction of the center of mass of the space tether system, OZ o The direction of the momentum moment vector along the axis of orbit, OY o The axis is determined according to the right-hand rule, and f is the true anomaly angle corresponding to the center of mass of the system; Figure 3 As shown, the orbital motion coordinate system Cx0y0z0 is established, with its origin C located at the center of mass of the space tether system, and the coordinate axes are related to the coordinate system OX o Y o Z o The axes of the tether are parallel; establish the tether coordinate system Cx t y t z t , whose origin C is located at the center of mass of the space tether system, Cx t The direction of the axis is along the tether axis and points to the parent star. t Axis, Cz t The position of the axis is determined by the angles β and θ relative to the orbital coordinate system. Figure 4 As shown, there are two angles between the tether coordinate system and the orbital motion coordinate system: β and θ. Among them, the β angle is called the out-of-plane angle, and the θ angle is called the in-plane angle. The two angles are defined by the "2-3" Euler rotation; establish the end-body satellite tether coordinate system Kx t y t z t , whose coordinate axes are related to the coordinate system Cx t y t z t Axis parallel, but in the form of Cx t y t z t Around x t The shaft rotates by a torsion angle get.

[0083] like Figure 5 As shown, the geocentric orbital coordinate system OXYZ rotates along the OZ axis by the true anomaly angle f and the orbital vector r to obtain the orbital motion coordinate system Cx0y0z0, and its transformation quaternion is Q D The orbital motion coordinate system Cx0y0z0 is converted into the tether coordinate system Cx by rotating the in-plane angle θ and the out-plane angle β according to the rotation sequence of "2-3". t y t z t , whose transformation quaternion is Q T; Tether coordinate system Cx t y t z t Around Cz t Axis rotation angle Get the end-body satellite tether coordinate system Kx t y t z t , whose quaternion is Q W ; From the orbital motion coordinate system Cx0y0z0 to the end-body satellite tether coordinate system Kx t y t z t The transformation quaternion of the transformation quaternion is The end-body satellite tether coordinate system Kx is obtained by converting the geocentric orbital coordinate system OXYZ t y t z t The quaternion is Q = [q0, q1, q2, q3]. According to the description form of the quaternion rotation matrix, from the orbital motion coordinate system Cx0y0z0 to the end-body satellite tether coordinate system Kx t y t z t The rotation matrix of The form is:

[0084]

[0085] The direct conversion relationship between quaternion and Euler angle is:

[0086]

[0087] The end-body satellite tether coordinate system Kx is obtained by converting the geocentric orbital coordinate system OXYZ t y t z t The rotation matrix L in quaternion form q for:

[0088]

[0089] in,

[0090]

[0091] The constraint matrix and constraint equations are established based on the dumbbell bar assumption of the spatial rotating tether system and the unit quaternion assumption.

[0092] Constraint 1: Based on Assumption 1, quaternion Q = [q0, q1, q2, q3] T Satisfying the unit constraint, the derivative of formula (5) yields formula (6).

[0093] q0 2 +q12 +q2 2 +q3 2 =1 (5)

[0094]

[0095] Constraint 2: According to assumptions 2 and 3, the space rotation tether system ignores the flexibility, torsion, elasticity and other characteristics of the tether, and the coordinate system Kx of the end-body satellite tether is t y t z t Kx t Axis rotation angular velocity ω x =0, according to the relationship between quaternion and angular velocity, the quaternion expression of this constraint is:

[0096]

[0097] The mathematical expressions of formulas (6) and (7) are organized into constraint matrices and constraint equations.

[0098]

[0099] The center of mass position and rotation state of the space rotating tether system are determined by the semi-major axis r, true anomaly f, tether length l and quaternion Q, which constitute the generalized coordinates P = [r, f, l, Q T ] T .

[0100] The non-potential force on the space rotating tether system model is the thrust F of equal magnitude and opposite direction on the two end-body satellites (parent satellite A and daughter satellite B). A =-F B = F. The generalized force and moment matrices of the tether system are obtained by means of virtual work:

[0101]

[0102] in, is the end-body satellite tether coordinate system [r,f,l] T The mapping matrix of the defined coordinate system. M sum The relationship between the rotational torque of the center of mass of the space tether system, the quaternion Q and the angular velocity ω is:

[0103]

[0104] The total kinetic energy of the space tether system T tot is the kinetic energy T of the center of mass of the space tether system in orbit C , the kinetic energy of the space tether system relative to the center of mass T r sum:

[0105] Ttot =T C +T r (12)

[0106] Among them, the kinetic energy of the center of mass of the space tether system running on orbit can be described as:

[0107]

[0108] m=m A +m B +m t is the total mass of the space tether system; is the mass of the parent star; is the mass of the parent star when the tether is not deployed; m t =ρ t l is the mass of the released tether; ρ t is the linear density of the tether material; T in the equation r It can be written as the rotational kinetic energy T of the space tether system relative to the center of mass rot The kinetic energy of the end body satellite when the tether is deployed is T ext sum:

[0109] T r =T rot +T ext (14)

[0110] The rotational kinetic energy of the space tether system is:

[0111]

[0112] Where ω is the rotation angular velocity vector of the space tether system in the end-body satellite tether coordinate system, and its expression is shown in formula (11). ||I|| is the inertia tensor matrix of the space tether system, and its specific form is as follows:

[0113]

[0114] Among them, I is assumed by the dumbbell bar x =0, For the system to bypass Ky t , Kz t Moment of inertia:

[0115]

[0116] Among them, l A , l B They are the distances from the center of mass of the space tether system to the center of mass of the parent star and the sub-star A and B respectively:

[0117]

[0118] After integrating and calculating equation (17), the moment of inertia is can be written as:

[0119]

[0120] Among them, m * is the equivalent mass of the rotation of the space tether system:

[0121]

[0122] The rotational kinetic energy of the system is:

[0123]

[0124] Kinetic energy of the end-body satellite motion when the tether is deployed:

[0125]

[0126] The potential energy of the space tether system can be written as the sum of the potential energies of the individual components of the system:

[0127]

[0128] in, They are the vector radii pointing to the center of mass of the parent star A and the center of mass of the daughter star B:

[0129]

[0130] Vector and The components in the geocentric orbital coordinate system are:

[0131]

[0132] The sizes of the vector radii are:

[0133]

[0134] Therefore, the potential energy in equation (23) can be written as:

[0135]

[0136] Consider that the length of the tether is much smaller than the center of mass loss of the space tether system, that is, ||l A,B || / r<<1, then the potential energy can be expanded according to the Maclaurin series and the first three terms are retained to obtain:

[0137]

[0138] In the formula,

[0139] The expression for potential energy can be simplified to:

[0140]

[0141] Here, μ is the gravitational constant.

[0142] The Lagrange function is the difference between kinetic energy and potential energy:

[0143] L=T tot -W (30)

[0144] The specific form of the Lagrange equation with nonholonomic constraints is as follows:

[0145]

[0146] Where L is the Lagrange function of the space tether system, Σ is the constraint matrix of the space tether system, λ is the Lagrange multiplier matrix, τ is the generalized force and torque matrix of the space tether system, and P is the generalized coordinate of the space tether system. In order to eliminate the Lagrange multiplier matrix term in the Lagrange equation (31), the matrix γ is introduced to satisfy the following conditions:

[0147]

[0148] And because there is the following relationship between the transformation matrices:

[0149] S·Γ=I (33)

[0150] The specific form of the matrix γ is selected as follows:

[0151]

[0152] in, are the last two columns of the mapping matrix Γ between the angular velocity ω and the rate of change of the quaternion q over time, so The specific form is as follows:

[0153]

[0154] It can be calculated that γ satisfies:

[0155] γ T Σ T λ=0 (36)

[0156] The nonholonomic constrained Lagrange equation (31) is multiplied by γ on the left T After that, the Lagrange equation with nonholonomic constraints eliminating the Lagrange multiplier term is obtained as follows:

[0157]

[0158] in,

[0159]

[0160] Substituting equations (30) and (38) into the nonholonomic constrained Lagrange equation (37) without the Lagrange multiplier term, we obtain the quaternion-based dynamic model of the spatial rotating tether system.

[0161] Table 1 shows the relevant parameters used in this embodiment.

[0162] Table 1 Related parameters

[0163]

[0164] According to the quaternion space rotation tether system dynamics modeling method, we have established a space rotation tether system dynamics model for low-Earth orbit based on the quaternion space rotation tether system dynamics modeling method disclosed in the present invention, proving that the present invention is practical and feasible. The simulation results are as follows: Figure 6-Figure 7 shown.

[0165] Figure 6 It is the change curve from state 1 to state 3 (initial rotation plane angular velocities are 0.2° / s, 0.5° / s, 1.0° / s respectively) of a specific embodiment under uncontrolled conditions. Figure 7 ] is a quaternion and determinant |J(q)| trajectory in which an out-of-plane angle of 90° appears in a specific embodiment.

[0166] Figure 6 It shows that the common change characteristics of state 1 to state 3 are that the quaternions q0 and q3 change periodically between -1 and 1, q1 and q2 are stable near 0, and the oscillation frequency increases with the increase of angular velocity; Figure 7 It shows that when the space rotating tether system gradually maneuvers from the traditional in-plane rotation motion (in-plane angle is 0) to the space three-dimensional rotation motion perpendicular to the orbital plane (out-of-plane angle is 90°), the corresponding quaternion trajectory still changes continuously, and the determinant |J(q)|=-1 always holds true, which shows that the model of the specific embodiment is solvable and no singularity phenomenon will occur.

[0167] It can be seen from this embodiment that the dynamic characteristics of the space rotating tether system dynamics model of the low-Earth orbit established based on the quaternion-based space rotating tether system dynamics modeling method disclosed in the present invention are consistent with the traditional model, and no singularity phenomenon will occur, which has strong application value.

Claims

1. A quaternion-based spatial rotation tether system dynamics modeling method, characterized in that: The steps include: Step 1: Introduce quaternions instead of Euler angles to represent the conversion relationship between coordinate systems; Step 2: Based on the dumbbell bar hypothesis, the spatial rotating tether system is regarded as a rigid body and the corresponding constraint equations are proposed; Step 3: Use quaternions to describe the motion characteristics of the space rotation tether system, replacing the in-plane angle and out-of-plane angle; Step 4: Derive the Lagrange equation of nonholonomic constraints in quaternion form based on quaternions; Step 5: Solve the quaternion-based dynamic model; Step 6: Solve the quaternion-based spatial rotation tether system dynamics model to complete the modeling.

2. The quaternion-based spatial rotation tether system dynamics modeling method according to claim 1 is characterized in that: The step 1 is specifically as follows: Based on the space rotating tether system, the geocentric orbital coordinate system OXYZ and the geocentric orbital motion coordinate system OX are established. o Y o Z o , orbital motion coordinate system Cx0y0z0, tether coordinate system Cx t y t z t , end-body satellite tether coordinate system Kx t y t z t ; The transformation relationship between these coordinate systems is as follows: The transformation quaternion Q from the geocentric orbital coordinate system OXYZ to the orbital motion coordinate system Cx0y0z0 D : Where f is the true anomaly of the space rotating tether system, and Represents the three imaginary units in quaternions; From the orbital motion coordinate system Cx0y0z0 to the tether coordinate system Cx t y t z t The transformation quaternion Q T : Among them, β represents the out-of-plane angle of the space rotating tether system, and θ represents the in-plane angle of the space rotating tether system; From orbital motion coordinate system Cx0y0z0 to end-body satellite tether coordinate system Kx t y t z t Transformation quaternion in, Represents a transformation quaternion The four components of represents the torsion angle of the formal system of rotating tethers in space; The direct conversion relationship between quaternion and Euler angle is: From the geocentric orbital coordinate system OXYZ to the end-body satellite tether coordinate system Kx t y t z t The transformed quaternion is Q: From the geocentric orbital coordinate system OXYZ to the end-body satellite tether coordinate system Kx t y t z t The rotation matrix L q The quaternion Q is expressed in the form of:

3. The quaternion-based spatial rotation tether system dynamics modeling method according to claim 2 is characterized in that: The step 2 is specifically as follows: The spatial rotating tether system is considered as a rigid body, and the dumbbell bar hypothesis is proposed as follows: Assumption 1: The quaternions used are all unit quaternions, that is, the modulus of the quaternion is the unit modulus; Assumption 2: The tether is regarded as a rigid rod with uniform density, and the flexibility, torsion and elastic properties of the tether are ignored; Assumption 3: Since the size of the two satellites is much smaller than the length of the tether, the two satellites are simplified to mass points; Assumption 4: The space tether system is only affected by the earth's gravity, active control thrust and uncertain disturbances, and J2 perturbation, atmospheric drag, solar pressure and other celestial gravitational effects are ignored; Based on the dumbbell bar assumption, two constraints are proposed: Constraint 1: Select quaternion Q = [q0, q1, q2, q3] T Satisfy the unit constraint: Constraint 2: Ignore the torsion characteristics of the tether, so the torsion angular velocity of the tether is 0: Constraints (7) and (8) can be written as constraint equations as follows: Among them, the matrix Σ is the constraint matrix, r is the orbital vector length of the center of mass of the space tether system when it is orbiting; l is the length of the released tether.

4. The quaternion-based spatial rotation tether system dynamics modeling method according to claim 3 is characterized in that: The step 3 is specifically as follows: The quaternion, rope length, semi-major axis and true anomaly angle are used to describe the center of mass position and rotation state of the space tether system. The generalized coordinate P is shown in formula (10): P=[r,f,l,q0,q1,q2,q3] T (10)。 5. The method for dynamic modeling of a spatial rotating tether system based on quaternion according to claim 4, characterized in that: The step 4 is specifically as follows: The generalized force is a pair of equal and opposite control input thrusts F and -F applied at the center of mass A of the parent star and the center of mass B of the daughter star, F = [0, F y ,F z ] T , its quaternion form is: Among them, S represents the quaternion The conversion matrix M is the conversion matrix of the derivative to angular velocity. sum It represents the thrust torque generated by the control input thrusts F and -F of equal magnitude and opposite direction; The total kinetic energy T of the space rotating tether system tot is the kinetic energy T of the center of mass of the space tether system in orbit C , the kinetic energy of the space tether system relative to the center of mass T r The sum of , its quaternion form is: Among them, m A represents the mass of the parent star A in the space rotating tether system, m B represents the mass of neutron star B in the space rotating tether system, m t represents the mass of the tether in the space rotating tether system, and m represents the total mass of the space rotating tether system, that is, m = m A +m B +m t ; Equivalent mass m of the space tether system rotation * : The potential energy in quaternion form is: Among them, μ is the gravitational constant; Subtracting the kinetic energy from the potential energy, we get the Lagrange function:

6. The method for dynamic modeling of a spatial rotating tether system based on quaternion according to claim 5, characterized in that: The step 5 is specifically as follows: The specific form of the Lagrange equation with nonholonomic constraints is as follows: Where λ is the Lagrange multiplier matrix; τ is the generalized force corresponding to the generalized coordinate P in the quaternion dynamics model of the space rotation tether system; The matrix Υ is used to eliminate the Lagrange multiplier terms: Υ satisfies the following conditions: The specific form of the Lagrange equation that eliminates the nonholonomic constraints of the Lagrange multiplier term is as follows:

7. The quaternion-based spatial rotation tether system dynamics modeling method according to claim 6 is characterized in that: The step 6 is specifically as follows: Substituting formula (11)-formula (14) into the Lagrange equation (18) with the nonholonomic constraints of the Lagrange multiplier term eliminated, after simplification, the dynamic model of the spatial rotation tether system based on quaternion is obtained as follows: u=[0,0,-F z l,F y [l] T

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