Aircraft spin angular velocity selection method based on dynamic stability criterion

Abstract

The application discloses a spinning angular velocity selection method of an aircraft based on a dynamic stability criterion and belongs to the technical field of aircraft control. The method is as follows: a dynamic equation of the aircraft is established by considering the introduction of a Magnus moment and gyroscopic effect under active spinning conditions; a general dynamic stability criterion of the spinning aircraft is obtained based on the dynamic equation of the aircraft and in combination with the Routh-Hurwitz method; and the dynamic stability criterion of the classical trajectory design and the coning motion is fused to select a corresponding spinning angular velocity, so that the aircraft stably flies in the spinning process. The application avoids the problems of attitude divergence and guidance precision attenuation caused by the out-of-bound coning motion parameters in the traditional design, improves the trajectory design precision, ensures that the aircraft keeps the gradual stability of the coning motion mode in a complex aerodynamic environment, reduces the attitude angle control error of the traditional method, and provides a systematic solution for the high-precision guidance and stable flight of the spinning aircraft.

Description

TECHNICAL FIELD

[0001] The application relates to a method for selecting the spin angular velocity of an aircraft based on a dynamic stability criterion, and belongs to the technical field of aircraft control. BACKGROUND

[0002] Compared with a conventional non-spin aircraft, the spin aircraft not only performs pitching and yawing channel movement, but also causes Magnus effect and gyro effect due to the spin movement. The cross-channel aerodynamic and inertial coupling effect dominated by the two effects makes the spin aircraft exhibit a unique coning motion mode.

[0003] Specifically, the spin aircraft rotates around its longitudinal axis and performs periodic movement around its velocity axis. The complex motion mode makes the attitude control and guidance accuracy of the aircraft face great challenges. When the coning parameter exceeds a critical threshold, the nonlinear dynamics characteristics of the aircraft are significantly enhanced, resulting in a series of chain effects such as attitude divergence and guidance accuracy attenuation, which seriously affect the stability and mission execution capability of the aircraft.

[0004] Therefore, how to realize stable spinning of the aircraft has become a key problem to be solved in the current aircraft design and control field. SUMMARY

[0005] To solve the problems in the background art, the application provides a method for selecting the spin angular velocity of an aircraft based on a dynamic stability criterion.

[0006] To achieve the above object, the application adopts the following technical scheme: a method for selecting the spin angular velocity of an aircraft based on a dynamic stability criterion, the method comprising the following steps:

[0007] S1: establishing an aircraft dynamics equation considering the introduction of Magnus moment and gyro effect under active spinning conditions;

[0008] S101: setting aircraft related parameters, including: aircraft mass, lateral force coefficient, lift coefficient, restoring moment coefficient, damping moment coefficient, Magnus moment coefficient, and angular velocity vector component under the current system, polar moment of inertia and equatorial moment of inertia;

[0009] S102: making a simplified assumption:

[0010] S10201: ignoring the change of the velocity vector and focusing on the change of the attack angle and the sideslip angle;

[0011] S10202: the order of magnitude of the attack angle alpha and the sideslip angle beta during flight is smaller than that of the pitch angle and the roll angle, so the small angle assumption of cos(alpha) = 1, sin(alpha) = alpha and cos(beta) = 1, sin(beta) = beta is satisfied;

[0012] S103: Using the relative derivative formula of vector and the angular momentum theorem, the attitude dynamics equation of the aircraft rotating around the mass center in the body system is obtained:

[0013]

[0014] In formula (1):

[0015] I x is the polar moment of inertia;

[0016] ω x is the x-axis component of the angular velocity vector in the body system;

[0017] is the first derivative of the x-axis component of the angular velocity vector in the body system;

[0018] ω y is the y-axis component of the angular velocity vector in the body system;

[0019] is the first derivative of the y-axis component of the angular velocity vector in the body system;

[0020] ω z is the z-axis component of the angular velocity vector in the body system;

[0021] is the first derivative of the z-axis component of the angular velocity vector in the body system;

[0022] is the damping moment coefficient of the x-axis component of the angular velocity vector;

[0023] m ωy is the damping moment coefficient of the y-axis component of the angular velocity vector;

[0024] is the damping moment coefficient of the z-axis component of the angular velocity vector;

[0025] is the Magnus moment coefficient of the y-axis component of the angular velocity vector;

[0026] is the Magnus moment coefficient of the z-axis component of the angular velocity vector;

[0027] is the restoring moment coefficient of the y-axis component of the angular velocity vector;

[0028] is the restoring moment coefficient of the z-axis component of the angular velocity vector;

[0029] q is the dynamic pressure;

[0030] S is the reference area of the aircraft;

[0031] l is the reference length of the aircraft;

[0032] V is the speed of the aircraft;

[0033] I is the equatorial moment of inertia;

[0034] S104: Based on the small angle assumption of the angle of attack and the sideslip angle, the components of the velocity vector in the body frame are obtained as follows:

[0035]

[0036] S105: From the relative derivative and the absolute derivative of the vector, the acceleration of the vector is expressed as follows:

[0037]

[0038] In equation (3):

[0039] t is the flight time;

[0040] Ω = [ω x ω y ω z ] T is the angular velocity of the aircraft in the body frame;

[0041] After rearranging equation (3), the expressions of the acceleration in the y-axis and the z-axis of the body frame are as follows:

[0042]

[0043] In equation (4):

[0044] m is the mass of the aircraft;

[0045] is the first derivative of the angle of attack;

[0046] is the first derivative of the sideslip angle;

[0047] F by is the projection of the total external force in the y-axis of the body frame;

[0048] F bz is the projection of the total external force in the z-axis of the body frame;

[0049] S106: By combining equations (1)-(4), the angular motion equation of the aircraft is obtained as follows:

[0050]

[0051] In equation (5):

[0052] is the lift coefficient of the y-axis component of the angular velocity vector in the body frame;

[0053] is the side force coefficient of the z-axis component of the angular velocity vector in the body frame.

[0054] S2: Based on the aircraft dynamics equation, the general dynamic stability criterion of the spinning aircraft is obtained by combining the Routh-Hurwitz method;

[0055] S201: The formula (5) is rearranged into a matrix form of angular differential equation:

[0056]

[0057]

[0058] In formula (6) and formula (7):

[0059] a1, a2, a3, a4, a5, b1, b2, b3, b4 and b5 are coefficients defined for simplifying equation derivation,

[0060]

[0061] S202: According to the characteristic points selected according to the nominal trajectory, the [αβ] T and [ω z ω y ] T are once differentiated to obtain the conversion relationship between the angle of attack and the sideslip angle and the angular rate:

[0062]

[0063] In formula (8):

[0064] is the second derivative of the angle of attack;

[0065] is the second derivative of the sideslip angle;

[0066] S203: The [ω y ω z ] T and its differential items are eliminated to obtain the second-order differential equation group about [αβ] T :

[0067]

[0068] S204: The angle of attack and sideslip angle stability are judged for the linearized differential equation group, and after combining the coefficients, the following is obtained:

[0069]

[0070] In formula (10):

[0071] H, M, P and T are coefficients defined by simplifying equation derivation,

[0072] a, b, c and d are intermediate quantities,

[0073] S205: Perform Laplace transformation on formula (9) and carry out dynamic stability characteristic analysis:

[0074]

[0075] In formula (11):

[0076] s is the Laplace operator;

[0077] S206: Using the coefficient freezing method, combine the attack angle and sideslip angle in formula (11) into one formula, and get its characteristic equation as:

[0078] s 4 +h1s 3 +h2s 2 +h3s+h4=0 (12)

[0079] In formula (12):

[0080] h1, h2, h3 and h4 are coefficients defined by simplifying equation derivation, h1=2H, h2=P 2 +H 2 -2M, h3=2(P 2 T-MH), h4=M 2 +(PT) 2 ;

[0081] S207: According to the Routh-Hurwitz stability criterion, the sufficient and necessary condition for each characteristic root of the characteristic equation to have a negative real part is:

[0082]

[0083] According to condition formula (9), each coefficient is expanded and arranged to get the equivalent condition for stability:

[0084]

[0085] S208: According to H>0, P 2 T-MH>0, then H 2 (P 2 -4M)>0, and combined with H(P 2 T-MH)-(PT)2 Under the condition that σ > 0, the following can be obtained:

[0086]

[0087] The stability coefficient is defined as σ = 1 - 2 * (1 - 1 / 2) = 0.5

[0088] S209: formula (15) is obtained, that is, the stability condition of the spinning aircraft, wherein the stability coefficient σ is used to reflect the stability of the system, and the smaller the stability coefficient σ, the better the dynamic stability of the system.

[0089] S3: the dynamic stability criterion of fusing the classical trajectory design and the coning motion is selected, and the corresponding spin angular velocity is selected, so that the aircraft stably flies in the spinning process.

[0090] S301: a nominal three-degree-of-freedom trajectory is designed;

[0091] S30101: the three-degree-of-freedom trajectory parameters are adjusted;

[0092] S30102: it is judged whether the range and height meet the requirements, if the requirements are met, S302 is performed; otherwise, S30101 is repeated until the requirements are met.

[0093] S302: according to the nominal three-degree-of-freedom trajectory, the characteristic point parameters are selected point by point in the trajectory segment requiring spinning, the dynamic stability criterion is used to judge the stable rotating speed range; according to the judgment result, the rotating-stable-rotating speed logic is designed, if the trajectory segment meets the spinning condition, S303 is performed to enter the spinning task, otherwise, the three-degree-of-freedom trajectory is designed again in S301;

[0094] S303: according to the rotating-stable-rotating speed logic, the three-degree-of-freedom trajectory is expanded into a six-degree-of-freedom trajectory containing the Magnus effect and the gyro effect, and the six-degree-of-freedom trajectory is simulated and verified;

[0095] S304: if the attitude angle error of the six-degree-of-freedom trajectory meets the requirements, the spinning trajectory design is completed; otherwise, the rotating-stable-rotating logic design of S302 is performed again.

[0096] Compared with the prior art, the beneficial effects of the present application are:

[0097] The application is based on the coupling mechanism of Magnus effect and gyro effect, a dynamic stability criterion is derived, a quantitative theoretical boundary is provided for spin angular velocity design, and the problems of attitude divergence and guidance accuracy degradation caused by out-of-bound cone motion parameters in traditional design are avoided; secondly, the three-degree-of-freedom trajectory design paradigm is broken through, a six-degree-of-freedom extended framework integrating spin effect is constructed, the trajectory design accuracy is improved through point-by-point characteristic parameter constraint and rotation speed logic optimization; at the same time, the angular velocity is dynamically selected combined with real-time flight state, and the stability coefficient is checked online, so that the spacecraft can maintain the progressive stability of the coning motion mode in the complex aerodynamic environment; finally, while fully utilizing the Magnus effect to increase the lift, the gyro effect is used to effectively suppress the lateral disturbance, so that the spacecraft can fly stably during the spinning process without divergence, and the attitude angle control error of the traditional method is reduced, thereby providing a systematic solution for high-precision guidance and stable flight of the spinning spacecraft. BRIEF DESCRIPTION OF DRAWINGS

[0098] Figure 1 A flowchart of the S3 iterative design of the application. DETAILED DESCRIPTION

[0099] The technical solutions in the application will be described clearly and completely in combination with the drawings in the embodiments of the application. Obviously, the described embodiments are only a part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0100] A spinning angular velocity selection method for a spacecraft based on a dynamic stability criterion, the method comprising the following steps:

[0101] S1: establishing a spacecraft dynamics equation considering the introduction of Magnus moment and gyro effect under the condition of active spinning;

[0102] S101: setting the related parameters of the spacecraft, including the mass of the spacecraft, the lateral force coefficient, the lift coefficient, the restoring moment coefficient, the damping moment coefficient, the Magnus moment coefficient, the angular velocity vector component in the body system, the polar moment of inertia and the equatorial moment of inertia;

[0103] S102: since the model of the spinning spacecraft is relatively complex and the dynamics equation has too many coupling terms, in order to simplify the analysis, the following simplifying assumptions are made in the dynamic stability analysis of the present research:

[0104] S10201: since the angular motion is a fast motion process relative to the motion of the center of mass, the change of the velocity vector is ignored in the construction of the angular motion equation, and the changes of the angle of attack and the sideslip angle are focused on;

[0105] S10202: The attack angle a and the sideslip angle β are in the order of magnitude of attitude angles smaller than the pitch angle and the roll angle, usually less than 5°, so the small angle assumptions cos(a) = 1, sin(a) = a and cos(β) = 1, sin(β) = β are satisfied;

[0106] S103: The attitude dynamics equation of the aircraft rotating around the center of mass in the body system is obtained by using the relative derivative formula of the vector and the angular momentum theorem:

[0107]

[0108] In formula (1):

[0109] I x is the polar moment of inertia;

[0110] ω x is the x-axis component of the angular velocity vector in the body system;

[0111] is the first derivative of the x-axis component of the angular velocity vector in the body system;

[0112] ω y is the y-axis component of the angular velocity vector in the body system;

[0113] is the first derivative of the y-axis component of the angular velocity vector in the body system;

[0114] ω z is the z-axis component of the angular velocity vector in the body system;

[0115] is the first derivative of the z-axis component of the angular velocity vector in the body system;

[0116] is the damping moment coefficient of the x-axis component of the angular velocity vector;

[0117] m ωy is the damping moment coefficient of the y-axis component of the angular velocity vector;

[0118] is the damping moment coefficient of the z-axis component of the angular velocity vector;

[0119] is the Magnus moment coefficient of the y-axis component of the angular velocity vector;

[0120] is the Magnus moment coefficient of the z-axis component of the angular velocity vector;

[0121] is the restoring moment coefficient of the y-axis component of the angular velocity vector;

[0122] Restoring moment coefficient for the z-axis component of the angular velocity vector;

[0123] q is the dynamic pressure;

[0124] S is the reference area of the aircraft;

[0125] l is the reference length of the aircraft;

[0126] V is the speed of the aircraft;

[0127] I is the equatorial moment of inertia;

[0128] S104: With the small angle assumption of the angle of attack and the sideslip angle, the components of the velocity vector in the body frame are obtained as follows:

[0129]

[0130] S105: From the relative and absolute derivative relationship of the vector, its acceleration can be expressed as follows:

[0131]

[0132] In equation (3):

[0133] t is the flight time;

[0134] Ω = [ω x ω y ω z ] T is the angular velocity vector of the aircraft in the body frame;

[0135] After rearranging equation (3), the expressions of the acceleration in the y-axis and z-axis of the body frame are as follows:

[0136]

[0137] In equation (4):

[0138] m is the mass of the aircraft;

[0139] is the first derivative of the angle of attack;

[0140] is the first derivative of the sideslip angle;

[0141] F by is the projection of the resultant external force in the y-axis of the body frame;

[0142] F bz is the projection of the resultant external force in the z-axis of the body frame;

[0143] S106: By simultaneously solving equations (1)-(4), the angular motion equation of the aircraft is obtained as follows:

[0144]

[0145] In formula (5):

[0146] is the lift coefficient of the y-axis component of the angular velocity vector in the body system;

[0147] is the side force coefficient of the z-axis component of the angular velocity vector in the body system.

[0148] In summary, the dynamic modeling of the spinning aircraft is completed, laying a foundation for the subsequent stability analysis.

[0149] S2: Based on the aircraft dynamics equation, further analysis is made in the stability level, and the general dynamic stability criterion of the spinning aircraft is obtained by combining the Routh-Hurwitz method;

[0150] S201: In the motion model ignoring high-order small quantities, formula (5) is rearranged into a matrix form of angular differential equation:

[0151]

[0152] In formula (6) and formula (7):

[0153] a1, a2, a3, a4, a5, b1, b2, b3, b4 and b5 are coefficients defined for simplifying equation derivation,

[0154]

[0155] S202: According to the characteristic points selected according to the nominal trajectory, the frozen coefficient method is used to carry out one differentiation on [αβ] T and [ω z ω y ] T to obtain the conversion relationship between the angle of attack and the angle of sideslip and the angular rate:

[0156]

[0157] In formula (8):

[0158] is the second derivative of the angle of attack;

[0159] is the second derivative of the angle of sideslip;

[0160] S203: The [ω y ω z ] T and its differential items are eliminated to obtain a second-order differential equation group about [αβ] T .

[0161]

[0162] S204: Angle of attack and sideslip angle stability judgment is performed on the kinetic linearization differential equation set, and each coefficient is combined to obtain:

[0163]

[0164] In formula (10):

[0165] H, M, P, and T are coefficients defined in the simplified equation derivation,

[0166] a, b, c, and d are intermediate quantities,

[0167] S205: The formula (9) is subjected to a Laplace transformation, and dynamic stability characteristic analysis is carried out:

[0168]

[0169] In formula (11):

[0170] s is a Laplace operator;

[0171] S206: Using the coefficient freezing method, the coefficients of the formula can be regarded as constants in a relatively short period of time, so the differential equation set can be regarded as a linear constant system, and the angle of attack and sideslip angle in formula (11) are combined into one formula, and the characteristic equation thereof is obtained as:

[0172] s 4 +h1s 3 +h2s 2 +h3s+h4=0(12)

[0173] In formula (12):

[0174] h1, h2, h3, and h4 are coefficients defined in the simplified equation derivation, h1=2H, h2=P 2 +H 2 -2M, h3=2(P 2 T-MH), h4=M 2 +(PT) 2 ;

[0175] S207: According to the Routh-Hurwitz stability criterion, the sufficient and necessary condition for each characteristic root of the characteristic equation to have a negative real part is:

[0176]

[0177] According to conditional formula (9), the stable equivalent condition is obtained by expanding and arranging each coefficient:

[0178]

[0179] S208: According to the stable equivalent condition obtained in S207, when the first formula and the third formula are established, the second formula is naturally established. According to H>0, P 2 T-MH>0, H 2 (P 2 -4M)>0, combined with the condition that H(P 2 T-MH)-(PT) 2 >0, the following can be obtained:

[0180]

[0181] The stability coefficient is defined as

[0182] S209: The formula (15) is obtained, which is the stability condition of the spinning spacecraft. The stability coefficient σ is used to reflect the stability of the system. The smaller the stability coefficient σ, the better the dynamic stability of the system. The coefficients M and P in the criterion contain the spinning angular velocity term, so the boundary of the spinning angular velocity at each time can be obtained by using the criterion inverse solution combined with the actual flight state of the spacecraft.

[0183] S3: The dynamic stability criterion of the classical trajectory design and the conical motion is fused, and the corresponding spinning angular velocity is selected, so that the spacecraft can fly stably during spinning without divergence.

[0184] S301: A nominal three-degree-of-freedom trajectory is designed, and its theoretical system is based on a three-degree-of-freedom rigid body dynamics model. Instantaneous equilibrium is used to decouple attitude motion and mass center dynamics. If the designed trajectory meets the task requirements, S302 is performed;

[0185] S30101: Adjust the three-degree-of-freedom trajectory parameters;

[0186] S30102: Determine whether the range and altitude meet the requirements. If they meet the requirements, S302 is performed; otherwise, repeat S30101 until the requirements are met.

[0187] S302: According to the nominal three-degree-of-freedom trajectory, the characteristic point parameters are selected point by point in the trajectory segment that requires spinning. The dynamic stability criterion is used to determine the stable speed range. According to the judgment result, the spin-stable-rotation speed logic is designed. If the trajectory segment meets the spinning condition, S303 is performed to enter the spinning task. Otherwise, return to S301 to redesign the three-degree-of-freedom trajectory;

[0188] S303: According to the rotation-stabilization-rotation speed logic, the three-degree-of-freedom trajectory is expanded into a six-degree-of-freedom trajectory containing the Magnus effect and the gyro effect, and the six-degree-of-freedom trajectory is simulated and verified;

[0189] S304: If the six-degree-of-freedom trajectory attitude angle error meets the requirements, the spin trajectory design is completed; otherwise, the rotation-stabilization-rotation logic design of S302 is re-executed.

[0190] It is obvious to those skilled in the art that the present application is not limited to the details of the above exemplary embodiments, and can be implemented in other forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be regarded as exemplary and non-limiting, the scope of the present application is defined by the appended claims rather than the above description, and all changes falling within the meaning and scope of the equivalent conditions of the claims are intended to be included in the present application. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0191] In addition, it should be understood that although the present specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the description of the specification is only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be properly combined to form other embodiments that those skilled in the art can understand.

Claims

1. A method for selecting an angular velocity of spin of an aircraft based on a dynamic stability criterion, characterized in that: The method comprises the following steps: S1: establishing an aircraft dynamics equation considering the introduction of Magnus moment and gyroscopic effect under active spin condition; The S1 comprises the following steps: S101: setting aircraft related parameters, including: aircraft mass, lateral force coefficient, lift coefficient, restoring moment coefficient, damping moment coefficient, Magnus moment coefficient, and body system under angular velocity vector component, polar moment of inertia and equatorial moment of inertia; S102: making a simplified assumption: S10201: ignoring the change of velocity vector, and focusing on the change of angle of attack and sideslip angle; S10202: attack angle during flight and sideslip angle are of the order of magnitude of the pitch and roll angles, thus satisfying and the small angle assumption. S103: obtaining an attitude dynamics equation of the aircraft rotating around the center of mass in the body system by using the relative derivative formula of vector and the angular momentum theorem: Formula in which: I is the moment of inertia about the axis of rotation; is the x component of the angular velocity vector in the body frame; is the first derivative of the angular velocity vector x-axis component under the current system; y is the y component of the angular velocity vector in the body frame; is the first derivative of the angular velocity vector y component under the current system; is the angular velocity vector z-axis component under the current system; is the first derivative of the angular velocity vector z-axis component under the current system; damping torque coefficient for the angular velocity vector x-axis component; damping torque coefficient for the angular velocity vector y-axis component; damping torque coefficient for the angular velocity vector z-axis component; Mg is the Magnus moment coefficient for the angular velocity vector y component; Mg is the Magnus moment coefficient for the angular velocity vector z-axis component; is the restoring moment coefficient for the angular velocity vector y-axis component; is the restoring moment coefficient for the angular velocity vector z-axis component; Dynamic pressure; S is the reference area of the aircraft; Lref is a reference length for the aircraft; V is the speed of the aircraft; Ieq is the equivalent moment of inertia for the rotor system; and S104: combining the small angle assumption of angle of attack and sideslip angle, obtaining the component of velocity vector in the body system: S105: obtaining the acceleration of the velocity vector according to the relative derivative and absolute derivative of vector as follows: Formula in which: is the time of flight; is the angular velocity of the aircraft in the body frame; Grooming type The expressions of the accelerations in the y and z axes of the system are as follows: Formula in the formula mass of the aircraft; is the first derivative of the angle of attack; is the first derivative of the sideslip angle; Fy is the projection of the resultant force on the y-axis of the system; Fz is the projection of the resultant force on the z axis of the system; S106: Simultaneous - , obtaining angular motion equation of the aircraft: Formula in which: Cm is the lift coefficient for the y-component of the angular velocity vector y under the present system; Cz lateral force coefficient for the z-axis component of the angular velocity vector; S2: obtaining a general dynamic stability criterion of the spinning aircraft based on the aircraft dynamics equation and combining the Routh-Hurwitz method; S3: fusing the dynamic stability criterion of the classical trajectory design and the coning motion, and selecting the corresponding spin angular velocity, so that the aircraft stably flies in the spinning process.

2. The method of claim 1, wherein: The S2 comprises the following steps: S201 : rewriting the formula of the angle differential equation into a matrix form S201 : rewriting the formula of the angle differential equation into a matrix form Formula and Formula in which: are coefficients defined for simplifying equation derivation, , , , , , , , , , ; S202: Select feature points according to the nominal trajectory, and use the frozen coefficient method to obtain the relationship between the angle of attack and the angle of sideslip and the angular rate and Once differentiated, the conversion relationship between the angle of attack and the angle of sideslip and the angular rate is obtained: Formula in which: second derivative of the angle of attack; second derivative of the sideslip angle; S203: obtaining and its differential terms, to obtain a second-order differential equation system about ​ S204: judging the stability of angle of attack and sideslip angle for the linearized differential equation of dynamics, and obtaining the following equation after combining the coefficients: Formula in which: are coefficients defined for simplifying equation derivation, , , , , and are intermediate quantities, , , , ; S205: subjecting the compound of formula Pulling the change and carrying out dynamic stability characteristics analysis: Formula in which: is the Laplacian operator; S206: Using the coefficient freezing method, the formula The angle of attack and the sideslip angle are combined into one formula, and the characteristic equation is obtained as Formula in which: are coefficients defined for simplifying equation derivation, , , , ; S207: according to the Routh-Hurwitz stability criterion, the sufficient and necessary condition for each eigenvalue of the characteristic equation to have a negative real part is: According to the conditional expression The stable equivalent conditions are obtained by expanding and arranging each coefficient. S208: According to , , then get , combined with the conditions of , get: The stability coefficient is defined as ; S209: get formula is the stability coefficient of the spin-stabilized vehicle, and is the stability coefficient of the spin-stabilized vehicle, and The smaller the stability coefficient is, the better the dynamic stability of the system is.

3. The method of claim 2, wherein: The S3 comprises the following steps: S301: designing a nominal three-degree-of-freedom trajectory; S302: according to the nominal three-degree-of-freedom trajectory, selecting feature point parameters in the trajectory segment requiring spinning point by point, judging the stable speed range by using the dynamic stability criterion; according to the judgment result, designing the speed logic of spinning-stable-rotating, if the trajectory segment meets the spinning condition, then performing S303 to enter the spinning task, otherwise, returning to S301 to redesign the three-degree-of-freedom trajectory; S303: according to the speed logic of spinning-stable-rotating, expanding the three-degree-of-freedom trajectory into a six-degree-of-freedom trajectory containing the Magnus effect and gyroscopic effect, and simulating and verifying the six-degree-of-freedom trajectory; S304: if the attitude angle error of the six-degree-of-freedom trajectory meets the requirement, then completing the spinning trajectory design; otherwise, re-executing the spinning-stable-rotating logic design of S302.

4. The method of claim 3, wherein: The S301 comprises the following steps: S30101: adjusting the three-degree-of-freedom trajectory parameters; S30102: judging whether the range and height meet the requirements, if yes, then performing S302; otherwise, repeating S30101 until the requirements are met.

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