Method for exciting chaotic state of gliding aircraft based on Lorenz system

Abstract

A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system belongs to the field of aircraft control technology. Select a nominal trajectory and record the time-varying sequence of the state variables of the nominal trajectory; obtain the complete differential equations of the Lorenz system; calculate the desired three-axis velocity increments of the aircraft re-entry system; generate the lateral additional overload and longitudinal additional overload of the aircraft in the chaotic trajectory re-entry system; obtain the flight state variables of the next time step; repeat until the chaotic maneuver flight ends, and complete the chaotic flight excitation for the aircraft. The present invention uses the Lorenz system to design maneuver commands, improving the unpredictability of the gliding segment trajectory of the aircraft. The generated chaotic trajectory automatically satisfies constraints such as heat flux, overload, and dynamic pressure, ensuring overall controllability. Maneuver commands are generated based on the real-time state and deviation, with weak dependence on the information of enemy aircraft, supporting online command generation, and enhancing tactical flexibility.

Description

Technical Field

[0001] The present invention relates to a method for exciting the chaotic state of a glide vehicle based on the Lorenz system, belonging to the technical field of aircraft control. Background Art

[0002] Hypersonic glide vehicles, with their characteristics of high speed and high maneuverability, have broad application prospects in the strategic and tactical fields. However, with the rapid development of modern interception technologies, especially the continuous improvement of the all-dimensional and multi-level near-space detection system, the flight trajectories of such vehicles are facing increasingly severe challenges in identification and tracking.

[0003] The flight trajectories of traditional glide vehicles often have a certain regularity and predictability, which enables modern detection systems to quickly lock and track their flight paths and then implement effective interception. Therefore, the survivability and penetration efficiency of glide vehicles are greatly threatened.

[0004] To address this challenge, an innovative method is urgently needed to break the predictability of the glide vehicle's flight trajectory and improve its stealth and penetration capabilities. Based on this, the present invention proposes a method for exciting the chaotic state of a glide vehicle based on the Lorenz system. The Lorenz system is a typical chaotic system, and its motion trajectory has high complexity and unpredictability. By introducing the chaotic characteristics of the Lorenz system into the flight control of the glide vehicle, chaotic characteristics can be imparted to its flight trajectory, making it difficult for detection systems to accurately predict and track.

[0005] The present invention is proposed to enhance the penetration efficiency of glide vehicles and their survivability in the modern war environment through the excitation of the chaotic state. This method not only has important theoretical value but also has significant engineering practical significance, and is expected to open up new ideas for the design and application of glide vehicles. Summary of the Invention

[0006] To solve the problems in the background art, the present invention provides a method for exciting the chaotic state of a glide vehicle based on the Lorenz system.

[0007] To achieve the above object, the present invention adopts the following technical solution: A method for exciting the chaotic state of a glide vehicle based on the Lorenz system, the method comprising the following steps:

[0008] S1: Select a reentry glide trajectory as the nominal trajectory for constructing the chaotic trajectory, and record the change sequence of the state variables of the nominal trajectory over time t;

[0009] S2: According to the differential equations of the Lorenz system, establish the corresponding relationship between the state variables of the nominal trajectory and the state variables of the vehicle reentry dynamics, and at the same time set the parameters of the Lorenz system to obtain the complete differential equations of the Lorenz system;

[0010] The complete differential equations of the Lorenz system described in S2 are as follows:

[0011]

[0012] In Equation (1):

[0013] [x, y, z] T is the three-dimensional state variable of the Lorenz system;

[0014] is the differential value corresponding to the three-dimensional state variable;

[0015] Pr > 0 is the Prandtl number, related to the flow field;

[0016] Ra > 0 is the Rayleigh number, related to the flow field;

[0017] β > 0 is the spatial parameter, which reflects the aspect ratio of the roll in the convection problem.

[0018] S3: Based on the differential equations of the complete Lorenz system, use the three-axis position deviation of the vehicle relative to the nominal trajectory in the vehicle reentry system as the input, and calculate the desired three-axis velocity increment of the vehicle reentry system;

[0019] The calculation process of the desired three-axis velocity increment of the vehicle reentry system described in S3 is as follows:

[0020] S301: Take the three-axis position deviation of the vehicle reentry system as the input and the desired three-axis velocity increment of the vehicle reentry system as the output, then the complete differential equations of the Lorenz system are rewritten as follows:

[0021]

[0022] In Equation (2):

[0023] [Δx, Δy, Δz] T is the three-axis position deviation of the vehicle reentry system;

[0024] ΔV = [ΔV x , ΔV y , ΔV z T is the desired three-axis velocity increment of the vehicle reentry system;

[0025] S302: Introduce the range control parameter [R x , R​y , R z T and the chaos construction speed control parameter k to obtain the following new differential equation:

[0026]

[0027] S303: Set the parameters of the Lorenz system according to the maneuver range requirement, maneuver time requirement, and overload constraint

[0028] Pr = 10, Ra = 28, β = 8 / 3, R x = 5000, R z = 10000, R y = 5000, k = 1100, to obtain the following final input-output relationship:

[0029]

[0030] S304: The three-axis position deviation [Δx, Δy, Δz] of the vehicle reentry system obtained by calculating through each simulation step T , that is, the desired three-axis velocity increment ΔV = [ΔV x , ΔV y , ΔV z T

[0031] S4: Combine the state variables of the nominal trajectory at the corresponding moment and the desired velocity increment, calculate the three-axis desired velocity of the chaotic trajectory reentry system, and combine the actual velocity in the current state. Generate the lateral additional overload and longitudinal additional overload of the vehicle under the chaotic trajectory reentry system by the PD tracking method;

[0032] The calculation process of the three-axis desired velocity of the chaotic trajectory reentry system described in S4 is as follows:

[0033] S401: Define the state variables of the nominal trajectory at the current moment as [θ, φ, h, V, γ, ψ] T 0, where: θ is the longitude, φ is the latitude, h is the altitude, V is the velocity, γ is the track angle, and ψ is the course angle, to obtain the velocity vector in the north-east-down coordinate system as:

[0034]

[0035] S402: Convert the velocity vector in the north-east-down coordinate system to the vehicle reentry system for expression as follows:

[0036]

[0037] In Equation (6):

[0038] ​​ is the attitude transformation matrix of the vehicle re - entry system relative to the geocentric - fixed coordinate system;

[0039] is the attitude transformation matrix of the geocentric - fixed coordinate system relative to the north - celestial - east coordinate system;

[0040] are the velocity components of the nominal trajectory at the current moment in the re - entry system;

[0041] S403: Similarly to S401 - S402, define the state variables of the current chaotic flight as [θ, φ, h, V, γ, ψ] T , and obtain the velocity components of the current chaotic flight in the re - entry system

[0042] S404: From the velocity components of the nominal trajectory at the current moment in the re - entry system and the desired three - axis velocity increment of the vehicle in the re - entry system ΔV = [ΔV x , ΔV y , ΔV z T obtain the desired velocity components of the chaotic flight:

[0043]

[0044] S405: From the desired velocity components of the chaotic flight and the velocity components of the current chaotic flight in the re - entry system obtain the additional lateral overload Δn z and the additional longitudinal overload Δn y :

[0045]

[0046] In formula (8):

[0047] K p is the proportional coefficient;

[0048] K d is the differential coefficient;

[0049] is the y - axis velocity component of the actual flight in the re - entry system at the previous simulation step;

[0050] is the desired y - axis velocity component of the re - entry system at the previous simulation step;

[0051] is the z - axis velocity component of the actual flight in the re - entry system at the previous simulation step;

[0052] ​is the expected reentry system z-axis velocity component at the previous simulation time step.

[0053] S5: Combine the nominal ballistic maneuver overload and the additional overload, solve for the required maneuver overload of chaotic maneuver flight, inversely solve the corresponding angle of attack and bank angle, substitute them into the reentry glide dynamics model, and obtain the flight state variables of the next time step through the fourth-order Runge-Kutta integration method;

[0054] S501: Calculate the lateral overload n z0 and the longitudinal overload n y0 from the nominal ballistic state variables, and combine the additional lateral overload Δn z and the additional longitudinal overload Δn y to obtain the required lateral overload n z and the required longitudinal overload n y of chaotic maneuver flight:

[0055]

[0056] S502: Calculate the required lateral overload n z and the required longitudinal overload n y of the gliding vehicle:

[0057]

[0058] In Equation (10):

[0059] is the dynamic pressure of the vehicle, where: ρ is the atmospheric density, and V is the vehicle speed;

[0060] S is the reference aerodynamic area of the vehicle;

[0061] C L is the lift coefficient, which is a function of the angle of attack α;

[0062] C D is the drag coefficient, which is a function of the angle of attack α;

[0063] mg is the gravity force on the vehicle;

[0064] S503: Given the required lateral overload n z and the required longitudinal overload n y at this time according to Equation (9), inversely solve the corresponding angle of attack α and bank angle σ through the Newton iteration method;

[0065] S504: Combine the state variables [θ, φ, h, V, γ, ψ] T of the current chaotic flight, the angle of attack α and the bank angle σ, and calculate the differential values of each state variable from the reentry glide dynamics equation:

[0066]

[0067] In Equation (11):

[0068] r = R0 + h is the distance from the center of the earth to the aircraft, where: R0 is the radius of the earth;

[0069] g is the acceleration of gravity of the earth;

[0070] m is the weight of the aircraft;

[0071] S505: According to the differential values of each state variable The next state variable is obtained by the fourth-order Runge-Kutta integration method, thereby completing the update of the aircraft state.

[0072] S6: Repeat S2 - S5 until the chaotic maneuvering flight ends, and complete the excitation of the chaotic flight for the aircraft.

[0073] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0074] For the reentry gliding process of a hypersonic glide vehicle, the present invention designs maneuvering instructions by using the classical Lorenz system, actively excites the chaotic state of the vehicle, and the trajectory designed based on this method has state sensitivity, disorder, and global boundedness. Under the condition of overall controllability, the unpredictability of the gliding section trajectory of the vehicle is greatly improved by using the deviation generated during the flight process. At the same time, the generated chaotic trajectory is above the nominal trajectory, automatically satisfying the constraints such as heat flux, overload, and dynamic pressure, ensuring overall controllability. In addition, this method generates maneuvering instructions based on the real-time state and deviation, has weak dependence on the information of enemy aircraft, supports online generation of instructions, and enhances tactical flexibility. Description of the Drawings

[0075] Figure 1 is the flow chart of the present invention;

[0076] Figure 2 is the three-dimensional trajectory schematic diagram of the complete Lorenz system;

[0077] Figure 3 is the schematic diagram of the longitude-latitude-altitude curve of the nominal trajectory and the chaotic maneuvering trajectory;

[0078] Figure 4 is the schematic diagram of the position curve of the nominal trajectory and the chaotic maneuvering trajectory in the reentry system. Detailed Embodiments

[0079] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work shall fall within the protection scope of the present invention.

[0080] A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system, the method comprising the following steps:

[0081] S1: Select a reentry gliding trajectory as the nominal trajectory for constructing the chaotic trajectory. The nominal trajectory includes three stages: the active section, the gliding section, and the downward pressure section. Its range is about 12,000 km, and the flight time is about 1100 s. Record the variation sequence of the state variables (longitude θ, latitude φ, altitude h, speed magnitude V, flight path angle γ, and course angle ψ) of the nominal trajectory over time t.

[0082] S2: According to the differential equation of the Lorenz system, establish the corresponding relationship between the state variables of the nominal trajectory and the reentry dynamics state variables of the aircraft. At the same time, set the parameters of the Lorenz system according to the characteristics such as the range and speed of the excited chaos to obtain the complete Lorenz system differential equation; according to the basic situation of the nominal trajectory, set the altitude maneuver range of the chaotic trajectory to 5 km, the lateral maneuver range to 20 km, the continuous maneuver time to 500 s, and the maximum maneuver overload not exceeding 10.

[0083] The complete Lorenz system differential equation described in S2 is as follows:

[0084]

[0085] In Equation (1):

[0086] [x, y, z] T is the three-dimensional state variable of the Lorenz system;

[0087] is the differential value corresponding to the three-dimensional state variable;

[0088] Pr > 0 is the Prandtl number, related to the flow field;

[0089] Ra > 0 is the Rayleigh number, related to the flow field;

[0090] β > 0 is the spatial parameter, which reflects the aspect ratio of the roll in the convection problem.

[0091] Under this equation, the formed three-dimensional trajectory is as Figure 2 shown.

[0092] S3: Based on the differential equations of the complete Lorenz system, using the three-axis position deviations of the aircraft relative to the nominal trajectory in the aircraft re-entry system as inputs, calculate the desired three-axis velocity increments of the aircraft in the re-entry system;

[0093] The calculation process of the desired three-axis velocity increments of the aircraft in the re-entry system described in S3 is as follows:

[0094] S301: Taking the three-axis position deviations of the aircraft in the re-entry system as inputs and the desired three-axis velocity increments of the aircraft in the re-entry system as outputs, the differential equations of the complete Lorenz system are rewritten as follows:

[0095]

[0096] In Equation (2):

[0097] [Δx, Δy, Δz] T is the three-axis position deviation of the aircraft in the re-entry system;

[0098] ΔV = [ΔV x , ΔV y , ΔV z T is the desired three-axis velocity increment of the aircraft in the re-entry system;

[0099] S302: Introduce the range control parameters [R x , R y , R z T and the chaos construction speed control parameter k to obtain the new differential equations as follows:

[0100]

[0101] S303: According to the maneuver range requirements, maneuver time requirements, and overload constraints, set the parameters of the Lorenz system

[0102] Pr = 10, Ra = 28, β = 8 / 3, R x = 5000, R z = 10000, R y = 5000, k = 100, to obtain the final input-output relationship as follows:

[0103]

[0104] S304: Through the three-axis position deviations [Δx, Δy, Δz] of the aircraft in the re-entry system calculated at each simulation step T , that is, the desired three-axis velocity increments of the aircraft in the re-entry system are obtained

[0105] ΔV = [ΔV x, ΔV y , ΔV z T .

[0106] S4: Combine the state variables of the nominal trajectory at the corresponding moment and the expected velocity increment, calculate the three-axis expected velocity of the chaotic trajectory reentry system, and combine the actual velocity in the current state. Generate the lateral additional overload and longitudinal additional overload of the aircraft in the chaotic trajectory reentry system by the PD tracking method;

[0107] The calculation process of the three-axis expected velocity of the chaotic trajectory reentry system described in S4 is as follows:

[0108] S401: Define the state variables of the nominal trajectory at the current moment as [θ, φ, h, V, γ, ψ] T 0, where: θ is the longitude, φ is the latitude, h is the altitude, V is the velocity, γ is the track angle, and ψ is the course angle. The velocity vector in the north-east-down coordinate system is obtained as:

[0109]

[0110] S402: Convert the velocity vector in the north-east-down coordinate system to the aircraft reentry system for expression as follows:

[0111]

[0112] In Equation (6):

[0113] is the attitude transformation matrix of the aircraft reentry system relative to the geocentric inertial coordinate system;

[0114] is the attitude transformation matrix of the geocentric inertial coordinate system relative to the north-east-down coordinate system;

[0115] are the velocity components of the nominal trajectory at the current moment in the reentry system;

[0116] S403: Similarly to S401 - S402, define the state variables of the current chaotic flight as [θ, φ, h, V, γ, ψ] T , and obtain the velocity components of the current chaotic flight in the reentry system

[0117] S404: From the velocity components of the nominal trajectory at the current moment in the reentry system and the expected three-axis velocity increment of the aircraft reentry system ΔV = [ΔV x , ΔV y , ΔV z T obtain the expected velocity components of the chaotic flight:

[0118] ​​

[0119] S405: The expected velocity component of chaotic flight and the velocity component of chaotic flight at the current moment in the reentry system Obtain the additional lateral overload Δn through the PD tracking method z and the additional longitudinal overload Δn y :

[0120]

[0121] In Equation (8):

[0122] K p is the proportionality coefficient;

[0123] K d is the differential coefficient;

[0124] is the y-axis velocity component of the actual flight in the reentry system at the previous simulation step;

[0125] is the expected y-axis velocity component of the reentry system at the previous simulation step;

[0126] is the z-axis velocity component of the actual flight in the reentry system at the previous simulation step;

[0127] is the expected z-axis velocity component of the reentry system at the previous simulation step.

[0128] S5: Combine the nominal ballistic maneuver overload and the additional overload, solve for the required maneuver overload of chaotic maneuver flight, inversely solve the corresponding angle of attack and bank angle, substitute them into the reentry glide dynamics model, and obtain the flight state variables of the next step through the fourth-order Runge-Kutta integration method;

[0129] S501: Calculate the lateral overload n z0 and the longitudinal overload n y0 from the nominal ballistic state variables, and combine the additional lateral overload Δn z and the additional longitudinal overload Δn y to obtain the required lateral overload n z and the required longitudinal overload n y :

[0130]

[0131] S502: Calculate the required lateral overload n z and the required longitudinal overload n y of the gliding vehicle:

[0132]

[0133] In Equation (10):

[0134] is the dynamic pressure of the aircraft, where: ρ is the atmospheric density and V is the speed of the aircraft;

[0135] S is the reference aerodynamic area of the aircraft;

[0136] C L is the lift coefficient and is a function of the angle of attack α;

[0137] C D is the drag coefficient and is a function of the angle of attack α;

[0138] mg is the gravity force acting on the aircraft;

[0139] S503: According to Equation (9), the required lateral overload n z and the required longitudinal overload n y at this time are known. The corresponding angle of attack α and bank angle σ are obtained by inverse solution through the Newton iteration method;

[0140] S504: Combining the state variables [θ, φ, h, V, γ, ψ] T of the current chaotic flight, the angle of attack α and the bank angle σ, the differential values of each state variable are calculated from the reentry glide dynamics equations:

[0141]

[0142] In Equation (11):

[0143] r = R0 + h is the distance from the center of the earth to the aircraft, where: R0 is the radius of the earth;

[0144] g is the acceleration due to gravity of the earth;

[0145] m is the weight of the aircraft;

[0146] S505: According to the differential values of each state variable the next state variables are obtained through the fourth-order Runge-Kutta integration method, thereby completing the update of the aircraft state.

[0147] S6: Repeat S2 - S5 until the chaotic maneuver flight ends, completing the excitation of the chaotic flight for the aircraft.

[0148] It is obvious to those skilled in the art that the present invention is not limited to the details of the above-described exemplary embodiments, and that the present invention can be implemented in other forms without departing from the spirit or essential characteristics of the present invention. Therefore, in any regard, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Accordingly, all changes that fall within the meaning and scope of the equivalent conditions of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims involved.

[0149] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment only contains an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system, characterized in that: The method includes the following steps: S1: Select a reentry glide trajectory as the nominal trajectory for constructing the chaotic trajectory, and record the change sequence of the state variables of the nominal trajectory over time t; S2: According to the differential equations of the Lorenz system, establish the correspondence between the state variables of the nominal trajectory and the reentry dynamics state variables of the aircraft, and at the same time set the parameters of the Lorenz system to obtain the complete differential equations of the Lorenz system; S3: Based on the complete differential equations of the Lorenz system, use the three-axis position deviation of the aircraft relative to the nominal trajectory in the aircraft reentry system as the input to calculate the desired three-axis velocity increment in the aircraft reentry system; S4: Combine the state variables of the nominal trajectory at the corresponding moment and the desired velocity increment, calculate the three-axis desired velocity of the chaotic trajectory in the reentry system, and combine with the actual velocity in the current state to generate the lateral additional overload and longitudinal additional overload of the aircraft under the chaotic trajectory reentry system by the PD tracking method; S5: Combine the nominal trajectory maneuver overload and the additional overload, solve the required maneuver overload for chaotic maneuvering flight, inversely solve the corresponding angle of attack and bank angle, substitute them into the reentry glide dynamics model, and obtain the flight state variables of the next time step through the fourth-order Runge-Kutta integration method; S6: Repeat S2 - S5 until the chaotic maneuvering flight ends, and complete the chaotic flight excitation for the aircraft.

2. A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system according to claim 1, characterized in that: The complete differential equations of the Lorenz system described in S2 are as follows: In Equation (1): [x, y, z] T are the three-dimensional state variables of the Lorenz system; is the differential value corresponding to the three-dimensional state variable; Pr > 0 is the Prandtl number, related to the flow field; Ra > 0 is the Rayleigh number, related to the flow field; β > 0 is the spatial parameter, reflecting the aspect ratio of the roll in the convection problem.

3. A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system according to claim 2, characterized in that: The calculation process of the desired three-axis velocity increment of the aircraft reentry system described in S3 is as follows: S301: Take the three-axis position deviation of the aircraft reentry system as the input and the desired three-axis velocity increment of the aircraft reentry system as the output, then the complete differential equations of the Lorenz system are rewritten as follows: In Equation (2): [Δx, Δy, Δz] T is the three-axis position deviation of the aircraft reentry system; ΔV = [ΔV x , ΔV y , ΔV z T is the three-axis velocity increment of the desired aircraft reentry system;​ S302: Introduce the range control parameter [R x , R y , R z T and the chaotic construction speed control parameter k to obtain the following new differential equation:​ S303: According to the maneuver range requirement, maneuver time requirement, and overload constraint, set the parameters of the Lorenz system Pr = 10, Ra = 28, β = 8 / 3, Rx = 5000, Rz = 10000, Ry = 5000, k = 100 to obtain the final input-output relationship as follows: S304: The three-axis position deviation [Δx, Δy, Δz] of the aircraft reentry system obtained by calculating through each simulation step T , that is, the desired three-axis velocity increment ΔV of the aircraft reentry system is obtained as ΔV = [ΔV x , ΔV y , ΔV z T .​ 4. A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system according to claim 3, characterized in that: The calculation process of the three-axis desired velocity of the chaotic trajectory in the reentry system described in S4 is as follows: S401: Define the nominal ballistic state variables at the current moment as [θ, φ, h, V, γ, ψ] T 0, where: θ is the longitude, φ is the latitude, h is the altitude, V is the velocity, γ is the track angle, and ψ is the course angle. The velocity vector in the north-east-down coordinate system is obtained as follows: S402: Convert the velocity vector in the north-east-down coordinate system to the aircraft reentry system for expression as follows: In Equation (6): is the attitude transformation matrix of the aircraft reentry system relative to the geocentric inertial coordinate system; is the attitude transformation matrix of the Earth-centered inertial coordinate system relative to the north-east-down coordinate system; is the velocity component of the nominal trajectory at the current moment in the reentry system; S403: Similarly to S401 - S402, define the state variables of the current chaotic flight as [θ, φ, h, V, γ, ψ] T , and obtain the velocity components of the current chaotic flight in the reentry system S404: The velocity components of the nominal trajectory at the current moment in the reentry system and the desired three-axis velocity increment of the vehicle in the reentry system ΔV = [ΔV x , ΔV y , ΔV z T are used to obtain the desired velocity components of the chaotic flight:​ S405: Expected velocity component of chaotic flight and the velocity component of chaotic flight at the current moment in the reentry system Obtain the additional lateral overload Δn through the PD tracking method z and the additional longitudinal overload Δn y : In Equation (8): K p is the proportionality coefficient; K d is the differential coefficient; is the y-axis velocity component of the actual flight in the reentry system at the previous simulation time step; is the desired reentry system y-axis velocity component at the previous simulation time step; is the z-axis velocity component of the actual flight in the reentry system at the previous simulation time step; is the desired reentry system z-axis velocity component at the previous simulation time step.

5. A method for exciting the chaotic state of a gliding aircraft based on the Lorenz system according to claim 4, characterized in that: The said S5 includes the following steps: S501: Calculate the lateral overload n from the nominal ballistic state variables z0 and the longitudinal overload n y0 , combined with the additional lateral overload Δn z and the additional longitudinal overload Δn y to obtain the required lateral overload n z and the required longitudinal overload n y for chaotic maneuvering flight: S502: Calculate the required lateral overload n of the gliding aircraft z and the required longitudinal overload n y : In Equation (10): is the dynamic pressure of the aircraft, where: ρ is the atmospheric density and V is the speed of the aircraft; S is the reference aerodynamic area of the aircraft; C L is the lift coefficient and is a function of the angle of attack α; C D is the drag coefficient and is a function of the angle of attack α; mg is the gravity force received by the aircraft; S503: According to Equation (9), the required lateral overload n z and the required longitudinal overload n y at this time are known, and the corresponding angle of attack α and bank angle σ are solved by the Newton iteration method in reverse; S504: Combine the state variables [θ, φ, h, V, γ, ψ] of the current chaotic flight T , angle of attack α, and bank angle σ, and calculate the differential values of each state variable from the reentry glide dynamics equation: In Equation (11): r = R0 + h is the distance from the center of the earth to the aircraft, where: R0 is the radius of the earth; g is the acceleration of gravity of the earth; m is the weight of the aircraft; S505: According to the differential values of each state variable The next state variable is obtained through the fourth-order Runge-Kutta integration method, thereby completing the update of the aircraft state.

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