Hypersonic gliding trajectory high-precision analytical solution method capable of considering lateral maneuver influence

Abstract

The invention provides a hypersonic gliding trajectory high-precision analytical solution method capable of considering lateral maneuver influence. The hypersonic gliding trajectory high-precision analytical solution method comprises the following steps: step 1, establishing a reentry flight dynamics model; 2, establishing an auxiliary geocentric rotating coordinate system and a generalized dynamical model; 3, simplifying the dynamic model; replacing an independent variable in the model equation with energy from time, and further simplifying the equation according to stable gliding trajectory characteristics; step 4, performing hierarchical processing on the equation; a regular perturbation method is applied, and kinetic models about a zero-order state, a first-order state and a second-order state are obtained after arrangement; 5, analyzing and solving the linear time-varying system; sequentially expressing the zero-order kinetic model, the first-order kinetic model and the second-order kinetic model as a linear time-varying system form, and solving by using a matrix spectrum decomposition method to obtain an analytical solution expression; and for integral terms in the formula, a Newton interpolation polynomial approximation integrand function is used, and an analytical solution in a complete analytical form is obtained after solving.

Description

Technical Field

[0001] The present invention relates to a high-precision analytical solution for a hypersonic gliding trajectory capable of taking into account the influence of lateral maneuvers, and belongs to the field of aerospace technology. Background Art

[0002] During a hypersonic glide vehicle's flight mission, it must glide for extended periods within the atmosphere at altitudes between 20 and 70 kilometers, with glide distances reaching tens of thousands of kilometers. It also possesses robust lateral maneuverability, with bank maneuvers reaching thousands of kilometers. However, this high-speed flight environment presents severe aerodynamic ablation issues and cumulative trajectory errors. To effectively address these challenges, designing a guidance law capable of rapid online trajectory reconstruction during flight is a key strategy. The key to achieving this strategy lies in obtaining a high-precision analytical solution for the hypersonic glide trajectory. While the lateral maneuver range of conventional reentry gliding flights generally does not exceed 1,500 kilometers, the bank maneuver range in the flight scenario considered by this invention reaches as high as 4,000 kilometers. This significantly increases the coupling effect between longitudinal and lateral motion and significantly increases the nonlinearity of the reentry flight dynamics model. Therefore, the required three-dimensional analytical solution for the hypersonic glide trajectory must be able to adapt to the complex flight conditions of the vehicle during large-scale bank maneuvers and meet the guidance law's stringent requirements for trajectory reconstruction accuracy. Summary of the Invention

[0003] To this end, the present invention proposes a high-precision analytical solution for hypersonic glide trajectories that can take into account the effects of lateral maneuvers, including the following steps:

[0004] Step 1: Establish a reentry flight dynamics model. A force analysis of the hypersonic glide vehicle's reentry flight is conducted in both the Earth-centered, Earth-fixed coordinate system and the local north-east coordinate system, which account for the Earth's curvature and rotation. Six equations are used to develop a reentry flight dynamics model for a rotating Earth.

[0005] Step 2: Establish an auxiliary geocentric rotating coordinate system and a generalized dynamic model. To simplify the dynamic model, a generalized equator fixed to the Earth is created along the initial flight direction. An auxiliary geocentric rotating coordinate system is defined based on this equator. Generalized longitude, generalized latitude, and generalized heading angle are defined within this coordinate system. Based on the characteristics of these three generalized states, the generalized dynamic model is derived by analogy with conventional equations.

[0006] Step 3: Simplify the dynamic model. Replace the independent variable in the model equation with energy instead of time, and further simplify the equation based on the characteristics of the steady glide trajectory to obtain a dynamic model with longitudinal range, lateral range, and heading angle as independent variables that is convenient for subsequent processing.

[0007] Step 4: Perform order-based processing on the equations. Applying the principles of the canonical perturbation method, we obtain dynamic models for the zero-order, first-order, and second-order states. Although these models are complex in form, they can all be expressed as special linear time-varying systems, which can then be solved using spectral decomposition analysis.

[0008] Step 5: Analytically solve the linear time-varying system. Represent the zero-order, first-order, and second-order dynamic models as linear time-varying systems, and use matrix spectral decomposition to obtain analytical solutions. For the integral terms, approximate the integrand using Newton interpolation polynomials. Solving this solution yields a fully analytical solution, which includes steps 5.1 through 5.3.

[0009] Step 5.1: First, design the longitudinal lift-to-drag ratio and the lateral lift-to-drag ratio as quadratic polynomials with respect to energy. Substituting these into the zero-order longitudinal range dynamics model allows direct integration to obtain a zero-order longitudinal range analytical solution. For the zero-order lateral range and heading angle dynamics models, solve their linear time-varying systems using matrix spectral decomposition to obtain analytical solutions including integral terms. Then, approximate the integrands using Newton interpolation polynomials to obtain fully analytical zero-order lateral range and heading angle solutions.

[0010] Step 5.2: For the first-order longitudinal range dynamics model, although it contains an integral term, the integrand only contains zero-order states. Therefore, the zero-order analytical solution directly solved is substituted in, and the integrand is approximated using Newton interpolation polynomials to obtain the first-order longitudinal range analytical solution. For the first-order lateral range and heading angle dynamics models, the matrix spectral decomposition method is also used to solve the linear time-varying system of the two, and the integrand is approximated using Newton interpolation polynomials to obtain the first-order lateral range and heading angle analytical solutions.

[0011] Step 5.3: For the second-order longitudinal range dynamics model, the integrand in the integral term contains only zero-order and first-order states. Substitute the previously obtained zero-order and first-order analytical solutions directly into the integrand and approximate the integrand using Newton interpolation polynomials to obtain a fully analytical solution for the second-order longitudinal range. For the second-order lateral range and heading angle dynamics models, use the matrix spectral decomposition method to solve their linear time-varying systems. Then, approximate the integrand using Newton interpolation polynomials to obtain fully analytical solutions for the second-order lateral range and heading angle.

[0012] The advantages and beneficial effects of the present invention are:

[0013] The present invention proposes a high-precision analytical solution for a hypersonic glide trajectory that can take into account the effects of lateral maneuvers. First, a new reentry flight dynamics model based on generalized longitude and latitude coordinates is constructed based on the motion characteristics of the aircraft under large-bank maneuvers. Secondly, based on a comprehensive consideration of factors such as longitudinal and transverse coupling effects, earth curvature, and earth rotation, the model is reasonably simplified to form a reduced-order dynamics model with longitudinal range, transverse range, and heading angle as state variables, which still maintains nonlinear characteristics. Finally, the nonlinear model is decomposed into three linear time-varying subsystems by the regularized perturbation method, and analytically solved with the help of the matrix spectral decomposition method, successfully obtaining a high-precision trajectory analytical solution. Based on this analytical solution, it is possible to accurately predict the reentry trajectory of a hypersonic glide vehicle, thereby providing key technical support for the guidance and control of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram for defining the generalized equator and the auxiliary geocentric rotating coordinate system AGR.

[0015] Figure 2 Ground trajectory diagrams for ballistic simulation and two analytical solutions. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention is further described in detail with reference to the accompanying drawings and technical solutions.

[0017] The following is a further description of the high-precision analytical solution of the hypersonic glide trajectory that can take into account the influence of lateral maneuvers proposed by the present invention:

[0018] Step 1: Establish a re-entry flight dynamics model for a hypersonic glide vehicle. Based on force analysis and assuming that the earth is a uniformly rotating homogeneous sphere, the center-of-mass motion equation of the vehicle is obtained as follows:

[0019]

[0020] Where λ and φ are the longitude and latitude of the center of mass of the aircraft, H is the altitude of the aircraft, V is the speed relative to the rotating earth, γ is the local ballistic inclination angle, ψ is the local heading angle (north-east is positive), m is the mass of the aircraft, σ is the roll angle, D and L are the aerodynamic drag and aerodynamic lift, respectively, g = μ / (R e +H) 2 is the local gravitational acceleration, μ=3.986005×10 14 m 3 / s 2 is the Earth's gravitational constant, R e =6356766m,ω e=7.292116e-5rad / s are the average radius of the Earth and the angular velocity of the Earth's rotation respectively.

[0021] Step 2: To simplify the dynamic model later, we first establish an auxiliary geocentric rotation coordinate system. A generalized equator fixed to the earth is created along the initial flight direction, where M0 represents the initial position of the aircraft. Based on this, we define an auxiliary geocentric rotation (AGR) coordinate system. Among them, C E It is the center of the earth. The axis points to the initial re-entry point, The axis lies in the generalized equatorial plane and is aligned with The axes are perpendicular, The axis is perpendicular to the generalized equatorial plane. Then, taking the generalized equator as the reference and M0 as the zero point, we can define the generalized longitude and latitude by imitating the definition of traditional longitude and latitude. Therefore, in the AGR coordinate system, we can use the height H, generalized longitude and broad latitude Describe the position information of the aircraft, and use the speed V, ballistic inclination γ and generalized heading angle Describes the velocity vector information of the aircraft, where the generalized longitude λ and generalized latitude like Figure 1 As shown, the generalized heading angle is the angle between the component of the velocity vector in the local horizontal plane and the local generalized meridian, which can then be used to define the longitudinal range. He Hengcheng

[0022] Next, we can build a generalized dynamic model in this coordinate system. Since the aircraft flies toward the target approximately along the generalized equator, we have x C ≈0 and Therefore, using generalized states to describe the motion of the aircraft is beneficial to improving the linearization accuracy of the dynamic model. Similar to the conventional equations (Formulas (1), (2), and (6)), and ignoring the centrifugal force term and the ballistic inclination term with very small values, the longitudinal range x can be obtained. D , horizontal range x C and generalized heading angle The equation is as follows:

[0023]

[0024] Step 3: Simplify the dynamic model.

[0025] Let the mechanical energy E per unit mass be:

[0026]

[0027] The time rate of change of mechanical energy per unit mass is After reasonable simplification, we can get:

[0028]

[0029] Dividing formulas (1), (2), and (6) by formula (11) and approximating the trajectory inclination to zero, we can obtain the model with energy as the independent variable:

[0030]

[0031] For simplicity, we define the longitudinal lift L1 = Lcos(σ), the lateral lift L2 = Lsin(σ), and the mean center of the earth R * =R e +H middle , where H middle =(H0+H f ) / 2, is the initial gliding height H0 and the terminal height H f The average height obtained by solution.

[0032] The long-period trajectory oscillation phenomenon can be effectively suppressed by using trajectory damping control technology. Therefore, assuming that the trajectory inclination angle change rate γ≈0 and the trajectory inclination angle γ≈0, formula (5) can be obtained after reasonable simplification and algebraic transformation:

[0033]

[0034] Substituting formula (15) into formulas (12), (13), and (14), after a series of derivations and simplifications, we obtain a set of third-order equations that need to be solved for the coupled longitudinal range, transverse range, and generalized heading angle:

[0035]

[0036] Step 4: Use the regular perturbation method to perform order processing on the model to obtain the dynamic models of the zero-order state, the first-order state and the second-order state.

[0037] In step 3, the simplified generalized dynamic model (Formulas (16)-(18)) has been obtained. However, it can be found that the formula is still very complicated, which is reflected in (1) the serious coupling between longitudinal and lateral motion under large lateral maneuvers; (2) the strong nonlinear term 2R in the denominator * Vω e cos(φ)sin(ψ). Therefore, canonical perturbation theory is applied here for further processing.

[0038] First construct a linear auxiliary function:

[0039] f d (E)≈c0+c1E(19)

[0040] Among them, the coefficients c0 and c1 satisfy:

[0041]

[0042] φ0, ψ0 represent the initial latitude and heading angle respectively, φ f ,ψ f Represent the terminal latitude and heading angle respectively.

[0043] According to the regular perturbation principle and reasonably ignoring the small quantities in the formula, formulas (16)-(18) can be rewritten as:

[0044]

[0045] Among them, ε=1. This quantity has no actual physical meaning and is only needed to classify the above system according to the principle of perturbation method.

[0046] Next, by applying the perturbation method, we can obtain the following dynamic models for the zero-order state (superscript 0), the first-order state (superscript 1), and the second-order state (superscript 2). The zero-order dynamic model is as follows:

[0047]

[0048] The first-order kinetic model is as follows:

[0049]

[0050] The second-order kinetic model is as follows:

[0051]

[0052] Where, φ GE Represents the latitude of a point on the generalized equator, used to replace the latitude on the trajectory; ψ GE Represents the heading angle corresponding to the generalized equator, which is used to replace the heading angle function on the trajectory; h(E,ε) is a mathematical auxiliary function, which is defined as follows:

[0053]

[0054] Although the above model is very complex, it can be expressed as a special linear time-varying system and solved using the matrix spectral analysis method.

[0055] Step 5, solve the analytical solutions of the zero-order, first-order and second-order dynamic models obtained by the above decoupling.

[0056] Step 5.1: First, find the analytical solution to the zero-order dynamic model. From the equations obtained above, we can see that the longitudinal lift-to-drag ratio L1 / D and the lateral lift-to-drag ratio L2 / D have a significant impact on flight motion. In general trajectory planning, the reference profile is usually designed as a piecewise function composed of constants, linear functions, and quadratic polynomials:

[0057]

[0058] Where a2 = 1.57 × 10 -15 、a1=1.497×10 -7 , a0=4.862, b2=-8.78×10 -16 b1 = -8.29 × 10 -8 , b0=0.857 are the reference profile parameters designed in advance.

[0059] Since the zero-order longitudinal equation (Formula (24)) is relatively independent, we first integrate it and obtain the zero-order longitudinal analytical solution as follows:

[0060]

[0061] Among them, E0 is the initial energy.

[0062] Next, we solve the analytical solution of the zero-order cross range and heading angle. Combining formulas (28) and (29), we can express it as follows:

[0063]

[0064] Where A is a matrix containing the Earth radius component:

[0065]

[0066] f1(E), f2(E), f3(E), f4(E) are shorthand notations for some complex terms, which are expanded as follows:

[0067]

[0068] Using the matrix spectral decomposition method to solve Equation (36), the analytical solutions of the cross range and heading angle can be summarized as follows:

[0069]

[0070] Where, They represent the initial values of the zero-order cross range and the zero-order generalized heading angle, respectively. f5(E,E0) is specifically expanded as follows:

[0071]

[0072] The term containing the lateral lift-to-drag ratio modulus is simplified as a mathematical function below:

[0073]

[0074] Here are Among them, sgn0 represents the initial maneuvering direction of the aircraft, n BR Represents the number of roll reversals that have occurred.

[0075] The integrand in the integral terms in equations (39) and (40) is simply expressed as g1(E,x E ), g2(E,x E ), g3(E,x E ), g4(E,x E ):

[0076]

[0077] Among them, h1(x E ,E0),h2(x E ,E0),h3(x E ,E0),h4(x E ,E0) is also a shorthand function for some complex terms:

[0078]

[0079] Using the roots of the 10th-order Chebyshev polynomial {ξ N(i) , i=0,2,…,9} is the Newton interpolation polynomial n1(x E )、n2(x E )、n3(x E ) and n4(x E ), respectively in [E f ,E0] interval segment approximate function h1(x E ,E0),h2(x E ,E0)、h3(x E ,E0) and h4(x E ,E0), we get:

[0080]

[0081] In the formula, {a Ni(j) , i=1,2,…,14;j=0,1,…,9} are the coefficients of Newton interpolation polynomials, i represents the sequence number of Newton interpolation polynomials of different fitting quantities, and j represents the order of coefficients in each Newton polynomial, for example, a N1(0) Represents the first fitting quantity n1(x E ) is the coefficient of the 0th order term.

[0082] Using the above approximate polynomial, we can solve the integral form of each term, which can be expressed as:

[0083]

[0084] Among them, N1(x E ,E0)~N4(x E ,E0) represent the integral forms of the corresponding four approximate polynomials.

[0085] This way we can obtain the zero-order analytical solution in a completely analytical form.

[0086] Considering the roll reversal, we construct a sequence {E Node(j) ,j=0,1,…,n BR +1}. Therefore, formulas (39) and (40) can be restated as:

[0087]

[0088] Among them, N1(E,E0), N2(E,E0), N3(E node(j) ,E node(j-1) ), N4(E node(j) ,E node(j-1) ) is defined as Eq. (46), where E represents the current energy when calculating the analytical solution, E0 represents the initial energy when calculating the analytical solution, and E node(j) 、E node(j-1) Represents the energy at key points such as the starting point, end point, and roll reversal point sequence. Since the integrand near these key points will undergo sudden changes, it is necessary to integrate separately between these key points to improve the accuracy of the analytical solution.

[0089] Thus, the fully analytical form of the zero-order cross range and heading angle is obtained.

[0090] Step 5.2, solve the analytical solution of the first-order kinetic model. Here we first look at the first-order longitudinal analytical solution. According to formula (27):

[0091]

[0092] The integrand can be viewed as a function of only energy h5(x E ,E0):

[0093]

[0094] Among them, h(E,0) can be substituted into formula (33) to obtain the calculated value.

[0095] Similarly, the Newton interpolation polynomial with the roots of the 10th-order Chebyshev polynomial as sampling points can be used to approximate the above integrand, similar to the previous N1(E, E0) to N4(E, E0), and the integral form of Equation (49) can be rewritten as:

[0096]

[0097] For the first-order analytical solution of the cross range and heading angle, a special linear time-varying system can be obtained:

[0098]

[0099] Among them, f7(E) and f8(E) are functions of energy E only:

[0100]

[0101] Using the matrix spectral decomposition method to solve equation (52) we can obtain:

[0102]

[0103] Use Newton polynomials to approximate the integrands in equations (55) and (56). Define g5(E,x E ), g6(E,x E )for:

[0104]

[0105] Decompose the above formula:

[0106]

[0107] in,

[0108]

[0109] Using the Newton polynomial with the roots of the 10th-order Chebyshev polynomial as sampling points, h6(x E )~h9(x E ) is fitted to n6(x E )~n9(x E ), which is the following approximate function:

[0110]

[0111] Using the same approximate polynomial, we can get h6(x E ,E0)~h9(x E ,E0) in the form of N6(E,E0) to N9(E,E0):

[0112]

[0113] The fully analytical first-order cross-range and heading angle analytical solutions can be expressed as:

[0114]

[0115] Step 5.3, solve the analytical solution of the second-order kinetic model. Since the right side of the second-order longitudinal equation (Formula (30)) only contains zero-order and first-order states, we first find the analytical solution of the longitudinal equation, as follows:

[0116]

[0117] The zero-order state and the first-order state in the above equation can be calculated using the zero-order analytical solution and the first-order analytical solution, respectively. Therefore, the integrand can also be regarded as a function of energy only, and can be approximated using Newton polynomials. First, define the integrand on the right side of the equal sign in equation (65) as:

[0118]

[0119] Use the approximation polynomial for h 10 (x E ,E0) and integrate to get N 10 (E,E0):

[0120]

[0121] So we have:

[0122]

[0123] For the second-order range and heading angle dynamics model, a special linear time-varying system is also established:

[0124]

[0125] Among them, f9(E),f 10 (E) is the extracted and Unrelated expressions:

[0126]

[0127]

[0128] Here, φ GE Represents the latitude of a point on the generalized equator, used to replace the latitude on the trajectory; ψ GE Represents the heading angle corresponding to the generalized equator, which is used to replace the heading angle on the trajectory.

[0129] Similarly, the second-order solution expressions of the traverse range and generalized heading angle can be obtained by using the spectral decomposition method:

[0130]

[0131] For the sake of simplicity in subsequent expressions, the integrand in the formula is also recorded as h 11 (x E ,E0),h 12 (x E ,E0),h 13 (x E ,E0),h 14 (x E ,E0):

[0132]

[0133] Approximate h using Newton polynomials with roots of 10th-order Chebyshev polynomials as sampling points 11 (x E ,E0)~h 14 (x E ,E0), as follows:

[0134]

[0135] By integrating the above equations, equations (72) and (73) can be restated as:

[0136]

[0137]

[0138] Among them, N 11 (E,E0)~N 14 (E,E0) is also obtained using the approximate polynomial h 11 (x E ,E0)~h 14 (x E ,E0) in the form of integration:

[0139]

[0140] Finally, I would like to emphasize again that the coefficients {a Ni(j) ,i=1,2,…,14;j=0,1,…,9} are only related to E0 and only need to be solved once. There is no need to recalculate these coefficients for different E. In addition, the process of solving these coefficients is similar to formulas (47) and (48), and ξ Q(i) Again, this only needs to be calculated once in advance.

[0141] So far, we have completed the derivation of the zero-order, first-order, and second-order analytical solutions.

[0142] In order to prove the universality of the guidance method, 7 examples with different flight directions are considered here, in which the mass and aerodynamic model of the aircraft are all CAV-H. Although the present invention involves many formulas and parameters, most of them are polynomial fitting coefficients, which can be directly generated by the corresponding solver without manual setting. Next, they are compared with ballistic simulation and existing analytical solutions. The common conditions of these 7 cases are λ0=0deg, φ0=50deg,

[0143] V0=7000m / s, γ0=0deg, E0=-3.579×10 7 J / kg and E f =-6×10 7 The initial heading angles and terminal results of these seven examples are shown in Table 1.

[0144] Table 1 Comparison between analytical solution and trajectory simulation terminal results

[0145]

[0146]

[0147] The simulation results are shown in Table 1 and Figure 2 As shown in Table 1, the analytical solution has a significant computational efficiency advantage over the trajectory simulation, which will greatly improve the efficiency of trajectory planning and has great value in online guidance. Figure 2 As can be seen in the figure, because the new analytical solution fully considers the effects of longitudinal and lateral coupling, its accuracy is very high. Even under extreme maneuvering conditions, the new analytical solution's results are almost consistent with the ballistic simulation. Here, the terminal position error of the new analytical solution is kept within 200 kilometers, while the error of the existing analytical solution is as high as 3000 kilometers.

Claims

1. A high-precision analytical solution method for hypersonic glide trajectories that can take into account the effects of lateral maneuvers, characterized by: The steps include: Step 1: Establish a reentry flight dynamics model. Perform a force analysis of the hypersonic glide vehicle's reentry flight in both the Earth-centered, Earth-fixed coordinate system and the local North-East coordinate system, taking into account the Earth's curvature and rotation, to obtain a reentry flight dynamics model under the background of a rotating Earth. Step 2: Establish an auxiliary geocentric rotating coordinate system and a generalized dynamic model. To simplify the dynamic model, a generalized equator fixed to the Earth is created along the initial flight direction. An auxiliary geocentric rotating coordinate system is defined based on this equator. In this coordinate system, generalized longitude, generalized latitude, and generalized heading angle are defined to obtain the generalized dynamic model. Step 3: Simplify the dynamic model; replace the independent variable in the model equation with energy instead of time, and further simplify the equation based on the characteristics of the steady glide trajectory to obtain a dynamic model with longitudinal range, lateral range and heading angle as independent variables that is convenient for subsequent processing; Step 4: Perform order processing on the equations; apply the canonical perturbation method and obtain the dynamic models of the zero-order state, the first-order state, and the second-order state after sorting; Step 5: Analytically solve the linear time-varying system; express the zero-order, first-order, and second-order dynamic models in the form of linear time-varying systems in turn, and use the matrix spectral decomposition method to obtain the analytical solution expression; for the integral term in the formula, use Newton interpolation polynomials to approximate the integrand, and after solving, obtain the analytical solution in a completely analytical form.

2. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1, characterized in that: In step 1, specifically: establish a hypersonic glide vehicle reentry flight dynamics model, assume that the earth is a uniformly rotating homogeneous sphere, and obtain the center of mass motion equation of the vehicle as follows: Where λ and φ are the longitude and latitude of the center of mass of the aircraft, H is the altitude of the aircraft, V is the speed relative to the rotating earth, γ is the local ballistic inclination angle, ψ is the local heading angle, m is the mass of the aircraft, σ is the roll angle, D and L are the aerodynamic drag and aerodynamic lift, respectively, g = μ / (R e +H) 2 is the local gravitational acceleration, μ=3.986005×10 14 m 3 / s 2 is the Earth's gravitational constant, R e =6356766m,ω e =7.292116e-5rad / s are the average radius of the Earth and the angular velocity of the Earth's rotation respectively.

3. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1 is characterized by: In step 2, specifically: establish an auxiliary geocentric rotation coordinate system; create a generalized equator fixed to the earth along the initial flight direction, where M0 represents the initial position of the aircraft; define an auxiliary geocentric rotation (AGR) coordinate system based on this Among them, C E It is the center of the earth. The axis points to the initial reentry point, The axis lies in the generalized equatorial plane and is aligned with The axes are perpendicular, The axis is perpendicular to the generalized equatorial plane; then, taking the generalized equator as the reference and M0 as the zero point, the generalized longitude and latitude are defined by imitating the definition of traditional longitude and latitude; therefore, in the AGR coordinate system, using the height H, generalized longitude and broad latitude Describe the position information of the aircraft using velocity V, ballistic inclination γ and generalized heading angle Describe the velocity vector information of the aircraft and define the longitudinal range He Hengcheng Since the aircraft flies toward the target approximately along the generalized equator, there is x C ≈0 and Using generalized states to describe the motion of the aircraft is beneficial to improving the linearization accuracy of the dynamic model; the centrifugal force term and the ballistic inclination term with very small values are reasonably ignored to obtain the longitudinal range x D , horizontal range x C and generalized heading angle The equation is as follows:

4. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1, characterized in that: In step 3, specifically: simplify the dynamic model and let the mechanical energy E per unit mass be: The time rate of change of mechanical energy per unit mass is After reasonable simplification, we get: After approximating the trajectory inclination to 0, the model with energy as the independent variable is obtained: Define longitudinal lift L1 = Lcos(σ), lateral lift L2 = Lsin(σ) and mean center of the earth R * =R e +H middle , where H middle =(H0+H f ) / 2, is the initial gliding height H0 and the terminal height H f The average height obtained by solution; Assume the trajectory inclination rate of change and the ballistic inclination angle γ≈0, after reasonable simplification and algebraic transformation, we get: A set of third-order equations that need to be solved for the coupled longitudinal range, transverse range, and generalized heading angle are obtained:

5. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 4, characterized in that: In step 4, specifically: Apply regularized perturbation method for further processing; First construct a linear auxiliary function: f d (E)≈c0+c1E(19) Among them, the coefficients c0 and c1 satisfy: φ0, ψ0 represent the initial latitude and heading angle respectively, φ f ,ψ f Represent the terminal latitude and heading angle respectively; According to the regular perturbation method and reasonably ignoring the small quantities in the formula, formulas (16)-(18) are rewritten as: Among them, ε = 1. This quantity has no actual physical meaning and is only needed to classify the above system according to the principle of perturbation method. Next, applying the perturbation method principle, we obtain the following dynamic model for the zero-order state (with a superscript of 0), the first-order state (with a superscript of 1), and the second-order state (with a superscript of 2). The zero-order dynamic model is as follows: The first-order kinetic model is as follows: The second-order kinetic model is as follows: Where, φ GE Represents the latitude of a point on the generalized equator, used to replace the latitude on the trajectory; ψ GE Represents the heading angle corresponding to the generalized equator, which is used to replace the heading angle function on the trajectory; h(E,ε) is a mathematical auxiliary function, which is defined as follows:

6. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1, characterized in that: In step 5, the following steps are further performed: first, the longitudinal lift-to-drag ratio and the lateral lift-to-drag ratio are respectively designed as quadratic polynomials with respect to energy, and the equations are brought into the zero-order longitudinal range dynamics model for direct integration to obtain the zero-order longitudinal range analytical solution; for the zero-order lateral range and heading angle dynamics models, the linear time-varying systems of the two need to be solved by the matrix spectral decomposition method to obtain the analytical solution including the integral term, and then the integrand is approximated by using the Newton interpolation polynomial to calculate the fully analytical zero-order lateral range and heading angle analytical solutions.

7. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1, characterized in that: In step 5, it further includes: for the first-order longitudinal range dynamics model, the zero-order analytical solution directly solved is brought in, and the integrand is approximated by Newton interpolation polynomials in the same way to solve the first-order longitudinal range analytical solution of the full analytical solution; for the first-order lateral range and heading angle dynamics models, the linear time-varying systems of the two are solved by the matrix spectral decomposition method in the same way, and the integrand is approximated by Newton interpolation polynomials to calculate the full analytical first-order lateral range and heading angle analytical solutions.

8. The high-precision analytical solution method for hypersonic glide trajectories capable of considering the influence of lateral maneuvers according to claim 1, characterized in that: In step 5, it further includes: for the second-order longitudinal range dynamics model, the integrand in the integral term only contains zero-order and first-order states, directly bringing the previously obtained zero-order and first-order analytical solutions into play, and using Newton interpolation polynomials to approximate the integrand to obtain a fully analytical second-order longitudinal range analytical solution; for the second-order lateral range and heading angle dynamics model, using the matrix spectral decomposition method to solve the linear time-varying systems of the two, and then using Newton interpolation polynomials to approximate the integrand to obtain a fully analytical second-order lateral range and heading angle analytical solution.

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