A general translational point mission orbit design method

Abstract

The application discloses a general-purpose mean motion mission orbit design method, comprising the following steps: defining a target three-body system and other celestial bodies affecting the target three-body system; determining a first-order ordinary differential equation set for representing an ephemeris model; calculating a first coefficient set according to ephemeris of the target three-body system and the other celestial bodies at a current time; determining a second coefficient set, and determining a third coefficient set according to the first coefficient set and the second coefficient set; substituting the third coefficient set into the first-order ordinary differential equation set to obtain a general-purpose ephemeris model; and based on the general-purpose ephemeris model, adopting a self-adaptive variable step size homotopy iteration strategy to obtain mean motion mission orbit parameters meeting mission orbit design requirements through iterative calculation. The method disclosed by the application solves the problem that a simple model solution is not convergent in a complex model by establishing a link between a circular restricted three-body model and a high-precision ephemeris model, and adopting a smooth transition and gradual approximation method.

Description

Technical Field

[0001] This invention belongs to the field of deep space exploration orbit design technology, and in particular relates to a general translational point mission orbit design method. Background Technology

[0002] The design of translational point orbits has received increasing attention in the industry in recent years. Currently, a relatively complete and mature design process for translational point orbits has been established, achieving good results in practice. The existing design process for translational point orbits is a step-by-step approximation process. First, initial values ​​are obtained using an approximate linearized series solution of a circularly constrained three-body system. Then, these values ​​are corrected by substituting them into a numerical model of the circularly constrained three-body system. Finally, the corrected parameters are further corrected by substituting them into a real force model that considers all major perturbation factors. Ultimately, a numerical solution usable in engineering is obtained.

[0003] However, after extensive engineering practice, the existing design process for translational point orbital paths has the following problems when used: 1) In practice, because the circular restricted three-body model is far too simplified compared to the real ephemeris model, the corrected results of the circular restricted three-body model fail to converge under the ephemeris model for some parameter combinations, especially some extreme parameter configurations. This necessitates manual intervention, either by introducing a relatively refined elliptical restricted three-body model as a transition between the two, or by manually adjusting the parameters and attempting iterative convergence again. This manual design mode, involving human intervention in the loop, reduces work efficiency to some extent, especially for batch processing and calculation problems, frequently causing task interruptions. Furthermore, this approach is completely unacceptable for a fully automated translational point orbit design software.

[0004] 2) Theoretically speaking, the current circular restricted three-body model is established in a rotating coordinate system, while the ephemeris model is usually established in an inertial coordinate system. The two lack consistency in terms of equation expression and data interface relationship, making it impossible to see the relationship between them, let alone make an effective and smooth transition between them. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a general method for designing translational point mission orbits. By establishing a connection between a circular restricted three-body model and a high-precision ephemeris model, and by adopting a smooth transition and stepwise approximation method, the problem of non-convergence of simple model solutions to complex models is solved.

[0006] To address the aforementioned technical problems, this invention discloses a general method for designing translational point mission trajectories, comprising: Define the target three-body system and other celestial bodies that influence it; the target three-body system refers to the system consisting of the main celestial body. The second day A gravitational system consisting of a detector and a gravitational probe; Determine the set of first-order ordinary differential equations used to characterize the ephemeris model; The first set of coefficients is calculated based on the ephemeris of the target three-body system and other celestial bodies at the current moment; Determine the second set of coefficients, and based on the first and second sets of coefficients, determine the third set of coefficients; substitute the third set of coefficients into the first-order ordinary differential equations to obtain the general ephemeris model; Based on a general ephemeris model, an adaptive variable step size homotopy iteration strategy is adopted to obtain the translational point mission orbit parameters that meet the mission orbit design requirements through iterative calculation.

[0007] In the aforementioned general translational point mission orbit design method, the target three-body system and other celestial bodies that affect the target three-body system are defined, including: For the main celestial body The second day The names are assigned values ​​respectively to clarify the target three-body system; Identify other celestial bodies that affect the defined target three-body system and assign them names.

[0008] In the aforementioned general translational point mission orbit design method, the first-order ordinary differential equations used to characterize the ephemeris model are expressed as follows:

[0009] in, This represents the set of coefficients of a system of first-order ordinary differential equations. For the set of coefficients The elements of the set, ; Represents the normalized position vector in the rotating coordinate system. , and Representing position vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized velocity vector in the rotating coordinate system. , and Representing velocity vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized time in the rotating coordinate system. Indicates the current moment. Normalized time of the rotating coordinate system relative to the current time The first derivative; Indicates the main celestial body at the current moment gravitational constant, Indicates the current moment of the second day's body The gravitational constant; Indicates the second day's body Relative Main Body The magnitude of the position vector; Represents the potential function The second-order gradient.

[0010] In the aforementioned general translational point mission trajectory design method, for the coefficient set of the first-order ordinary differential equation system... ,have: when When the coefficient set of a system of first-order ordinary differential equations is called the first coefficient set, the coefficient set is called the first coefficient set. At this point, a set of first-order ordinary differential equations is used to characterize the high-precision ephemeris model; when When the coefficient set of the first-order ordinary differential equation system is the second coefficient set, the coefficient set is... At this point, the first-order ordinary differential equation system is used to characterize the circularly restricted three-body model; when When the coefficient set of a system of first-order ordinary differential equations is the third coefficient set, the coefficient set is... At this point, the first-order ordinary differential equations are used to characterize the general ephemeris model.

[0011] In the aforementioned general translational point mission orbit design method, the ephemeris of the target three-body system and other celestial bodies at the current moment is obtained by consulting the JPL DE440 ephemeris table, including: the main celestial body at the current moment. Projection of the position vector in the inertial coordinate system The main celestial body at the current moment Projection of the velocity vector in the inertial coordinate system The main celestial body at the current moment gravitational constant The current moment of the second day Projection of the position vector in the inertial coordinate system The current moment of the second day Projection of the velocity vector in the inertial coordinate system The current moment of the second day gravitational constant Other celestial bodies at the current moment Projection of the position vector in the inertial coordinate system Other celestial bodies at the current moment Projection of the velocity vector in the inertial coordinate system Other celestial bodies at the current moment gravitational constant ;in, , This refers to the set of other celestial bodies that influence the target three-body system.

[0012] In the aforementioned general translational point mission trajectory design method, The definition of a rotating coordinate system is as follows: the origin of the rotating coordinate system is the principal celestial body. and the second body The center of mass, the x-axis is formed by the main celestial body The center of mass points to the second body The center of mass, the z-axis along the second body Orbiting the main celestial body The normal to the instantaneous two-body orbital plane, the y-axis, and the x-axis and z-axis satisfy the right-hand rule; The inertial coordinate system is defined as follows: when the target three-body system is a Sun-Earth three-body system, the inertial coordinate system is the heliocentric, centroid, and ecliptic inertial coordinate system; when the target three-body system is an Earth-Moon three-body system, the inertial coordinate system is the geocentric J2000.0 coordinate system.

[0013] In the aforementioned general translational point mission trajectory design method, based on the ephemeris of the target three-body system and other celestial bodies at the current moment, the first set of coefficients is calculated, including: Based on the ephemeris of the target three-body system and other celestial bodies at the current moment, the following intermediate parameters are calculated: according to , and The normalized gravitational constants of the target three-body system were calculated respectively. and other celestial bodies normalized gravitational constant : ,

[0014] according to , , , , , celestial bodies were calculated separately. Relative celestial bodies position vector Velocity vector and acceleration vector : , ,

[0015] in, or or , or or , ; , ; Constructing celestial bodies Relative celestial bodies Auxiliary functions :

[0016] Determine the auxiliary function first derivative Second derivative :

[0017]

[0018] according to , , , , , , , The second day's body was calculated Relative Main Body gravitational acceleration vector The second day Relative Main Body The first derivative of the gravitational acceleration vector The second day Relative Main Body The second derivative of the gravitational acceleration vector Main celestial bodies and the second body The acceleration vector of the center of mass Main celestial bodies and the second body The first derivative of the acceleration vector of the center of mass :

[0019] ,

[0020] ,

[0021] The second celestial body was calculated Relative Main Body The magnitude of the position vector , first derivative , The second derivative : , ,

[0022] The normalized time of the rotating coordinate system was calculated. relative to the current time first derivative Normalized time of rotating coordinate system relative to the current time The second derivative : ,

[0023] The second celestial body was calculated Relative Main Body angular momentum vector , model , For the current moment first derivative , For the current moment The second derivative : ,

[0024]

[0025]

[0026] The three-axis unit vectors of the rotating coordinate system are calculated as follows: , ,

[0027] in, , and These represent the unit vectors along the x-axis, y-axis, and z-axis of the rotating coordinate system, respectively. Based on the intermediate parameters obtained from the calculation: , , , , , , , , , , , , The first set of coefficients is calculated. : , ,

[0028] , ,

[0029] , , ,

[0030] ,

[0031]

[0032] in, , , These are the three constant coefficients of the high-precision ephemeris model. , , These are the three velocity influence coefficients for the high-precision ephemeris model. , , , , , These are the six positional influence coefficients of the high-precision ephemeris model. This is the gravitational field acceleration influence coefficient of the high-precision ephemeris model.

[0033] In the aforementioned general translational point mission trajectory design method, a second set of coefficients is determined, and based on the first and second sets of coefficients, a third set of coefficients is determined, including: make: , , , , , , , , , , , , Then the second set of coefficients for: ;in, , , These are the three constant coefficients of the circular restricted three-body model. , , These are the three velocity influence coefficients for the circularly constrained three-body model. , , , , , These are the six positional influence coefficients for the circular restricted three-body model. The gravitational field acceleration influence coefficient for the circularly confined three-body model; According to the first set of coefficients Second set of coefficients Determine the third set of coefficients :

[0034] in, , , These are the three constant coefficients of the general ephemeris model. , , These are the three velocity influence coefficients of the general ephemeris model. , , , , , These are the six positional influence coefficients of the general ephemeris model. The gravitational field acceleration influence coefficient of the general ephemeris model; Represents the homotopy coefficient. .

[0035] In the aforementioned general translational point mission orbit design method, substituting the third coefficient set into the first-order ordinary differential equation system yields the general ephemeris model, denoted as... , means as follows: .

[0036] In the aforementioned general translational point mission orbit design method, based on a general ephemeris model, an adaptive variable step-size homotopy iteration strategy is adopted. Through iterative calculation, the translational point mission orbit parameters that meet the mission orbit design requirements are obtained, including: S1. Based on the LP method, analytical perturbation expansion is used. Based on the north-south orientation and amplitude of the mission trajectory, the analytical high-order expansion solution of the circular restricted three-body model is employed to calculate the initial estimates of the mission trajectory parameters at the translational point. :

[0037] in, , and They represent Time position vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; express The estimated absolute time corresponding to the given moment, and having ; S2, Settings ,Will Bring into Integrating and iterating until convergence, then stopping, yields the translational point trajectory parameters convergent under the condition that the homotopy coefficient is 0. ; S3, based on a general ephemeris model, for By performing stepwise transition corrections, the parameters of the convergent translational point mission trajectory under the condition of homotopy coefficient 1 are obtained. ,include: 31) Let the adaptive step size be variable. initial value ; 32) Save the current homotopy coefficient, denoted as ; 33) According to Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 34) Update the homotopy coefficient Substitution The third set of coefficients is calculated. and substitute Iterative corrections are made during this process. 35) Determine if the iteration has converged; if the iteration has not converged, update the adaptive variable step size according to the first update strategy to obtain the updated adaptive variable step size. If the iteration converges, the adaptive variable step size is updated according to the second update strategy to obtain the updated adaptive variable step size. ; 36) Based on the updated adaptive variable step size Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 37) If If so, return to step 34) and continue iterating; if and Then update the homotopy coefficients to obtain the updated homotopy coefficients. Return to step 34) and continue iterating; if If convergence is achieved, the iteration ends, and the trajectory parameters of the translational point that converge under the condition that the homotopy coefficient is 1 are obtained. ; S4, Settings Then there is , bring in The process involves iterative differential correction until convergence, yielding the translational orbit parameters that meet the design requirements of the mission orbit. :

[0038] in, , and They represent Time position vector The components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector The components of the x, y, and z axes in the rotating coordinate system; express The absolute time corresponding to a given moment.

[0039] The present invention has the following advantages: (1) This invention discloses a general translational point mission orbit design method. By establishing the connection between the circular restricted three-body model and the high-precision ephemeris model, and by adopting a smooth transition and step-by-step approximation method, the problem of non-convergence of simple model solution to complex model is solved.

[0040] (2) This invention discloses a general translational point mission orbit design method. The high-precision ephemeris model is established in a rotating coordinate system and has a completely unified form with the circular restricted three-body model, which lays the foundation for establishing a homotopic smooth transition between the two to obtain a general ephemeris model.

[0041] (3) This invention discloses a general translational point mission orbit design method, which realizes the continuous transition from the circular restricted three-body model to the high-precision ephemeris model and establishes a smooth connection between the two, thereby ensuring that all parameter combinations and situations can converge through multi-step approximation and step-by-step convergence, which greatly improves the convergence and robustness of the algorithm.

[0042] (4) This invention discloses a general translational point mission trajectory design method and proposes an adaptive variable step size homotopy iteration strategy. In the process of gradually approximating from the circular restricted three-body model to the high-precision ephemeris model: for the difficult convergence case, the non-convergence case is automatically solved by adaptively reducing the step size and increasing the number of iterations; for the easy convergence case, the convergence efficiency is improved by adaptively increasing the step size; the adaptive variable step size homotopy iteration strategy takes into account both the convergence range and the computational efficiency, and realizes the balance between the convergence range and the convergence speed of the algorithm.

[0043] (5) This invention discloses a general translational point mission track design method. The whole process is fully automatic and does not require manual implementation. Compared with the existing methods, it is very suitable for tasks such as the underlying algorithm implementation of track design software and batch calculation in engineering tasks. It can greatly improve the design efficiency and quality of translational point tracks and has great promotion and application value. Attached Figure Description

[0044] Figure 1 This is a flowchart of a general translational point mission trajectory design method in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments disclosed in the present invention will be described in further detail below with reference to the accompanying drawings.

[0046] Reference Figure 1 In this embodiment, the general translational point mission trajectory design method includes: Step 1: Define the target three-body system and other celestial bodies that affect the target three-body system.

[0047] In this embodiment, the target three-body system refers to: a system consisting of a main celestial body The second day The gravitational system consisting of the probe and the detector. Other celestial bodies refer to the celestial bodies in the solar system other than the main body. The second day Celestial bodies other than the target three-body system that can affect it. The target three-body system and other celestial bodies that affect it are defined as: For the main celestial body The second day The names are assigned values ​​respectively to specify the main celestial body. The second day Specifically identifying the celestial body allows us to pinpoint the target three-body system and subsequently obtain the ephemeris of each body within it. For example, regarding the main celestial body... The second day Assign values ​​to the names respectively: , Then at this time the main celestial body It is the sun The next day It is Earth and the moon combination The target three-body system is the Sun-Earth three-body system. For example, regarding the main celestial body... The second day Assign values ​​to the names respectively: , Then at this time the main celestial body It is Earth The next day It is the moon. The target three-body system is the Earth-Moon three-body system.

[0048] Furthermore, after clarifying the specific target three-body system, the next step is to identify other celestial bodies that can influence it and assign them names. For example, if the target three-body system is identified as the Sun-Earth system, then the other celestial bodies that can influence it are: the Moon. And assign a value to its name. For example, if the target three-body system is clearly defined as the Earth-Moon three-body system, then the other celestial bodies affecting this Earth-Moon three-body system can be identified as: the Sun. ,Mars and Venus And assign a value to its name. .in, This refers to the set of other celestial bodies that influence the target three-body system.

[0049] Step 2: Determine the set of first-order ordinary differential equations used to characterize the ephemeris model.

[0050] In this embodiment, the first-order ordinary differential equations used to characterize the ephemeris model are expressed as follows:

[0051] in, This represents the set of coefficients of a system of first-order ordinary differential equations. For the set of coefficients The elements of the set, ; Represents the normalized position vector in the rotating coordinate system. , and Representing position vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized velocity vector in the rotating coordinate system. , and Representing velocity vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized time in the rotating coordinate system. Indicates the current moment. Normalized time of the rotating coordinate system relative to the current time The first derivative; Indicates the main celestial body at the current moment gravitational constant, Indicates the current moment of the second day's body The gravitational constant; Indicates the second day's body Relative Main Body The magnitude of the position vector; Represents the potential function The second-order gradient.

[0052] Furthermore, .in, This represents the normalized gravitational constant of the target three-body system. Other celestial bodies The normalized gravitational constant, Represents the main celestial body Distance to the detector Indicates the second day's body Distance to the detector Other celestial bodies Distance to the detector.

[0053] Furthermore, the rotating coordinate system is defined as follows: the origin of the rotating coordinate system is the principal celestial body. and the second body The center of mass, the x-axis is formed by the main celestial body The center of mass points to the second body The center of mass, the z-axis along the second body Orbiting the main celestial body The normal to the instantaneous two-body orbital plane, the y-axis, and the x-axis and z-axis satisfy the right-hand rule.

[0054] Preferably, for the coefficient set of a system of first-order ordinary differential equations , there is: when When the coefficient set of a system of first-order ordinary differential equations is called the first coefficient set, the coefficient set is called the first coefficient set. At this point, a system of first-order ordinary differential equations is used to characterize the high-precision ephemeris model. When the coefficient set of the first-order ordinary differential equation system is the second coefficient set, the coefficient set is... At this point, a system of first-order ordinary differential equations is used to characterize the circularly restricted three-body model. When the coefficient set of a system of first-order ordinary differential equations is the third coefficient set, the coefficient set is... At this point, the first-order ordinary differential equations are used to characterize the general ephemeris model.

[0055] Step 3: Calculate the first set of coefficients based on the ephemeris of the target three-body system and other celestial bodies at the current moment.

[0056] In this embodiment, the Julian day of the initial epoch is defined as... The Julian day corresponding to the current epoch is Then the number of seconds elapsed between the current epoch and the initial epoch. for: Therefore, starting from the initial epoch... Input is a constant, expressed in elapsed seconds. By inputting variables, the current epoch time can be calculated. Considering As a constant, in this embodiment, it is taken as replace To represent the current epoch, abbreviated as: current time. (Absolute time).

[0057] Preferably, the ephemeris of the target three-body system and other celestial bodies at the current moment can be obtained by consulting the JPL DE440 ephemeris table, including: the main celestial body at the current moment. Projection of the position vector in the inertial coordinate system The main celestial body at the current moment Projection of the velocity vector in the inertial coordinate system The main celestial body at the current moment gravitational constant The current moment of the second day Projection of the position vector in the inertial coordinate system The current moment of the second day Projection of the velocity vector in the inertial coordinate system The current moment of the second day gravitational constant Other celestial bodies at the current moment Projection of the position vector in the inertial coordinate system Other celestial bodies at the current moment Projection of the velocity vector in the inertial coordinate system Other celestial bodies at the current moment gravitational constant .in, , This refers to the set of other celestial bodies that influence the target three-body system.

[0058] Preferably, the inertial coordinate system is defined as follows: when the target three-body system is a Sun-Earth three-body system, the inertial coordinate system is a Sun-centered, centroid-centered, ecliptic inertial coordinate system; when the target three-body system is an Earth-Moon three-body system, the inertial coordinate system is a Geocentric J2000.0 coordinate system.

[0059] Preferably, the calculation process for the first set of coefficients is as follows: S31, for the sake of simplicity, the following intermediate parameters can be calculated based on the ephemeris of the target three-body system and other celestial bodies at the current moment: according to , and The normalized gravitational constants of the target three-body system were calculated respectively. and other celestial bodies normalized gravitational constant : ,

[0060] according to , , , , , celestial bodies were calculated separately. Relative celestial bodies position vector Velocity vector and acceleration vector : , ,

[0061] in, , , ; , .

[0062] Constructing celestial bodies Relative celestial bodies Auxiliary functions :

[0063] Determine the auxiliary function first derivative Second derivative :

[0064]

[0065] according to , , , , , , , The second day's body was calculated Relative Main Body gravitational acceleration vector The second day Relative Main Body The first derivative of the gravitational acceleration vector The second day Relative Main Body The second derivative of the gravitational acceleration vector Main celestial bodies and the second body The acceleration vector of the center of mass Main celestial bodies and the second body The first derivative of the acceleration vector of the center of mass :

[0066] ,

[0067] ,

[0068] The second celestial body was calculated Relative Main Body The magnitude of the position vector , first derivative , The second derivative : , ,

[0069] The normalized time of the rotating coordinate system was calculated. relative to the current time first derivative Normalized time of rotating coordinate system relative to the current time The second derivative : ,

[0070] The second celestial body was calculated Relative Main Body angular momentum vector , model , For the current moment first derivative , For the current moment The second derivative : ,

[0071]

[0072]

[0073] The three-axis unit vectors of the rotating coordinate system are calculated as follows: , ,

[0074] in, , and These represent the x-axis unit vector, y-axis unit vector, and z-axis unit vector of the rotating coordinate system, respectively.

[0075] S32, based on the intermediate parameters calculated in step S31 above: , , , , , , , , , , , , The first set of coefficients is calculated. : , ,

[0076] , ,

[0077] , , ,

[0078] ,

[0079]

[0080] in, , , These are the three constant coefficients of the high-precision ephemeris model. , , These are the three velocity influence coefficients for the high-precision ephemeris model. , , , , , These are the six positional influence coefficients of the high-precision ephemeris model. This is the gravitational field acceleration influence coefficient of the high-precision ephemeris model.

[0081] Step 4: Determine the second set of coefficients, and based on the first and second sets of coefficients, determine the third set of coefficients; substitute the third set of coefficients into the first-order ordinary differential equation system to obtain the general ephemeris model.

[0082] In this embodiment, it can be set that: , , , , , , , , , , , , Then the second set of coefficients for: .in, , , These are the three constant coefficients of the circular restricted three-body model. , , These are the three velocity influence coefficients for the circularly constrained three-body model. , , , , , These are the six positional influence coefficients for the circular restricted three-body model. The gravitational field acceleration influence coefficient is given for the circularly confined three-body model.

[0083] Furthermore, according to the first set of coefficients Second set of coefficients The homotopy method is used to determine the third coefficient set. :

[0084] in, , , These are the three constant coefficients of the general ephemeris model. , , These are the three velocity influence coefficients of the general ephemeris model. , , , , , These are the six positional influence coefficients of the general ephemeris model. The gravitational field acceleration influence coefficient of the general ephemeris model; Represents the homotopy coefficient. .

[0085] Furthermore, substituting the third set of coefficients into the system of first-order ordinary differential equations yields the general ephemeris model, denoted as... , means as follows:

[0086] Step 5: Based on the general ephemeris model, an adaptive variable step size homotopy iteration strategy is adopted to obtain the translational point mission orbit parameters that meet the mission orbit design requirements through iterative calculation.

[0087] In this embodiment, the specific calculation process for the translational point mission trajectory parameters that meet the mission trajectory design requirements is as follows: S51, obtain the initial values ​​for the iteration.

[0088] Based on the LP (Lindstedt-Poincaré) method, analytical perturbation expansion is employed. Using the north-south orientation and amplitude of the mission trajectory, and employing the analytical high-order expansion solution of a circularly restricted three-body model, initial estimates of the mission trajectory parameters at the translational point are calculated. :

[0089] in, , and They represent Time position vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; express The estimated absolute time corresponding to the given moment, and having .

[0090] S52, Settings ,Will Bring into Integrating and iterating until convergence, then stopping, yields the translational point trajectory parameters convergent under the condition that the homotopy coefficient is 0. .

[0091] S53, based on a general ephemeris model, for By performing stepwise transition corrections, the parameters of the convergent translational point mission trajectory under the condition of homotopy coefficient 1 are obtained. Specifically: 531) Let the adaptive variable step size be used. initial value ; 532) Save the current homotopy coefficient, denoted as ; 533) According to Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 534) Update the homotopy coefficient Substitution The third set of coefficients is calculated. and substitute Iterative corrections are made during this process. 535) Determine if the iteration has converged; if the iteration has not converged, update the adaptive variable step size according to the first update strategy to obtain the updated adaptive variable step size. If the iteration converges, the adaptive variable step size is updated according to the second update strategy to obtain the updated adaptive variable step size. ; 536) Based on the updated adaptive variable step size Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 537) If If so, return to step 534) and continue iterating; if and Then update the homotopy coefficients to obtain the updated homotopy coefficients. (Return to step 534) and continue iterating; if If convergence is achieved, the iteration ends, and the trajectory parameters of the translational point that converge under the condition that the homotopy coefficient is 1 are obtained. .

[0092] S54, Settings Then there is , bring in The process involves iterative differential correction until convergence, yielding the translational orbit parameters that meet the design requirements of the mission orbit. :

[0093] in, , and They represent Time position vector The components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector The components of the x, y, and z axes in the rotating coordinate system; express The absolute time corresponding to a given moment.

[0094] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0095] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A general method for designing the trajectory of a translational point mission, characterized in that, include: Define the target three-body system and other celestial bodies that influence it; the target three-body system refers to the system consisting of the main celestial body. The second day A gravitational system consisting of a detector and a gravitational probe; Determine the set of first-order ordinary differential equations used to characterize the ephemeris model; The first set of coefficients is calculated based on the ephemeris of the target three-body system and other celestial bodies at the current moment; Determine the second set of coefficients, and based on the first and second sets of coefficients, determine the third set of coefficients; substitute the third set of coefficients into the first-order ordinary differential equations to obtain the general ephemeris model; Based on a general ephemeris model, an adaptive variable step size homotopy iteration strategy is adopted to obtain the translational point mission orbit parameters that meet the mission orbit design requirements through iterative calculation.

2. The general translational point mission trajectory design method according to claim 1, characterized in that, Define the target three-body system and other celestial bodies that affect the target three-body system, including: For the main celestial body The second day The names are assigned values ​​respectively to clarify the target three-body system; Identify other celestial bodies that affect the defined target three-body system and assign them names.

3. The general translational point mission trajectory design method according to claim 1, characterized in that, The first-order ordinary differential equations used to characterize the ephemeris model are expressed as follows: in, This represents the set of coefficients of a system of first-order ordinary differential equations. For the set of coefficients The elements of the set, ; Represents the normalized position vector in the rotating coordinate system. , and Representing position vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized velocity vector in the rotating coordinate system. , and Representing velocity vectors respectively The components of the x, y, and z axes in the rotating coordinate system; This represents the normalized time in the rotating coordinate system. Indicates the current moment. Normalized time of the rotating coordinate system relative to the current time The first derivative; Indicates the main celestial body at the current moment gravitational constant, Indicates the current moment of the second day's body The gravitational constant; Indicates the second day's body Relative Main Body The magnitude of the position vector; Represents the potential function The second-order gradient.

4. The general translational point mission trajectory design method according to claim 3, characterized in that, For the coefficient set of a system of first-order ordinary differential equations ,have: when When the coefficient set of a system of first-order ordinary differential equations is called the first coefficient set, the coefficient set is called the first coefficient set. At this point, a set of first-order ordinary differential equations is used to characterize the high-precision ephemeris model; when When the coefficient set of the first-order ordinary differential equation system is the second coefficient set, the coefficient set is... At this point, the first-order ordinary differential equation system is used to characterize the circularly restricted three-body model; when When the coefficient set of a system of first-order ordinary differential equations is the third coefficient set, the coefficient set is... At this point, the first-order ordinary differential equations are used to characterize the general ephemeris model.

5. The general translational point mission trajectory design method according to claim 4, characterized in that, The ephemeris of the target three-body system and other celestial bodies at the current moment was obtained by consulting the JPL DE440 ephemeris table, including: the main celestial body at the current moment. Projection of the position vector in the inertial coordinate system The main celestial body at the current moment Projection of the velocity vector in the inertial coordinate system The main celestial body at the current moment gravitational constant The current moment of the second day Projection of the position vector in the inertial coordinate system The current moment of the second day Projection of the velocity vector in the inertial coordinate system The current moment of the second day gravitational constant Other celestial bodies at the current moment Projection of the position vector in the inertial coordinate system Other celestial bodies at the current moment Projection of the velocity vector in the inertial coordinate system Other celestial bodies at the current moment gravitational constant ;in, , This refers to the set of other celestial bodies that influence the target three-body system.

6. The general translational point mission trajectory design method according to claim 5, characterized in that, The definition of a rotating coordinate system is as follows: the origin of the rotating coordinate system is the principal celestial body. and the second body The center of mass, the x-axis is formed by the main celestial body The center of mass points to the second body The center of mass, the z-axis along the second body Orbiting the main celestial body The normal to the instantaneous two-body orbital plane, the y-axis, and the x-axis and z-axis satisfy the right-hand rule; The inertial coordinate system is defined as follows: when the target three-body system is a Sun-Earth three-body system, the inertial coordinate system is the heliocentric, centroid, and ecliptic inertial coordinate system; when the target three-body system is an Earth-Moon three-body system, the inertial coordinate system is the geocentric J2000.0 coordinate system.

7. The general translational point mission trajectory design method according to claim 5, characterized in that, Based on the ephemeris of the target three-body system and other celestial bodies at the current moment, the first set of coefficients is calculated, including: Based on the ephemeris of the target three-body system and other celestial bodies at the current moment, the following intermediate parameters are calculated: according to , and The normalized gravitational constants of the target three-body system were calculated respectively. and other celestial bodies normalized gravitational constant : ， according to , , , , , celestial bodies were calculated separately. Relative celestial bodies position vector Velocity vector and acceleration vector : ， ， in, or or , or or , ; , ; Constructing celestial bodies Relative celestial bodies Auxiliary functions : Determine the auxiliary function first derivative Second derivative : according to , , , , , , , The second day's body was calculated Relative Main Body gravitational acceleration vector The second day Relative Main Body The first derivative of the gravitational acceleration vector The second day Relative Main Body The second derivative of the gravitational acceleration vector Main celestial bodies and the second body The acceleration vector of the center of mass Main celestial bodies and the second body The first derivative of the acceleration vector of the center of mass : ， ， The second celestial body was calculated Relative Main Body The magnitude of the position vector , first derivative , The second derivative : ， ， The normalized time of the rotating coordinate system was calculated. relative to the current time first derivative Normalized time of rotating coordinate system relative to the current time The second derivative : ， The second celestial body was calculated Relative Main Body angular momentum vector , model , For the current moment first derivative , For the current moment The second derivative : ， The three-axis unit vectors of the rotating coordinate system are calculated as follows: ， ， in, , and These represent the unit vectors along the x-axis, y-axis, and z-axis of the rotating coordinate system, respectively. Based on the intermediate parameters obtained from the calculation: , , , , , , , , , , , , The first set of coefficients is calculated. : ， ， ， ， ， ， ， ， in, , , These are the three constant coefficients of the high-precision ephemeris model. , , These are the three velocity influence coefficients for the high-precision ephemeris model. , , , , , These are the six positional influence coefficients of the high-precision ephemeris model. This is the gravitational field acceleration influence coefficient of the high-precision ephemeris model.

8. The general translational point mission trajectory design method according to claim 7, characterized in that, Determine the second set of coefficients, and based on the first and second sets of coefficients, determine the third set of coefficients, including: make: , , , , , , , , , , , , Then the second set of coefficients for: ;in, , , These are the three constant coefficients of the circular restricted three-body model. , , These are the three velocity influence coefficients for the circularly constrained three-body model. , , , , , These are the six positional influence coefficients for the circular restricted three-body model. The gravitational field acceleration influence coefficient for the circularly confined three-body model; According to the first set of coefficients Second set of coefficients Determine the third set of coefficients : in, , , These are the three constant coefficients of the general ephemeris model. , , These are the three velocity influence coefficients of the general ephemeris model. , , , , , These are the six positional influence coefficients of the general ephemeris model. The gravitational field acceleration influence coefficient of the general ephemeris model; Represents the homotopy coefficient. .

9. The general translational point mission trajectory design method according to claim 8, characterized in that, Substituting the third set of coefficients into the system of first-order ordinary differential equations, we obtain the general ephemeris model, denoted as... , means as follows: 。 10. The general translational point mission trajectory design method according to claim 9, characterized in that, Based on a general ephemeris model, an adaptive variable-step homotopy iteration strategy is adopted to obtain the translational point mission orbit parameters that meet the mission orbit design requirements through iterative calculations, including: S1. Based on the LP method, analytical perturbation expansion is used. Based on the north-south orientation and amplitude of the mission trajectory, the analytical high-order expansion solution of the circular restricted three-body model is employed to calculate the initial estimates of the mission trajectory parameters at the translational point. : in, , and They represent Time position vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector Estimates of the components of the x, y, and z axes in the rotating coordinate system; express The estimated absolute time corresponding to the given moment, and having ; S2, Settings ,Will Bring into Integrating and iterating until convergence, then stopping, yields the translational point trajectory parameters convergent under the condition that the homotopy coefficient is 0. ; S3, based on a general ephemeris model, for By performing stepwise transition corrections, the parameters of the convergent translational point mission trajectory under the condition of homotopy coefficient 1 are obtained. ,include: 31) Let the adaptive step size be variable. initial value ; 32) Save the current homotopy coefficient, denoted as ; 33) According to Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 34) Update the homotopy coefficient Substitution The third set of coefficients is calculated. and substitute Iterative corrections are made during this process. 35) Determine if the iteration has converged; if the iteration has not converged, update the adaptive variable step size according to the first update strategy to obtain the updated adaptive variable step size. If the iteration converges, the adaptive variable step size is updated according to the second update strategy to obtain the updated adaptive variable step size. ; 36) Based on the updated adaptive variable step size Update the homotopy coefficients to obtain the updated homotopy coefficients. ; 37) If If so, return to step 34) and continue iterating; if and Then update the homotopy coefficients to obtain the updated homotopy coefficients. Return to step 34) and continue iterating; if If convergence is achieved, the iteration ends, and the trajectory parameters of the translational point that converge under the condition that the homotopy coefficient is 1 are obtained. ; S4, Settings Then there is , bring in The process involves iterative differential correction until convergence, yielding the translational orbit parameters that meet the design requirements of the mission orbit. : in, , and They represent Time position vector The components of the x, y, and z axes in the rotating coordinate system; , and They represent Moment velocity vector The components of the x, y, and z axes in the rotating coordinate system; express The absolute time corresponding to a given moment.

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