CN-121997456-A - Ground fire transfer track real-time two-dimensional calculation method based on variable step length method

CN121997456ACN 121997456 ACN121997456 ACN 121997456ACN-121997456-A

Abstract

The invention discloses a real-time two-dimensional calculation method of a ground fire transfer orbit based on a variable step length method, which mainly comprises the following steps of 1, setting flight time firstly, obtaining gravitation constants of the earth, a Mars and the sun, 2, initializing a system, 3, judging a time stage, 4, screening the time step, 5, calculating a motion orbit of a spacecraft based on Newton's law of motion and universal gravitation law, 6, solving the position and the speed of the spacecraft through a numerical integration method, 7, updating the mass change of the spacecraft in real time, 8, drawing the orbit of the spacecraft and outputting related data. The method may be used to simulate the orbital behaviour of a spacecraft between earth and spark, especially when considering a nuclear power propulsion system. The method can accurately calculate the motion trail of the spacecraft in the complex gravitational field based on classical mechanics and numerical simulation technology, and provides theoretical support for the design and optimization of the aerospace task.

Inventors

ZHANG JING
MA ZHIZHEN
WANG CHEN
ZHANG RAN

Assignees

西安交通大学

Dates

Publication Date: 20260508
Application Date: 20260126

Claims (4)

1. A real-time two-dimensional calculation method for a ground fire transfer track based on a variable step length method is characterized by comprising the following steps: Step 1, firstly setting the total flight time of a spacecraft, and dividing the total flight time into a propulsion stage and an unpowered sliding stage in a staggered manner, and acquiring gravitation constants of the earth, the Mars and the sun, wherein the gravitation constants of the earth, the Mars and the sun are adjusted according to a research purpose, and a calculation formula is shown as a formula (1); Formula (1) Represents the gravitational constant, N.m 2 ·kg -2 ; Indicating the mass of the sun, kg; Indicating mass of the earth, kg; Indicating the mass of Mars, kg; A position vector representing the earth relative to the sun, m; a first component, m, representing an array of position vectors of the earth relative to the sun; representing the second component of the velocity vector of the spacecraft with respect to earth, m s-1; Initializing a nuclear power propulsion system, setting initial mass, initial position, initial speed and initial orbit parameters of a spacecraft, and setting parameters of the nuclear power propulsion system, including thrust and fuel consumption rate; step 3, judging the time stage of the current time; step 4, performing time step screening to obtain the time step of the calculation, wherein the calculation formula is shown as formula (2): Formula (2) Wherein: representing a velocity vector of the spacecraft relative to the earth, m s-1; A position vector representing the Mars relative to the sun, m; Representing the velocity vector of the spacecraft relative to Mars, m s-1; Representing a real-time position vector of the spacecraft relative to the sun, m; representing spacecraft position vectors M; The real-time speed vector of the spacecraft relative to the sun at the moment t is represented by m.s -1 ; representing spacecraft velocity vectors Is m.s -1 S represents the ratio of the position module length to the speed module length of the spacecraft relative to the sun; s represents the ratio of the position module length to the velocity module length of the spacecraft relative to the earth; The ratio of the position module length to the velocity module length of the spacecraft with respect to the Mars, s, A time step s representing a variable step integration; Step 5, establishing a spacecraft orbit dynamics model containing earth, mars and solar gravitation constants based on Newton's law of motion and universal gravitation law, wherein if the model is in a sliding stage, the total acceleration vector is calculated in the formula (3) without the acceleration vector of the electric propeller on the spacecraft as shown in the formula (3) ; Formula (3) Wherein: a position vector representing the Mars relative to the sun, m; A unit vector representing a first component of the spacecraft velocity direction, m·s -1 ; a unit vector representing a second component of the spacecraft velocity direction, m·s -1 ; Represents the thrust of the electric propeller, N; Representing the number of the electric propellers; representing real-time mass of the spacecraft, kg; the acceleration vector of the sun to the spacecraft is represented by m.s -2 ; the acceleration vector of the earth to the spacecraft is represented by m.s -2 ; The acceleration vector of Mars to spacecraft is represented by m.s -2 ; The acceleration vector of the electric propeller to the spacecraft is represented by m.s -2 ; Representing the total acceleration vector, m.s -2 ; Step 6, performing time integration on a motion equation of the spacecraft by adopting a variable step length method, updating the position and the speed of the spacecraft in real time, and recording position and speed data of the spacecraft, wherein the position and the speed data are shown as a formula (4) and a formula (5); formula (4) Formula (5) The position vector of the spacecraft relative to the sun at the moment t is represented by m; Representation of Position vector of spacecraft relative to sun at moment, m; The real-time speed vector of the spacecraft relative to the sun at the moment t is represented by m.s -1 ; Representation of The speed vector of the spacecraft relative to the sun at the moment, m.s -1 ; A time step s representing a variable step integration; The total acceleration vector at the time t is represented by m.s -2 ; Representation of The total acceleration vector of moment, m.s -2 ; Step 7, considering the quality change of the nuclear power propulsion system, and updating the quality of the spacecraft in real time as shown in a formula (6); Formula (6) Representation of Real-time mass of spacecraft at moment, kg; Representation of Real-time mass of spacecraft at moment, kg; the mass flow rate of a single nuclear power propeller is shown as kg.s -1 ; and 8, drawing an orbit track of the spacecraft based on the recorded spacecraft position and speed data and the updated quality data, and outputting the data of the position, speed and quality of the spacecraft changing along with time.
2. The method for calculating the ground fire transfer orbit in real time based on the variable-stride length method according to claim 1, wherein the total acceleration vector of the motion equation in the step 6 is obtained by superposition of an acceleration vector of a sun to a spacecraft, an acceleration vector of an earth to the spacecraft, an acceleration vector of a spark to the spacecraft and an acceleration vector of an electric propeller to the spacecraft.
3. The method for real-time two-dimensional calculation of the ground fire transfer orbit based on the variable step length method is characterized in that the position and the speed of the spacecraft in the step 6 are obtained by time integration of a motion equation of the spacecraft by the variable step length method.
4. The method for real-time two-dimensional calculation of ground fire transfer orbit based on variable step length method according to claim 1, wherein in step 7, the mass change of the spacecraft is determined by the fuel consumption rate of the nuclear power propulsion system.

Description

Ground fire transfer track real-time two-dimensional calculation method based on variable step length method Technical Field The invention relates to the technical field of spacecraft orbit simulation, in particular to a ground fire transfer orbit real-time two-dimensional calculation method based on a variable-step length method, which is used for simulating orbit dynamics behavior of a spacecraft between the earth and a spark under the condition of considering a nuclear power propulsion (NEP) system. Background Numerical integration is one of the core technologies for solving differential equations in a dynamics system, and is widely applied to the fields of orbit dynamics, molecular dynamics, computational fluid dynamics and the like. In orbit dynamics simulation, trajectory computation of a spacecraft generally relies on a numerical integration method to solve equations of motion under the action of gravity, propulsion and other external forces. Common numerical integration methods include the euler method, the Longger-Kutta method, the octyl integration method, and the like. However, the fixed-step method may have limitations in efficiency and accuracy in complex orbit environments, particularly where the spacecraft trajectories involve strong gravitational gradient changes, long-distance deep space missions, or are subject to unstable disturbances, the conventional fixed-step method may have difficulty in achieving both computational accuracy and efficiency. The variable step size numerical integration method is a technology capable of adaptively adjusting time steps according to the system state, so that the calculation efficiency is improved on the premise of ensuring the accuracy. The core idea is to use a smaller step size when the state variable changes drastically to reduce the error, and to increase the step size when the state change is gentle to reduce the calculation cost. The step-length-variable method is widely used for track dynamics simulation, and can automatically adjust the step length, so that stable precision and calculation efficiency can be maintained in different stages of track calculation. The existing orbit dynamics simulation includes a variable-step length Longge-Kutta method and a variable-step length octyl integration method. The variable step length Longge-Kutta method adopts an embedded error estimation mechanism, has multi-perturbation adaptive capacity, and is mainly applied to short-term track forecasting tasks. The method has obvious defects, error accumulation is easy to occur in the long-term integration process, the precision fluctuation is obvious in the strong disturbance environment, and the calculation cost is high due to the fact that an embedding solution is additionally calculated in a single step. The variable-step length octyl integration method realizes step length adjustment through time transformation, can maintain the octyl property of the Hamiltonian system, and is suitable for long-term deep space detection track integration. However, the compatibility between the step length adjustment and the pungent property is contradictory, and the suitability for non-conservative forces such as electric propulsion is poor. The two technologies have common defects that the adaptive capacity to a multi-scale track scene is insufficient, the error tolerance setting is dependent on engineering experience, and an adaptive optimization mechanism is lacked. Disclosure of Invention In order to accurately simulate the orbit dynamics behavior of a spacecraft in a complex gravitational field, particularly under the condition of considering a nuclear power propulsion (NEP) system, the invention provides a ground fire transfer orbit real-time two-dimensional calculation method based on a variable-step length method based on the idea of the variable-step length method. According to the method, the motion trail of the spacecraft is accurately calculated through numerical integration and Newton's law of motion, and the quality change of the spacecraft is updated in real time, so that theoretical support is provided for design and optimization of a space mission. In order to achieve the above purpose, the present invention adopts the following technical scheme: A real-time two-dimensional calculation method for a ground fire transfer track based on a variable step length method comprises the following steps: Step 1, firstly setting the total flight time of a spacecraft, and dividing the total flight time into a propulsion stage and an unpowered sliding stage in a staggered manner, and acquiring gravitation constants of the earth, the Mars and the sun, wherein the gravitation constants of the earth, the Mars and the sun are adjusted according to a research purpose, and a calculation formula is shown as a formula (1); Formula (1) Represents the constant of universal gravitation, N.m 2·kg-2 Indicating the mass of the sun, kg; Indicating mass of the earth, kg; Indicating the mass