Numerical Simulation Method of Satellite Attitude Based on Lie Group Spectrum Algorithm

Abstract

The invention discloses a satellite attitude numerical simulation method based on the Lie group spectral algorithm. The method includes the following steps that 1, a satellite attitude kinematics and dynamics Lie group model is established based on the SO(3) group; 2, canonical coordinates are selected to convert a satellite attitude Lie group equation into an equivalent Lie algebra equation and an equivalent Lie group reconstruction equation; 3, the Lie algebra equation is solved with the spectral method to obtain the angular speed of satellite attitude rotation, and a satellite attitude matrix is solved with the Lie group reconstruction equation. According to the method, the satellite attitude kinematics and dynamics Lie group model is established based on the SO(3) group, satellite attitude expression is simple without singularity, and the unwinding phenomenon is avoided; as the Lie group spectral method is adopted to simulate the attitude dynamics model, the geometric structure and physical property of a satellite system can be kept for a long time, precision is high, and stability is high.

Description

technical field [0001] The invention relates to the technical field of satellite attitude control, in particular to a satellite attitude numerical simulation method based on a Lie group spectrum algorithm. Background technique [0002] The technical background related to the present invention will be described below, but these descriptions do not necessarily constitute the prior art of the present invention. [0003] The existing satellite attitude dynamics simulation technology mainly includes the establishment of satellite attitude dynamics model and numerical simulation algorithm. [0004] The existing satellite attitude description methods mainly include methods such as Euler angles, direction cosines and unit four elements. [0005] (1) Euler angle description method [0006] The most commonly used method for satellite attitude description is Euler angles. Generally use three Euler angles - (azimuth ψ, pitch angle θ, tilt angle ) represents the attitude of the non-...

AI Technical Summary

Problems solved by technology

[0025] The shortcomings of the existing technology mainly include the shortcomings of the model and the shortcomings of the numerical algorithm

The satellite attitude description based on Euler angles is local and has singularity, while the satellite attitude description based on unit quaternion will lead to unwinding phenomenon, which will lead to a lot of energy waste in satellite control

The Euler method in the numerical algorithm is a kind of explicit single-step algorithm. Although the operation speed is fast, it only has the first-order derivative accuracy.

The commonly used explicit Runge-Kutta method can have high-order accuracy, but the stability of the algorithm is poor

The implicit Runge-Kutta method has high computational complexity

Moreover, the above algorithms often cannot maintain the geometric and physical conservation quantities of the simulated dynamic system, such as the SO(3) group structure of rigid bodies, momentum, energy, etc.

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