Nonlinear Dynamic Behavior of the Satellite Rendezvous and Docking Based on the Symplectic Runge-Kutta Method

LI Qing-jun; YE Xue-hua; WANG Bo; WANG Yan

doi:10.3879/j.issn.1000-0887.2014.12.002

Volume 35 Issue 12

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LI Qing-jun, YE Xue-hua, WANG Bo, WANG Yan. Nonlinear Dynamic Behavior of the Satellite Rendezvous and Docking Based on the Symplectic Runge-Kutta Method[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1299-1307. doi: 10.3879/j.issn.1000-0887.2014.12.002

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Nonlinear Dynamic Behavior of the Satellite Rendezvous and Docking Based on the Symplectic Runge-Kutta Method

doi: 10.3879/j.issn.1000-0887.2014.12.002

Department of Engineering Mechanics, School of Mechanics and Civil.& Architecture,Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11172239;11372252）

Received Date: 2014-06-03
Rev Recd Date: 2014-10-09
Publish Date: 2014-12-15

Abstract

Abstract

The simulation of the satellite rendezvous and docking is one of most important problems for space platforms and so on. The nonlinear dynamic behavior of the satellite rendezvous and docking was investigated. According to the energy principle, the Lagrange function was given; then, the generalized coordinates, generalized momentum and Legendre transformation were introduced to derive the Hamilton equations; both the symplectic Runge-Kutta method and the 4th-order Runge-Kutta method were comparatively used to solve the Hamilton equations. Through numerical analysis, it is easily found that the natural properties of the nonlinear dynamic system are well preserved with the symplectic RungeKutta method, especially in the long-time chasing cases. The proposed symplectic method is applicable to the related astrodynamic problems.
- satellite rendezvous and docking,
- nonlinear dynamics,
- Hamilton system,
- symplectic RungeKutta method

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References(18)

References

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