Open Access

ARTICLE

Integration of the Coupled Orbit-Attitude Dynamics Using Modified Chebyshev-Picard Iteration Methods

Xiaoli Bai¹, John L. Junkins²

1 Rutgers, The State University of New Jersey, Piscataway, NJ, U.S.A
2 Texas A&M, College Station, TX, U.S.A

Computer Modeling in Engineering & Sciences 2016, 111(2), 129-146. https://doi.org/10.3970/cmes.2016.111.129

Abstract

This paper presents Modified Chebyshev-Picard Iteration (MCPI) methods for long-term integration of the coupled orbit and attitude dynamics. Although most orbit predictions for operational satellites have assumed that the attitude dynamics is decoupled from the orbit dynamics, the fully coupled dynamics is required for the solutions of uncontrolled space debris and space objects with high area-to-mass ratio, for which cross sectional area is constantly changing leading to significant change on the solar radiation pressure and atmospheric drag. MCPI is a set of methods for solution of initial value problems and boundary value problems. The methods refine an orthogonal function approximation of long-time-interval segments of state trajectories iteratively by fusing Chebyshev polynomials with the classical Picard iteration and have been applied to multiple challenging aerospace problems. Through the studies on integrating a torque-free rigid body rotation and a long-term integration of the coupled orbit-attitude dynamics through the effect of solar radiation pressure, MCPI methods are shown to achieve several times speedup over the Runge-Kutta 7(8) methods with several orders of magnitudes of better accuracy. MCPI methods are further optimized by integrating the decoupled dynamics at the beginning of the iteration and coupling the full dynamics when the attitude solutions and orbit solutions are converging during the iteration. The approach of decoupling and then coupling during iterations provides a unique and promising perspective on the way to warm start the solution process for the longterm integration of the coupled orbit-attitude dynamics. Furthermore, an attractive feature of MCPI in maintaining the unity constraint for the integration of quaternions within machine accuracy is illustrated to be very appealing.

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