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Numerical Solutions Of Differential-Algebraic Equations And Its Applications In Solving Tppc Problems, He-Sheng Wang, Wei-Lun Jhu, Chee-Fai Yung, Ping-Feng Wang

Journal of Marine Science and Technology

In this paper, we present a numerical method for solving nonlinear differential algebraic equations (DAE’s) based on the backward differential formulas (BDF) and the Pade series. Usefulness of the method is then illustrated by a numerical example, which is concerned with the derivation of the optimal guidance law for spacecraft. This kind of problems is called trajectory-prescribed path control (TPPC) in the literature. We reformulate the problem as a Hamiltonian DAE system (usually with a higher index). After establishing the system of spacecraft dynamics, we can derive the optimal guidance law of the system by the proposed numerical method.