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.
Wang, He-Sheng; Jhu, Wei-Lun; Yung, Chee-Fai; and Wang, Ping-Feng
"NUMERICAL SOLUTIONS OF DIFFERENTIAL-ALGEBRAIC EQUATIONS AND ITS APPLICATIONS IN SOLVING TPPC PROBLEMS,"
Journal of Marine Science and Technology: Vol. 19:
1, Article 9.
Available at: https://jmstt.ntou.edu.tw/journal/vol19/iss1/9