Numerical solutions of Hamiltonian DAE’s and applications

In this paper, we present a numerical method for nonlinear differential algebraic equations (DAE’s) based on the backward differential formulas (BDF) and the Padé 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. We will reformulate the problem as a Hamiltonian DAE system. After establishing the system of spacecraft dynamics, we can derive the optimal guidance law of the system by numerical method.