Numerical simulation of trajectory prescribed path control problems by the backward differentiation formulas

The equations which describe trajectory, prescribed path control problems naturally form nonlinear semiexplicit, differential-algebraic systems with index greater than one. It is known that not all fully implicit systems may be solved stably by the k-step backward differentiation formulas, yet these methods do produce convergent numerical solutions to some semiexplicit systems. In this note numerical results are presented for the simplest backward differentiation formula when applied to an index three, semiexplicit system concerning the reentry of the space shuttle. The application of this numerical method to a realistic problem illustrates some unresolved implementation difficulties.