  Direct shooting is an efficient method to solve numerical optimal control. It
utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control
problem making the problem solvable by nonlinear programming solvers. However,
conventional direct shooting raises a contradictory dynamics issue when using
an augmented state to handle {high-order} systems. This paper fills the
research gap by considering the direct shooting method for {high-order}
systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe
the system dynamics constraint directly. Additionally, we provide the global
error upper bounds of our proposed methods. A set of benchmark optimal control
problems shows that our methods provide more accurate solutions than existing
approaches.
