A method for determining optimum re-entry trajectories

The Pontryagin Maximum Principle is used to formulate the problem of finding optimum atmospheric vehicular reentry trajectories. The optimization problem is that of minimizing an integral which is a function of the state and control variables. The vehicle's motion is assumed to be influenced by a gravitational force and an aerodynamic force. The problem is formulated and the necessary equations are developed simultaneously for three sets of Euler angles. Computational procedures are suggested so that numerical trajectories may be generated.