TOUCH POINTS IN OPTIMAL ASCENT TRAJECTORIES WITH FIRST-ORDER STATE INEQUALITY CONSTRAINTS

Two and three-dimensional optimal ascent trajectories with a dynamic p ressure inequality constraint are analyzed for the existence of nontri vial touch points. These studies verify for the first time that such t rajectories can have the usual boundary area, where the constraint bec omes active, as well as touch points, which are isolated points where the trajectory touches the constraint boundary. Some of the costates a re discontinuous at the touch point. It is also possible to obtain add itional insights into the nature of the Lagrange multipliers without s olving the optimal control problem, specifically, for the numerical ex ample treated, some of the costate variables can be shown to be zero a t a touch point, if it exists.