Some Inequality Constraint Problems in the Calculus of Variations

摘要

Four related memoranda dealing with inequality constraints in the calculus of variations are collected in this report. The first is a detailed derivation of the solution to a problem appearing in (AIAA Journal I: 2544 - 2550, 1963). The second is the solution to the simplest possible problem including both a control variable and a state variable inequality constraint. The third adds a slight complexity to the second leading to transcendental equations in the solution. The fourth is a description of a straightforward method of calculating neighboring extremal paths when an interval of the nominal extremal is on a control variable or a first-order state variable inequality constraint boundary. (Author)