Accession Number:

AD0421495

Title:

SINGULARITIES IN A VARIATIONAL PROBLEM WITH AN INEQUALITY,

Descriptive Note:

Corporate Author:

BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD

Report Date:

1963-07-01

Pagination or Media Count:

27.0

Abstract:

The variational problem of Lagrange is considered with an inequality in the form a phi x,y 0 or b phi x,y,y 0, which is of frequent occurrence in applications of the calculus of variations to Control Theory and Optimization Techniques. The question of existence and uniqueness of the continuation of a minimizing arc is investigated at points of the boundary phi 0. Various phenomena, including splitting of extremals, dead-end, entry into, and exit from the boundary, are treated and the conditions for their occurrence are derived. The nature of the continuation is related to the index associated with an extremal. An appendix extends the results to a control problem of the Mayer type. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE