SINGULARITIES IN A VARIATIONAL PROBLEM WITH AN INEQUALITY,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1963
- Accession Number
- AD0421495
Entities
People
- Boris Garfinkel
- Gregory T. Mcallister
Organizations
- Ballistic Research Laboratory