Singularities of the Hamiltonian vectorfield in nonautonomous variational problems

• Type: Article in International Scientific Journal
• Date: 2003

Authors

Mena Matos, H (Author) FCUP

Journal

Title: Journal of Mathematical Analysis and Applications

Vol. 283

Pages: 610-632

ISSN: 0022-247X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-FWK

DOI: 10.1016/s0022-247x(03)00303-2

Abstract (EN): Variational problems with n degrees of freedom give rise (by Pontriaguine maximum principle) to a Hamiltonian vectorfield in T*R-n, that presents singularities (nonsmoothness points) when the Lagrangian is not convex. For one degree of freedom nonautonomous problems of the calculus of variations where the Hamiltonian vectorfield in T*R depends explicitly on the time, we consider the associated autonomous vectorfield in T*R x R and classify its singularities up to an equivalence that takes into account the special role played by the time coordinate, i.e., that respects the foliation of T*R x R into planes of constant time.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23