We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A SETTING FOR HIGHER ORDER DIFFERENTIAL EQUATION FIELDS AND HIGHER ORDER LAGRANGE AND FINSLER SPACES.
- Authors
Bucataru, Ioan
- Abstract
We use the Frölicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [15] to formulate and discuss the projective metrizability problem for higher order differential equation fields. We provide necessary and sufficient conditions for higher order projective metrizability in terms of homogeneous semi-basic 1- forms. Such a semi-basic 1-form is the Poincare-Cartan 1-form of a higher order Finsler function, while the potential of such semi-basic 1-form is a higher order Finsler function.
- Subjects
DIFFERENTIAL equations; LAGRANGE spaces; FINSLER spaces; CALCULUS of variations; HOMOGENEITY
- Publication
Journal of Geometric Mechanics, 2013, Vol 5, Issue 3, p257
- ISSN
1941-4889
- Publication type
Article
- DOI
10.3934/jgm.2013.5.257