The projective symplectic geometry of higher order variational problems: minimality conditions
C. Dur\'an, D. Otero
TL;DR
This paper explores the geometric structure of higher order variational problems by associating special curves to analyze minimality and conjugacy of extremals, providing a geometric framework for understanding these problems.
Contribution
It introduces a novel geometric approach linking isotropic, Lagrangian, and coisotropic curves to higher order variational problems, enhancing the understanding of extremal properties.
Findings
Characterization of extremals via isotropic, Lagrangian, and coisotropic curves
Description of minimality conditions in geometric terms
Analysis of conjugacy properties related to extremals
Abstract
We associate curves of isotropic, Lagrangian and coisotropic subspaces to higher order, one parameter variational problems. Minimality and conjugacy properties of extremals are described in terms of these curves.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics · Nonlinear Partial Differential Equations