Higher order mechanics on graded bundles
Mathematical Physics
2015-12-18 v2 Differential Geometry
math.MP
Abstract
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for this higher order situation and derive in this framework the phase equations from an arbitrary (also singular) Lagrangian or Hamiltonian, as well as the Euler-Lagrange equations. As important examples, we geometrically derive the classical higher order Euler-Lagrange equations and analogous reduced equations for invariant higher order Lagrangians on Lie groupoids.
Cite
@article{arxiv.1412.2719,
title = {Higher order mechanics on graded bundles},
author = {Andrew James Bruce and Katarzyna Grabowska and Janusz Grabowski},
journal= {arXiv preprint arXiv:1412.2719},
year = {2015}
}
Comments
28 pages, comments welcomed. Minor typos and editing artefacts corrected. No major revision