1212.4873 (Paul Popescu)

A Lagrangian form of Pfaff forms    [PDF]

Paul Popescu

The aim of the paper is to study some dynamic aspects coming from a Pfaff form, i.e. a time dependent differential form on a tangent bundle. The action on curves of a Pfaff form is natural associated with that of a second order Lagrangian linear in accelerations, while the converse association is not unique. An equivalence relation of Pfaff form, compatible with gauge equivalent Lagrangians, is considered. We express the Euler-Lagrange equation of the Lagrangian as a second order Lagrange derivative of a Pfaff form, considering controlled and higher order Pfaff forms. Hamiltonian forms of the dynamics generated are given, extending some quantization formulas given by Lukierski, Stichel and Zakrzewski. Using semi-sprays, local solutions of the E-L equations are given in some special particular cases.

View original: http://arxiv.org/abs/1212.4873