A unified framework for mechanics. Hamilton-Jacobi equation and applications

P. Balseiro, J. C. Marrero, D. Martin de Diego, E. Padron

Published 2010-01-04Version 1

In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical systems...). We recover all these, in principle, different cases using a unified framework based on skew-symmetric algebroids with a distinguished 1-cocycle. Several examples illustrate the theory.