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The Journal of Geometric Mechanics (JGM)
 

A Hamilton-Jacobi theory on Poisson manifolds

Pages: 121 - 140, Volume 6, Issue 1, March 2014      doi:10.3934/jgm.2014.6.121

 
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Manuel de León - Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c\ Nicolás Cabrera, n 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain (email)
David Martín de Diego - Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c\ Nicolás Cabrera, n 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain (email)
Miguel Vaquero - Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), c\ Nicolás Cabrera, n 13-15, Campus Cantoblanco, UAM, 28049 Madrid, Spain (email)

Abstract: In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical systems and time dependent systems with external forces.

Keywords:  Hamilton-Jacobi theory, Poisson manifolds, nonholonomic mechanics, time-dependent systems, external forces.
Mathematics Subject Classification:  Primary: 70H20, 70 G45, 70F25, 37J60.

Received: November 2012;      Revised: January 2014;      Available Online: April 2014.

 References