XXXII Workshop on Geometric Methods in Physics 30.06-6.07.2013

Constantin ARCUS

Mechanical Systems in the Generalized Lie Algebroids Framework

Mechanical systems called by use, mechanical (ro;eta)-systems, Lagrange
mechanical (ro;eta)-systems or Finsler mechanical (ro;eta)-systems are presented.
The canonical (ro;eta)-semi(spray) associated to a mechanical (ro;eta)-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical (ro;eta)-systems are the spaces necessary to develop a new Lagrangian formalism.
We obtain the (ro;eta)-semispray associated to a regular Lagrangian L and external force Fe and we derive the equations of Euler-Lagrange type. So, a new
solution for the WeinsteinÂ’s Problem in the general framework of generalized Lie algebroids is presented.

Event sponsored by:
Belgian Science Policy Office     PAI          University
of Bialystok
University of Bialystok

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