Mechanical Systems in the Generalized Lie Algebroids Framework

الأصل · EN

Mechanical systems called by use, mechanical(ρ,η) -systems, Lagrange mechanical(ρ,η) -systems or Finsler mechanical(ρ,η) -systems are presented. The canonical (ρ,η) -semi(spray) associated to a mechanical (ρ,η) -system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical (ρ,η)% -systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the (ρ,η)-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 Weinstein's Problem in the general framework of generalized Lie algebroids is presented.