2013/10/06 by Constantin M. Arcus, Arcus, Constantin M.
Mathematics · Physics and Astronomy · #00A69 #53B05 #53B50 #53C05 #58B34 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:00A69 #msc:53B05 #msc:53B50 #msc:53C05 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1310.2131
43 pages International journal of Geometric Methods in Modern Physics, 2013. arXiv admin note: substantial text overlap with arXiv:1108.2844, arXiv:1007.1541, arXiv:1109.1242, arXiv:1101.0960, arXiv:1108.5050
arxiv created 2013/10/06 · arxiv updated 2013/10/09
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.