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Mechanical systems in the generalized Lie algebroids framework

Constantin M. Arcuş

Secondary School "CORNELIUS RADU", Rădineşti Village 217196, Gorj County, România

https://doi.org/10.1142/S0219887814500236Cited by:7 (Source: Crossref)

Abstract

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 F_e 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.

In memory of Prof. Dr. Gheorghe RADU and Acad. Dr. Doc. Cornelius RADU.

Dedicated to Acad. Dr. Doc. Radu MIRON from Iassy University, Romania, on his 86th anniversary

Keywords:

AMSC: 00A69, 58B34, 53B05, 53B50, 53C05

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