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Title: Connections on the fibre bundle and application to the Lagrangian mechanics
Authors: Mehdi, M.
Farah, Farah 
Mortada, A
Affiliations: Department of Mathematics 
Keywords: Connections
Lagrangian mechanics
Fibre bundle
Issue Date: 2013
Part of: Journal of geometry and topology
Volume: 13
Issue: 2
Start page: 119
End page: 151
In this paper, we use the notion of Grifones connection over a tangent bundle in order to construct a connection over a sub-bundle. Then we characterize the solutions of non-holonomic Lagrangian mechanics and show that the geodesics of the connection constructed on the sub-bundle are the solutions of the non-holonomic Euler-Lagrange system. Finally, we will prove that the Hamiltonian associated to Lagrangian function is constant along the horizontal curves.
Type: Journal Article
Appears in Collections:Department of Mathematics

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