A Special Nonlinear Connection in Second Order Geometry
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Publication:3615312
zbMATH Open1164.53323arXiv0706.4362MaRDI QIDQ3615312
Publication date: 19 March 2009
Abstract: We show that, for mechanical system with external forces, the equations of deviations of solution curves of the corresponding Lagrange equations,determine a nonlinear connection on the second order osculator (second order tangent) bundle. In particular, Jacobi equations in Finsler and Riemann spaces determine such a nonlinear connection.
Full work available at URL: https://arxiv.org/abs/0706.4362
Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Higher-order theories for problems in Hamiltonian and Lagrangian mechanics (70H50)
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