Lagrangian Description of the Variational Equations

Details Lagrangian Description of the Variational Equations Lagrangian Description of the Variational Equations

2004-03-21

arxiv.org/abs/math-ph/0403041v1

Chaos, Solitons & Fractals, 18 (2003) 1065-1073

Physics

Mathematical Physics

Scientific paper

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system.

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