Physica Scripta · 2008 · 105 citations · 18 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsMathematical PhysicsClassical MechanicsHamiltonian DynamicsHamiltonian MechanicsLagrangian MechanicsLie AlgebrasNonlinear DynamicsDynamic Equations Of MotionFirst IntegralsHamilton-jacobi EquationsHamilton-jacobi TheoryHamiltonian Systems With SymmetryLagrange's Equations Of MotionNonlinear Oscillator AnalysisSymmetries
We exploit the relationships between the Lie symmetries of a mechanical system, the Jacobi Last Multiplier and the Lagrangian of the system to construct alternative Lagrangians and first integrals in the case that there is a generous supply of symmetry. A Liénard-type nonlinear oscillator is used as an example. We also exemplify the sometimes impossible connection between the general solution of a dynamical system and its first integrals.
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