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.
NUCCI, M.C., P. G. L. LEACH (2008). The Jacobi Last Multiplier and its Applications in Mechanics. PHYSICA SCRIPTA, 78(6), 065011-1-065011-6 [10.1088/0031-8949/78/06/065011].
The Jacobi Last Multiplier and its Applications in Mechanics
NUCCI, Maria Clara;
2008
Abstract
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.File in questo prodotto:
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