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.
The Jacobi Last Multiplier and its Applications in Mechanics / NUCCI, Maria Clara; P. G. L. LEACH. - In: PHYSICA SCRIPTA. - ISSN 0031-8949. - STAMPA. - 78:6(2008), pp. 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
