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Lie-point symmetries in Mechanics
(29K, Plain TeX)
ABSTRACT. We present some remarks on the existence and the properties of Lie point
symmetries of finite dimensional dynamical systems expressed either in
Newton-Lagrange or in Hamilton form. We show that the only Lie symmetries
admitted by Newton-Lagrange-type problems are essentially linear symmetries,
construct the most general problem admitting such a symmetry. In the case of
Hamilton problems, we discuss the differences and the relationships between the
existence of time-independent Lie point symmetries and the invariance
of the Hamiltonian under coordinate transformations