Il Nuovo Cimento B (1971-1996)

, Volume 107, Issue 9, pp 1085–1096 | Cite as

On Lie point symmetries in mechanics

  • G. Cicogna
  • G. Gaeta


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, and construct the most general problem admitting such a symmetry. In the case of Hamiltonian problems, we discuss the differences and the relationships between the existence of time-independent Lie point symmetries and the invariance properties of the Hamiltonian under coordinate transformations.

PACS 02.20

Group theory 

PACS 03.20

Classical mechanics of continuous media general mathematical aspects 


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Copyright information

© Società Italiana di Fisica 1992

Authors and Affiliations

  • G. Cicogna
    • 1
  • G. Gaeta
    • 2
  1. 1.Dipartimento di Fisica dell’UniversitàPisaItalia
  2. 2.C.Ph.Th., Ecole PolytechniquePalaiseauFrance

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