The energy and time variables of the elementary classical dynami-cal systems are described geometrically, as canonically conjugate coordinates of an extended phase-space. It is shown that the Galilei action of the inertial equivalence group on this space is canonical, but not Hamiltonian equivari-ant. Although it has no effect at classical level, the lack of equivariance makes the Galilei actio...

The maximal invariance group of Newton's equations for a free non-relativistic point particle is shown to be larger than the Galilei group. It is a semi-direct product of the static (nine-parameter) Galilei group and an SL(2, R) group containing time-translations, dilations and a one-parameter group of time-dependent scalings called expansions. This group was first discovered by Niederer in the...

In the framework of covariant classical mechanics (i.e. , generally relativistic classical mechanics on a spacetime with absolute time) developed by Jadczyk and Modugno, we analyse systematically the relations between symmetries of geometric objects. We show that the (holonomic) infinitesimal symmetries of the cosymplectic structure and of its horizontal potentials are also symmetries of spacel...