Dynamical symmetries and conserved quantities

The invariance properties of second order dynamical systems under velocity dependent transformations of the co-ordinates and time are studied. For Lagrangian systems the connection between Noether conserved quantities and dynamical symmetries is not too direct; however, it is shown that for general systems dynamical symmetries always possess associated conserved quantities, which are invariants of the symmetry group itself. In the special case of point symmetries this yields the result that the associated conserved quantity is an invariant of the first extended group. (author)