On construction of the effective potential in singular cases (Q5938497)

Given a Hamiltonian system with a \(k\)-dimensional symmetry group, we have \(k\) first integrals provided by Noether theorem. The effective potential of the system is defined as minimum of Hamilton function restricted to a level set of \(k\) first integrals, and it is considered as a function of these integrals. This potential is correctly defined for level sets on which the first integrals are functionally independent. Here the author demonstrates how to extend this construction to the case when the Noether first integrals are functionally dependent.