Noether-Mei symmetry and conserved quantity of Birkhoffian system. (Chinese. English summary) Zbl 1374.70052
Summary: The Noether-Mei symmetry and the conserved quantity of a Birkhoffian system are studied. The definition and the criteria of the Noether-Mei symmetry of the system are given. The conditions under which a Noether-Mei symmetry leads to a Noether conserved quantity or a Mei conserved quantity and the form of the conserved quantities are obtained. Two theorems for the Noether-Mei symmetry and the conserved quantity are established. At the end, an example is given to illustrate the application of the results.
MSC:
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
