Another kind of conserved quantity induced by Mei symmetry of mechanico-electrical system

Abstract

Another kind of conserved quantity deduced from Mei symmetry of mechanico-electrical system is studied. Under the infinitesimal transformation of groups, another kind of conserved quantity of Mei symmetry of mechanico-electrical system is obtained from the definition and the criterion of Mei symmetry of mechanico-electrical system. Finally, an example is given to illustrate the application of the result.

Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems

“…Equations in expression (13) are the generalized discrete Hamiltonian canonical equations, and equation ( 14) is the energy equation for nonholonomic system which can define the lattice on which the canonical Hamiltonian equations are discredited.…”

“…where ξ − = ξ(t − , q − , p − ), ξ + = ξ(t + , q + , p + ), (15) leave the discrete Hamiltonian canonical equations (13) and energy equation ( 14) invariant, they are called Lie symmetry transformations of the discrete nonholonomic Hamiltonian system corresponding to the holonomic one.…”