Lie symmetries and conserved quantities of rotational relativistic systems (Q1580401)

The authors consider rotational relativistic dynamical equations with holonomic and nonholonomic constraints. The first result is that, for the infinitesimal transformation generators \(\xi_0\) and \(\xi_s\) satisfying the determining equation \(\ddot\xi_s- q_s\ddot\xi_0- 2\dot\xi_0 h_s= X^{(1)}(h_s)\) \((s= 1,2,\dots, n)\) there exists a conserved quantity corresponding to Lie symmetries for rotational relativistic holonomic systems, if there exists a function \(G= G(t,q,\dot q)\) satisfying a special nonlinear differential equation. Other results are analogous to the above-stated result, but concern the rotational relativistic nonholonomic systems.