Classical dynamics, alternative carrier spaces and group-valued constants of motion (Q1573836)

This paper deals with a classical mechanical system which is described by a second order differential equation on a differentiable manifold \(Q\), identified as the configuration space. By using coordinates \((q_a)\) for \(Q\), \(a\in \{1,2,\dots, n\}\) the differential equation has the form \[ \frac{d^2}{dt^2} q_a= f_a \biggl( q,\frac{dq}{dt} \biggr). \tag{1} \] The authors show that (1) may admit alternative Lagrangian and Hamiltonian descriptions. When \(Q\) is in addition a Lie group, the bundle may be a double Lie group; in this case the authors find group-valued constants of motion.