Regularity properties of fiber derivatives associated with higher-order mechanical systems (Q2820914)

The authors investigate the dynamics of a higher-order autonomous dynamical system. They consider a Hamiltonian function on \( T^\ast T^{(k-1)}Q\) (where \(Q\) is a fiber bundle) that describes the dynamics of a \(k\)th-order autonomous dynamical system. The authors give a suitable definition of (hyper)regularity for these higher-order Hamiltonian functions in terms of their fiber derivative and apply it in the investigation. Also the Lagrangian approach is under consideration. The dynamics in Lagrangian submanifolds in terms of the solutions of the higher-order Euler-Lagrange equations is investigated.