Higher-order mechanical systems with constraints (Q5905588)

A Hamiltonian system with constraints in the sense of R. W. Weber is a \(2n\)-dimensional symplectic manifold with a set of \(r\) linearly independent one-forms, \(r\leq n\). The authors extend such an approach to the higher order mechanical systems by using their methods and results from the theory of higher order tangent bundles, which are gathered in their book ``Methods of differential geometry in analytical mechanics'' (Amsterdam 1989; Zbl 0687.53001). As an example, these new methods are applied to the case of an elastic beam.