Moving Frames for Cotangent Bundles

This paper has a very modest scope: we present our “operational system” for Hamiltonian mechanics on cotangent bundles M = T Q, based on moving frames. In a related work [10], we will present some concrete examples to convey the algorithmical nature of this formalism. A powerful tool in riemannian geometry is the “method of moving frames”, introduced by Élie Cartan. Actually, moving frames appeared earlier in Lagrangian Mechanics: Poincaré presented in 1901 a moving frame version of the Euler-Lagrange equations, later refered as the “quasi-coordinates” method. Cartan himself has advocated applying moving frames in mechanics [5], in particular using his equivalence method. See [9] for a modern exposition of Cartan’s paper.