Cartan–Lepage forms in geometric mechanics

We present variational principles for mechanics on the basis of the Cartan 1-form. We extend the theory to the Cartan–Lepage 2-forms related with dynamical forms and equations of motion. Explicit coordinate formulae for Lepage equivalents of dynamical forms are given.

► Variational principles for mechanics on the basis of the Cartan 1-form are presented.
► The theory is extended to the Cartan–Lepage 2-forms related with dynamical forms and equations of motion.
► Explicit coordinate formulae for Lepage equivalents of dynamical forms are given.