Question

How is the Routhian of classical mechanics defined?

Answer 1

The Hamiltonian is a function on the cotangent bundle to a configuration manifold H:T∗M→R. The Lagrangian is a function on the tangent bundle to the configuration manifold L:TM→R. What is the Routhian function R defined on?

My guess is TM⨁T∗M?

Answer 2

In each case the Lagrangian and Hamiltonian functions are replaced by a single function, the Routhian. ... As with the rest of analytical mechanics, Routhian mechanics is completely equivalent to Newtonian mechanics, all other formulations of classical mechanics, and introduces no new physics.