To make this concrete, if the are all cyclic coordinates, and the are all non cyclic, then
2.
The Routhian formulation is useful for systems with cyclic coordinates, because by definition those coordinates do not enter, and hence.
3.
The definition of a generalized momentum can be retained, and the advantageous connection between cyclic coordinates and conserved quantities will continue to apply.
4.
It is simply convenient to let the Hamiltonian equations remove the cyclic coordinates, leaving the non cyclic coordinates to the Lagrangian equations of motion.
5.
It is simply convenient to let the Hamiltonian equations remove the cyclic coordinates, leaving the non cyclic coordinates to the Lagrangian equations of motion.
6.
With these constants substituted into the Routhian, is a function of only the non cyclic coordinates and velocities ( and in general time also)
7.
"' Routhian mechanics "'is a hybrid formulation of Lagrangian and Hamiltonian mechanics, not often used but especially useful for removing cyclic coordinates.
8.
However, if cyclic coordinates occur there will still be equations to solve for all the coordinates, including the cyclic coordinates despite their absence in the Lagrangian.
9.
However, if cyclic coordinates occur there will still be equations to solve for all the coordinates, including the cyclic coordinates despite their absence in the Lagrangian.
10.
Thus the problem has been reduced to solving the Lagrangian equations in the non cyclic coordinates, with the advantage of the Hamiltonian equations cleanly removing the cyclic coordinates.
मोबाइल