Horizontal Lin contraints, Clebsch potentials and variational principles on principal fiber bundles

Cendra, H., A. Ibort and J. E. Marsden

Coll. in Group Theor. Meth. in Phys., World Sci., (R. Gilmore, ed.), XV, (1987), 446-450

Abstract:

The main point is how we should incorporate this idea to the extended Lagrangian picture. This is done by changing the Lin constraint used in the trivial bundle case by using a horizontal version of it, in such a way that it decouples the vertical and the horizontal degrees of freedom. This will be thoroughly described in §3. §2 will be devoted to the description of some notation and ideas about principal and associated fiber bundles, and finally in §4 we will show the explicit form of the equations of motion for invariant Lagrangians.