César Rodrigo
Departamento de Matemática, Universidad de Salamanca
The momentum map in Vakonomic Mechanics
Under certain conditions on the constraint submanifold, the
concepts of Cartan form and momentum map are introduced for vakonomic
dynamical systems. We also stablish the relation of these notions with the
corresponding ones derived by application of the Lagrange multipliers
method.
The theory is illustrated by three classical examples (the skateboard, the
ball rolling on a surface and the generalized elastica), letting an
insight
into the differences between the vakonomic and non-holonomic methods.