The inverse variational problem in nonholonomic mechanics
Presented by Prof. Jana MUSILOVá
Type: Oral presentation
Track: Diferential Geometry and Mathematical Physics
The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality of a mechanical system is introduced, based on a nonholonomic variational principle. Variational properties of mechanical systems of the first order with general constraints are presented. It is proved that constraint variationality is equivalent with the existence of a closed representative of the class of 2-forms characterizing the nonholonomic system. This result and resulting constraint Helmholtz conditions of variationality represent basic geometrical properties of constraint variational systems. Examples are presented as well, concerning planar motions and a particle in special relativity theory.