On the Legendre transformation for singular Lagrangians and related topics
Uwakmfon
The authors study the concept of projectability by the Legendre transformation FL:TQ to T*Q induced by a singular Lagrangian, and the restrictions on this concept when submanifolds of TQ are considered. The FL projectability of the characteristic vector fields and constraint functions relative to such a submanifold is analysed, thus giving a way of characterising the submanifolds of TQ according to their behaviour under FL, by means of the study of the tangency of the fields belonging to ker FL*. The application of some of the results to the theory of constrained systems is discussed.
