Global variational methods on smooth nonholonomic constraints

AbstractWe develop a variational theory for critical points of integral functionals in a space of curves on a manifold M, between a fixed point and a one-dimensional submanifold of M, and satisfying a nonholonomic constraint equation φ=0, where φ is a C2 function defined on TM×R.We obtain existence, regularity and multiplicity results, writing the integro-differential equations satisfied by critical points. Moreover, we present some results concerning a sort of exponential map relative to the integro-differential equations and some examples