Francesco Fassò (Università di Padova, Italy)
The strange world of nonholonomic systems (or, symmetry and integrability in nonholonomic mechanics)
Curious behaviours of mechanical nonholonomic systems (bodies that turn only in one direction, balls which do not fall, ...) are well known, but `strangeness' permeates this class of systems even at more conceptual levels. Nonholonomic systems differ from holonomic (i.e., Lagrangian or Hamiltonian) systems in the crucial fact that their equations of motion do not have a variational nature. This impacts on fundamental features of these systems, such as the link between symmetries and conservation laws (Noether theorem) and even the conservation of energy, and produces a strange world in which some of the basic categories which form our baggage from classical physics do not apply--or there are only some remnants of them. The talk aims at describing this situation, and its implications, in particular, for the integrability of nonholonomic mechanical systems.