Lagrangian and Hamiltonian dynamics of submanifolds
  Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their Lagrangians and Hamiltonians must satisfy rather restrictive Noether identities. For instance, this is the case of relativistic mechanics and classical string theory. 
G.Giachetta, L.Mangiarotti, G.Sardanashvily