  A section of a Hamiltonian system is a hypersurface in the phase space of the
system, usually representing a set of one-sided constraints (e.g. a boundary,
an obstacle or a set of admissible states). In this paper we give local
classification results for all typical singularities of sections of regular
(non-singular) Hamiltonian systems, a problem equivalent to the classification
of typical singularities of Hamiltonian systems with one-sided constraints. In
particular we give a complete list of exact normal forms with functional
invariants, and we show how these are related/obtained by the symplectic
classification of mappings with prescribed (Whitney-type) singularities,
naturally defined on the reduced phase space of the Hamiltonian system.
