  We provide a model for an open invariant neighborhood of any orbit in a
symplectic manifold endowed with a canonical proper symmetry. Our results
generalize the constructions of Marle and Guillemin and Sternberg for canonical
symmetries that have an associated momentum map. In these papers the momentum
map played a crucial role in the construction of the tubular model. The present
work shows that in the construction of the tubular model it can be used the so
called Chu map instead, which exists for any canonical action, unlike the
momentum map. Hamilton's equations for any invariant Hamiltonian function take
on a particularly simple form in these tubular variables. As an application we
will find situations, that we will call tubewise Hamiltonian, in which the
existence of a standard momentum map in invariant neighborhoods is guaranteed.
