The problem of defining Poisson brackets for a degenerate Lagrangian without introduction of canonical variables is discussed. More generally, we introduce and give a complete geometrical description of a class of Poisson brackets on a presymplectic manifold. The construction is illustrated by both finite-dimensional and field-theoretic examples.
We sNdy the inverse problem for Hamiltonian dynamics, with restriaion to the case of linear homogeneous vector fields An algebraic necessary and sufficient condition is derived We study also the problem of symmetries and integrability for a HamiltoNan linear vector field and show that such a field is always wmpletely integrable.
A case of relapsing polychondritis with aortic arch aneurysm and aortic arch syndrome is described. The pattern of vascular involvement supports the inclusion of relapsing polychondritis within the spectrum of systemic vasculitides.
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