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Hamiltonian structures and stability for rigid bodies with flexible attachments. (English) Zbl 0624.58010

The authors put together a continuum model for flexible structures and a finite-dimensional rigid body model and use the general Hamiltonian method to study nonlinear stability. A simple example is worked out, and it is investigated in detail. The procedures used can be adapted to realistic situations. The paper includes some results concerning the reduction of Poisson manifolds and a review of the energy-Casimir method.
Reviewer: Yu.E.Gliklikh

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70E99 Dynamics of a rigid body and of multibody systems
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