Archive for Rational Mechanics and Analysis

, Volume 98, Issue 1, pp 71-93

First online:

Hamiltonian structures and stability for rigid bodies with flexible attachments

  • P. S. KrishnaprasadAffiliated withDepartment of Electrical Engineering, University of Maryland
  • , J. E. MarsdenAffiliated withDepartment of Mathematics, University of California

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


The dynamics of a rigid body with flexible attachments is studied. A general framework for problems of this type is established in the context of Poisson manifolds and reduction. A simple model for a rigid body with an attached linear extensible shear beam is worked out for illustration. Second, the Energy-Casimir method for proving nonlinear stability is recalled and specific stability criteria for our model example are worked out. The Poisson structure and stability results take into account vibrations of the string, rotations of the rigid body, their coupling at the point of attachment, and centrifugal and Coriolis forces.