A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions

The geometrically exact model of an elastic rod, formulated in [23] the Simo–Reissner rod model has been proposed and investigated. We present a constrained Hamiltonian formulation of the elastic rod model as well as a constrained multi-Hamiltonian formulation of the model. In both formulations, quaternions are used to represent the group of rotations. The resulting Hamiltonian PDE and multi-Hamiltonian formulation have simple looking formats involving constant structure matrices.