| Contents |
| We will talk about reduction of Dirac structures by symmetry for nonholonomic systems on Lie groups with broken symmetry. We will review Lagrange-Dirac systems as well as Hamilton-Dirac systems over Lie groups and Lie-Dirac reduction of associated dynamics. Regarding dynamics of rigid body systems and fluids, we will show the reduction of Hamilton-Pontryagin principle and Lie-Dirac reduction with advected parameters by extending the so-called Euler-Poincare and Lie-Poisson reduction with advected parameters. In particular, we will show the Euler-Poincare-Dirac reduction with advective parameters and with nonholonomic constraints. Our theory will be demonstrated by some illustrative examples. |
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