| Abstract: |
| We extend the method of controlled Lagrangians to the Euler--Poincare equations with advected parameters. The main goal is to develop a theory for stabilizing mechanical systems with broken symmetry, such as an inverted pendulum or a spinning top, where the gravity breaks the rotational symmetry. Particularly, we consider a mechanical system whose configuration space is a semidirect product of a Lie group and a vector space, where the control is applied to the vector space part only, such as an inverted pendulum or a heavy top spinning on a movable base. We obtain the matching condition for the controlled Lagrangian system as well as conditions for stabilizing the system. |
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