Relaxed Matching for Stabilization of Mechanical Systems

Long, D. A., A. M. Bloch, J. E. Marsden and D. V. Zenkov

Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS), (2008)


The method of controlled Lagrangians is a technique for stabilizing relative equilibria of mechanical systems with symmetry. This paper develops a modification of kinetic shaping technique in the theory of controlled Lagrangians. The main idea is that the dynamics associated with the controlled Lagrangian is amended by non-conservative forces that act in the shape directions; this gives additional freedom and hence applicability to the method. The usefulness of this methodology is demonstrated on the pendulum on a rotor arm.