Energy shaping is the process whereby a mechanical system is transformed, using feedback, into another mechanical system. Typically one wishes that the closed-loop system have certain desirable properties, e.g., stability of an equilibrium point. In this talk we focus on some of the fundamental problems arising from energy shaping. The big objective is to understand the structure of the set of closed-loop systems. This appears to be difficult in general, so we content ourselves with providing some hopefully tractable pieces of the general problem, and giving some partial results.

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