A simple mechanical system is one whose Lagrangian is of the form kinetic minus potential energy. Given a set of directions in which one may apply forces to a simple mechanical system, one of the fundamental questions which can be then asked is, "Which configurations can I reach by applying the given forces?" In control theory this is called the "controllability question," and we provide, for simple mechanical systems, a computable answer to certain versions of this question. The controllability tests we derive may be used as a basis for the design of control laws which accomplish common tasks, e.g, system reconfiguration and stabilisation to a specified configuration. The theory will be illustrated by simple examples.

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