Original manuscript: 1996/01/15

The recent introduction of a new notion of controllability and a corresponding computable test has provided a deeper insight into mechanical control systems. This paper focuses on systems whose Lagrangian is the kinetic energy and whose configuration manifold is a Lie group. The theory developed by the Lewis and Murray, coupled with the notion of invariant affine connection, leads naturally to a simple algebraic test. Relevant examples illustrate the theory.

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