  A geometric formulation for stabilization of systems with one degree of
underactuation which fully solves the energy shaping problem for these system
is given. The results show that any linearly controllable simple mechanical
system with one degree of underactuation is stabilizable by energy shaping,
possibly via a closed-loop metric which is not necessarily positive-definite.
An example of a system with one degree of underactuation is provided for which
the stabilization by energy shaping method is not achievable using a
positive-definite closed-loop metric.
