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A geometric formulation for stabilization of systems with one degree ofunderactuation which fully solves the energy shaping problem for these systemis given. The results show that any linearly controllable simple mechanicalsystem 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 whichthe stabilization by energy shaping method is not achievable using apositive-definite closed-loop metric.

Stabilization of Systems with One Degree of Underactuation with Energy Shaping: A Geometric Approach