The retrograde (or backward-time evolution) point mapping numerical method introduced by C. S. Hsu is employed in conjunction with the Liapunov type sufficient conditions to determine the boundary of recovery region (or region of controllability with given control) or the degree of controllability for mechanical systems. The computational algorithm developed here is applicable to highly nonlinear and coupled mechanical systems. In addition, these systems are subjected to uncertainty in some parameters. As an example, the theory developed here is illustrated on a single degree of freedom Duffing system.

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