  Most passivity based trajectory tracking algorithms for mechanical systems
can only stabilise reference trajectories that have constant energy. This paper
overcomes this limitation by deriving a single variable Hamiltonian model for
the reference trajectory and solving along the constrained trajectory to obtain
a reference potential. This potential is then used as the model to shape the
energy of the true system such that its free solutions include the desired
reference trajectory. The proposed trajectory tracking algorithm interconnects
the reference and true systems through a virtual spring damper along with an
outer-loop energy pump/damper that stabilises the desired energy level of the
interconnected system, ensuring asymptotic tracking of the desired trajectory.
The resulting algorithm is a fully energy based trajectory tracking control for
non-stationary trajectories of conservative mechanical systems.
