  We describe a new algorithm for trajectory optimization of mechanical
systems. Our method combines pseudo-spectral methods for function approximation
with variational discretization schemes that exactly preserve conserved
mechanical quantities such as momentum. We thus obtain a global discretization
of the Lagrange-d'Alembert variational principle using pseudo-spectral methods.
Our proposed scheme inherits the numerical convergence characteristics of
spectral methods, yet preserves momentum-conservation and symplecticity after
discretization. We compare this algorithm against two other established methods
for two examples of underactuated mechanical systems; minimum-effort swing-up
of a two-link and a three-link acrobot.
