Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule

We address the design of time integrators for mechanical systems that are explicit in the forcing evaluations. Our starting point is the midpoint rule, either in the classical form for the vector space setting, or the Lie form for the rotation group. By introducing discrete, concentrated impulses we can approximate the forcing impressed upon the system over the time step, and thus arrive at first-order integrators. These can be then composed to yield a second order integrator with very desirable properties: symplecticity and momentum conservation.