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 in 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 then be composed to yield a second order integrator with very desirable properties: symplecticity and momentum conservation.

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vector space setting rotation forcing impressed lie form classical second order integrator mechanical systems midpoint rule time integrators properties symplecticity firstorder

P. Krysl,.Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule. 44 (5-6),.

P. Krysl,"Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule" 44

P. Krysl,"Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule"