Explicit momentum-conserving integrator for dynamics of rigid bodies approximating the midpoint Lie algorithm

We reformulate the midpoint Lie algorithm, which is implicit in the torque calculation, to achieve explicitness in the torque evaluation. This is effected by approximating the impulse imparted over the time step with discrete impulses delivered at either the beginning of the time step or at the end of the time step. Thus, we obtain two related variants, both of which are explicit in the torque calculation, but only first order in the time step. Both variants are momentum conserving and both are symplectic. Consequently, drawing on the properties of the composition of maps, we introduce another algorithm that combines the two variants in a single time step. The resulting algorithm is explicit, momentum conserving, symplectic, and second order. Its accuracy is outstanding and consistently outperforms currently known implicit and explicit integrators