Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Explicit Newmark algorithm for rotational dynamics

Petr Krysl*
University of California, San Diego La Jolla, California 92093-0085, USA

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The explicit Newmark algorithm for vector-space dynamics is the workhorse of structural dynamics. This paper derives the counterpart of the explicit vector-space algorithm for the rotational dynamics of rigid bodies from the midpoint rule in the Lie incarnation. By introducing discrete, concentrated impulses we can approximate the forcing imparted to the system over the time step, and thus we formulate two adjoint explicit first-order integrators. These may be composed to yield a second-order integrator which inherits the symplecticity and momentum conservation of the first-order integrators. In this manner, we get the classical Newmark algorithm for translational motion (vector space dynamics), or the rotation-group Newmark for rigid body rotation problems.

Keywords:  Rigid body dynamics; Explicit time integration; Midpoint algorithm; Symplectic Euler; Newmark; Midpoint Lie

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