Ignacio Romero Olleros’s scientific contributions

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature.

This work shows a simple finite element formulation that enables to impose concentrated moments and rotations to ANC beams which are finite elements that lack rotational degrees of freedom. The idea is based on an specific constraint that expresses in a simple form the relation between the deformation of the beam and the rotation of any of its sections. By controlling this sectional rotation, moments and angles can be easily imposed on any model.