Melvin Leok’s Professional Blog

I have been selected in an internal competition as one of Purdue University’s two nominees in 2009 for the Packard Fellowship for Science and Engineering. Every year, the Packard Foundation invites the presidents of 50 universities to nominate two professors each from their institutions. An advisory panel of distinguished scientists and engineers then selects 20 Fellows to receive individual awards of $875,000, payable over five consecutive years.

[ PDF | arXiv:0903.0332 [math.NA] ]

This paper presents an analytical model and a geometric numerical integrator for a rigid body connected to an elastic string, acting under a gravitational potential. Since the point where the string is attached to the rigid body is displaced from the center of mass of the rigid body, there exist nonlinear coupling effects between the string deformation and the rigid body dynamics. A geometric numerical integrator, refereed to as a Lie group variational integrator, is developed to numerically preserve the Hamiltonian structure of the presented model and its Lie group configuration manifold. These properties are illustrated by a numerical simulation.