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                Department of Mathematical Sciences
                   The Johns Hopkins University

                              SEMINAR

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Gregory S. Chirikjian                             October 11, 2001
Department of Mechanical Engineering              304 Whitehead Hall
The Johns Hopkins University                      Refreshments: 3:30 p.m.
                                                  Seminar: 4:00 p.m.

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             DEGENERATE DIFFUSIONS ON MOTION GROUPS:
          APPLICATIONS IN ROBOTICS AND POLYMER SCIENCE


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                               ABSTRACT

This talk reviews problems from different research fields that are
described using the same mathematical tools.  In particular, we
examine partial differential equations (PDEs) of the Fokker-Planck
type that describe processes which evolve on the Euclidean motion
groups.  It is shown that problems such as the workspace generation
of highly articulated robotic manipulators, the random motion of a
rolling wheel, and the statistical mechanics of macromolecules are
described by the same type of PDEs.  These PDEs are written in terms
of generators of motion groups, and solved using methods of noncommutative
harmonic analysis.  Namely, the Fourier transforms for motion groups
convert these PDEs into systems of linear ODEs in a generalized Fourier
space, which are solved in closed form.  The group-theoretic inverse
Fourier transform converts this solution to the motion-group domain.

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