Advanced Topics in Dynamics and Geometric Mechanics
CDS 280: Winter and Spring Terms 2007

Tuesdays
1:00PM - 2:25PM
Steele 114


Schedule

Date

Lecture

Speaker

May 29

No Meeting


May 22

Title: Geometric Quantization and Reduction (Continued)

Paul Skerritt


May 15

Title: Geometric Quantization and Reduction

Paul Skerritt


May 8

No meeting


May 1

No Meeting; see -> Structured Integrators Workshop


Apr 24

Title: Hamilton equations for gauge invariant problems

Marco Castrillon Lopez


Apr 17

Title: A Discrete Geometric Framework for Optimal Control on Lie Groups


Abstract: The optimal control of left-invariant Lie group mechanical systems derived from a discrete Pontryagin-d'Alembert principle is studied. Computational efficiency is addressed in terms of the choice of formulation (direct vs indirect), coordinate(free) representation, choice of initial trajectory, and trajectory refinement scheme. Rigid body reorientation on SO(3) with minimum control effort is used as an example (experimental analysis of run-time, convergence, and accuracy is presented as well).

Marin Kobilarov, USC


Apr 10

Title: Lie Quadratics


Abstract: The talk will describe some relationships between 1. motion planning, 2. Lie algebras, 3. linear differential equations, 4. nonlinear differential equations and 5. classical mechanics as well as recent results on asymptotics.

Lyle Noakes


Apr 3

Title: Optimally controlled motion sequences for atheletes


Abstract: During the last decades techniques in sports have been advanced continously. These enhancements usually lead to more efficient motion sequences allowing the athlete to improve his performance. Therefore, it is of big interest to compute and analyse motion sequences which are optimal with respect to a specific goal. By modelling the limbs and muscles as a multi-body system controlled via external forces, the computation of the optimal motion of this mechanical system can be formulated as an optimal control problem.


In this talk, firstly a new approach to the solution of optimal control problems for mechanical systems (DMOC) is proposed. It is based on a direct discretization of the Lagrange-d'Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete Euler-Lagrange equations then serve as constraints for the optimization of a given cost functional.


We illustrate the method by two numerical examples of optimally controlled motion sequences. In the first rather simple problem, the resulting multi-body system is formulated as an unconstrained mechanical system in generalized coordinates. To simplify the derivation of the forced discrete Euler-Lagrange equations, the second more complex problem is formulated as a higher dimensional constraint mechanical system with Lagrange multipliers. By applying the discrete null space method, we demonstrate how the constraint equations for the optimization problem can be reduced to the minimal possible dimension.


This is joint work with Helmut B�hmer (University of Paderborn), Oliver Junge (TU München), Sigrid Leyendecker (Caltech) and Jerry Marsden (Caltech)

Sina Ober-Blöbaum, University of Paderborn


Mar 27

Title: Stably Extending Two-Dimensional Bipedal Walking to Three Dimensions via Geometric Reduction

Aaron Ames, CDS


Mar 13, 20

Dynarum meeting and Spring Break


Mar 6

Optimal control for the Compass Biped

David Pekarek


Feb 27

Optimal Control, Rolling Balls, and Geometric Phases

Hernan Cendra


Feb 20

Reduction by Stages with an Application to Fluid Flow in a Cylinder

Tudor Ratiu


Feb 13

Lagrangian Coherent Structures for Tropical Storms

Philip DuToit


Feb 6

No meeting


Jan 30

No meeting


Jan 23

Dynarum meeting


Jan 16

Practice talks and posters for Dynarum

Jerry Marsden


Jan 9

Organizational meeting for Dynarum

Jerry Marsden