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Fotos Filme Projekte Schule Fun Norwegen                

Nonholonomic Mechanical

The Project:

Numerical simulation of nonholonomic mechanical systems


Nonholonomic mechanical systems are of great interest in robot technologyapplications and control, in particular robotic locomotion and robotic grasping. Roughly speaking a mechanical system with nonholonomic constraints is described by a constrained di erential equation (in Lagrangian or Hamiltonian form) such that the constrains are involving the velocity of the system and not only the positions. In this project the numerical simulation of some simple noholonomic mechanical systems will be considered. Possible examples are a vertical disk rolling on a plane, gure 2, a nonholonomically constrained particle in R3, a ball on a spinning plate, the snake-board (a variant of the skate-board), gure 1. The aim of the project is understanding the basic theoretical features of nonholonomically constrained systems, illustrate them via numerical simulation, and discuss which numerical approaches are best suited for such problems. In particular classical Runge-Kutta methods will be rst applied to the problems and then more specic geometric integrators will be also used. A comparison of the performance of the methods will be part of the presented results.


Figure 1: The snake-board.


Figure 2: The rolling disk

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Letzte Aktualisierung 09.01.2007 18:50

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