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Trajectory Planning for a Non‐Flat Mechanical System Using Time‐Reversal Symmetry
Author(s) -
Knoll Carsten,
Röbenack Klaus
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110398
Subject(s) - symmetry (geometry) , mechanical system , property (philosophy) , t symmetry , control theory (sociology) , point reflection , construct (python library) , inversion (geology) , computer science , mathematics , classical mechanics , physics , control (management) , geometry , geology , artificial intelligence , quantum mechanics , paleontology , philosophy , superconductivity , epistemology , structural basin , programming language
Abstract Some mechanical systems have a special discrete symmetry property associated with the inversion of the direction of the time flow. This "time‐reversal symmetry" allows one to construct solutions of the equations of motion from other known solutions. In the present contribution we examine to which systems this property can be applied. Furthermore, we demonstrate how it can be used to determine an open loop control for equilibrium point transition by solving a stabilization problem in the negative time direction. As a non‐flat mechanical example the popular pole‐cart system is considered. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)