Open AccessRouth equation of nonholonomic dynamical systems: from Chetaev condition to Euler condition
Author(s) -
Shen Hui-chuan
Publication year - 2005
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.54.2468
Subject(s) - nonholonomic system , nonlinear system , constraint (computer aided design) , lagrange multiplier , mathematical analysis , euler's formula , lagrangian , mathematics , physics , classical mechanics , computer science , mathematical optimization , geometry , artificial intelligence , robot , mobile robot , quantum mechanics
The Routh equation of a nonholonomic system with a nonlinear constraint equation that is expandable to MacLaurin progression on generalized velocity, can be obtained by Lagrangian multiplier method and d'Alembert principle in an ideal constraint condition. Chetaev condition is valid in linear nonholonomic system only, and is eguivalent to Vacco condition. The so-called “Euler condition" can unite Chetaev condition and Vacco condition, can unite d'Alembert principle and Hamilton principle, and can resolve all existing problems in nonlinear nonholonomic system.