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On Integrability of Fully Rheonomous Affine Constraints
Faculty of Industrial Science and Technology, Tokyo University of Science, Tokyo, Japan
- 1 Faculty of Industrial Science and Technology, Tokyo University of Science, Tokyo, Japan
International Journal of Modern Nonlinear Theory and Application·Volume 02 (2013)·Pages 130–134·Published 13 June 2013·DOI10.4236/ijmnta.2013.22016
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Abstract
This paper presents a complete integrability condition for fully rheonomous affine constraints in terms of the rheonomous bracket. We first define fully rheonomous affine constraints and develop geometric representation for them. Next, the rheonomous bracket is explained and some properties of it are derived. We then investigate a necessary and sufficient condition on complete integrability for the fully rheonomous affine constraints based on the rheonomous bracket as an extension of Frobenius’ theorem. The effectiveness and the availability of the new results are also evaluated via an example.
KeywordsFully Rheonomous Affine ConstraintsGeometric RepresentationRheonomous BracketPhillip Hall BasisComplete Integrability Condition
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