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Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and Integrability/Nonintegrability Conditions

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  • Tatsuya Kai

Abstract

We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition of A -rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of the A -rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for the A -rheonomous affine constrains. Then, we apply the integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.

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  • Tatsuya Kai, 2012. "Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and Integrability/Nonintegrability Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-32, August.
    • Handle: RePEc:hin:jnlmpe:543098
    DOI: 10.1155/2012/543098
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