Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 345942, 34 pages
Research Article

Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part II: Foliation Structures and Integrating Algorithms

Department of Applied Electronics, Faculty of Industrial Science and Technology, Tokyo University of Science, Chiba 278-8510, Japan

Received 6 May 2012; Revised 3 July 2012; Accepted 4 July 2012

Academic Editor: Wei-Chiang Hong

Copyright © 2012 Tatsuya Kai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates foliation structures of configuration manifolds and develops integrating algorithms for a class of constraints that contain the time variable, called A-rheonomous affine constrains. We first present some preliminaries on the A-rheonomous affine constrains. Next, theoretical analysis on foliation structures of configuration manifolds is done for the respective three cases where the A-rheonomous affine constrains are completely integrable, partially integrable, and completely nonintegrable. We then propose two types of integrating algorithms in order to calculate independent first integrals for completely integrable and partially integrable A-rheonomous affine constrains. Finally, a physical example is illustrated in order to verify the availability of our new results.