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

Abstract

This paper investigates foliation structures of configuration manifolds and develops integrating algorithms for a class of constraints that contain the time variable, calledA-rheonomous affine constrains. We first present some preliminaries on theA-rheonomous affine constrains. Next, theoretical analysis on foliation structures of configuration manifolds is done for the respective three cases where theA-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 integrableA-rheonomous affine constrains. Finally, a physical example is illustrated in order to verify the availability of our new results.