Partial Integrability Conditions and an Integrating Algorithm for Fully Rheonomous Affine Constraints

Tatsuya Kai

Department of Applied Electronics, Faculty of Industrial Science and Technology, Tokyo University of Science, Tokyo, Japan.

DOI: 10.4236/cs.2014.56015                

Abstract

In this paper, integrability conditions and an integrating algorithm of fully rheonomous affine constraints (FRACs) for the partially integrable case are studied. First, some preliminaries on the FRACs are illustrated. Next, necessary and sufficient conditions on the partially integrable case for the FRACs are derived. Then, an integrating algorithm to calculate independent first integrals of the FRACs for the partially integrable case is derived. Moreover, the existence of an inverse function utilized in the algorithm is proven. After that, an example is presented for evaluation of the effectiveness of the proposed method. As a result, it turns out that the proposed integrating algorithm can easily calculate independent first integrals for given partially integrable FRACs, and thus this new algorithm is expected to be applied to various research fields.

Keywords

Fully Rheonomous Affine Constraints, Geometric Representation, Rheonomous Bracket, Partial Integrability, Integrating Algorithm

Conflicts of Interest

The authors declare no conflicts of interest.

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