TITLE:
Partial Integrability Conditions and an Integrating Algorithm for Fully Rheonomous Affine Constraints
AUTHORS:
Tatsuya Kai
KEYWORDS:
Fully Rheonomous Affine Constraints, Geometric Representation, Rheonomous Bracket, Partial Integrability, Integrating Algorithm
JOURNAL NAME:
Circuits and Systems,
Vol.5 No.6,
June
13,
2014
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.