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Kai, T. and Kimura, H. (2006) Theoretical Analysis of Affine Constraints on a Configuration Manifold—Part I: Integrability and Nonintegrability Conditions for Affine Constraints and Foliation Structures of a Configuration Manifold. Transactions of the Society of Instrument and Control Engineers, 42, 212-221.

has been cited by the following article:

• 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.