T. Kai and H. Kimura, “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, Vol. 42, No. 3, 2006, pp. 212-221.

has been cited by the following article:

• TITLE: An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case

  AUTHORS: Tatsuya Kai

  KEYWORDS: Fully Rheonomous Affine Constraints; Geometric Representation; Rheonomous Bracket; Complete Integrability; Integrating Algorithm

  JOURNAL NAME: Applied Mathematics, Vol.4 No.12, December 25, 2013

  ABSTRACT: This paper develops an integrating algorithm for fully rheonomous affine constraints and gives theoretical analysis of the algorithm for the completely integrable case. First, some preliminaries on the fully rheonomous affine constraints are shown. Next, an integrating algorithm that calculates independent first integrals is derived. In addition, the existence of an inverse function utilized in the algorithm is investigated. Then, an example is shown in order to evaluate the effectiveness of the proposed method. By using the proposed integrating algorithm, we can easily calculate independent first integrals for given constraints, and hence it can be utilized for various research fields.