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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: On Integrability of Fully Rheonomous Affine Constraints

  AUTHORS: Tatsuya Kai

  KEYWORDS: Fully Rheonomous Affine Constraints; Geometric Representation; Rheonomous Bracket; Phillip Hall Basis; Complete Integrability Condition

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.2 No.2, June 18, 2013

  ABSTRACT: This paper presents a complete integrability condition for fully rheonomous affine constraints in terms of the rheonomous bracket. We first define fully rheonomous affine constraints and develop geometric representation for them. Next, the rheonomous bracket is explained and some properties of it are derived. We then investigate a necessary and sufficient condition on complete integrability for the fully rheonomous affine constraints based on the rheonomous bracket as an extension of Frobenius’ theorem. The effectiveness and the availability of the new results are also evaluated via an example.