A. M. Bloch, “Nonholonomic Mechanics and Control,” Springer-Verlag, New York, 2003. doi:10.1007/b97376
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.