On Integrability of Fully Rheonomous Affine Constraints

• 作者: Tatsuya Kai
• 来源期刊: 现代非线性理论与应用(英文)
• 学科: 数学
• 关键词: Fully Rheonomous AFFINE CONSTRAINTS GEOMETRIC Representation Rheonomous BRACKET Phillip HALL Basis Complete INTEGRABILITY Condition
• 年，卷（期）: 2013,（2）
• 页码范围: 130-134
• 页数: 5页
• 分类号: O1

摘要

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.