Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds-Part Ⅰ: Fundamental Properties and Integrability/Nonintegrability Conditions

Tatsuya Kai

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Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds-Part Ⅰ: Fundamental Properties and Integrability/Nonintegrability Conditions

机译：一类构型流形上的仿形约束的理论分析-第一部分：基本性质和可积/不可积条件

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We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrabilityonintegrability. First, we give the definition of A-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of the A-rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for the A-rheonomous affine constrains. Then, we apply the integrabilityonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.

机译：我们从可集成性/不可集成性的角度分析了在配置流形上定义的一类隆重仿射约束。首先，我们给出了A-rheomous仿射约束的定义，并介绍了其几何表示。还推导了A-rhenomous仿射约束的一些基本属性。接下来，我们定义斜方括号，并针对这三种情况分别导出一些必要条件和充分条件：A形律仿射约束的完全可积性，部分可积性和完全不可积性。然后，我们将可积性/不可积性条件应用于一些物理示例，以确认我们新结果的有效性。

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《Mathematical Problems in Engineering》 |2012年第7期|543098.1-543098.32|共32页
作者
Tatsuya Kai;
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Department of Applied Electronics, Faculty of Industrial Science and Technology, Tokyo University of Science, Chiba 278-8510, Japan;

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1. Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds-Part Ⅱ: Foliation Structures and Integrating Algorithms [J] . Tatsuya Kai Mathematical Problems in Engineering . 2012,第pta7期

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2. An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case [J] . Tatsuya Kai Applied Mathematics . 2013,第12期

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3. Mathematical modelling and theoretical analysis of nonholonomic kinematic systems with a class of rheonomous affine constraints [J] . Tatsuya Kai Applied Mathematical Modelling . 2012,第7期

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4. New hamiltonian formulation of rheonomous affine constraints based on the rheonomous bracket [C] . Kai Tatsuya 2012 IEEE International Conference on Control Applications. . 2012

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Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds-Part Ⅰ: Fundamental Properties and Integrability/Nonintegrability Conditions

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