Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and IntegrabilityNonintegrability Conditions

Abstract EN

We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability.

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 integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.