scholarly journals An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case

2013 ◽  
Vol 04 (12) ◽  
pp. 1720-1725 ◽  
Author(s):  
Tatsuya Kai
Keyword(s):  
Theoretical Analysis ◽  
Integrable Case ◽  
Completely Integrable ◽  
Affine Constraints

scholarly journals Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part II: Foliation Structures and Integrating Algorithms

2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
Tatsuya Kai
Keyword(s):  
Theoretical Analysis ◽  
First Integrals ◽  
Time Variable ◽  
Completely Integrable ◽  
Affine Constraints ◽  
Configuration Manifolds

This paper investigates foliation structures of configuration manifolds and develops integrating algorithms for a class of constraints that contain the time variable, calledA-rheonomous affine constrains. We first present some preliminaries on theA-rheonomous affine constrains. Next, theoretical analysis on foliation structures of configuration manifolds is done for the respective three cases where theA-rheonomous affine constrains are completely integrable, partially integrable, and completely nonintegrable. We then propose two types of integrating algorithms in order to calculate independent first integrals for completely integrable and partially integrableA-rheonomous affine constrains. Finally, a physical example is illustrated in order to verify the availability of our new results.

On the completely integrable case of the Rössler system

2012 ◽  
Vol 53 (5) ◽  
pp. 052701 ◽  
Author(s):  
Răzvan M. Tudoran ◽  
Anania Gîrban
Keyword(s):  
Integrable Case ◽  
Completely Integrable ◽  
Rossler System ◽  
Rössler System

An L–A pair for the Hess–Apel'rot system and a new integrable case for the Euler–Poisson equations on so(4) × so(4)

2001 ◽  
Vol 131 (4) ◽  
pp. 845-855 ◽  
Author(s):  
Vladimir Dragović ◽  
Borislav Gajić
Keyword(s):  
Three Dimensional ◽  
Classification Theorem ◽  
Geometric Integration ◽  
Integrable Case ◽  
Integration Procedure ◽  
Completely Integrable ◽  
Poisson Equations ◽  
Corrected Version ◽  
Explicit Formulae

We present an L–A pair for the Hess–Apel'rot case of a heavy rigid three-dimensional body. Using it, we give an algebro-geometric integration procedure. Generalizing this L–A pair, we obtain a new completely integrable case of the Euler–Poisson equations in dimension four. Explicit formulae for integrals that are in involution are given. This system is a counterexample to one of Ratiu's theorems. A corrected version of this classification theorem is proved.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-32 ◽  
Author(s):  
Tatsuya Kai
Keyword(s):  
Theoretical Analysis ◽  
Sufficient Conditions ◽  
Complete Integrability ◽  
Geometric Representation ◽  
Fundamental Properties ◽  
Affine Constraints ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Partial Integrability ◽  
Configuration Manifolds

We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition ofA-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of theA-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 theA-rheonomous affine constrains. Then, we apply the integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.

scholarly journals L p Norms of Eigenfunctions in the Completely Integrable Case

2003 ◽  
Vol 4 (2) ◽  
pp. 343-368 ◽  
Author(s):  
J. A. Toth ◽  
S. Zelditch
Keyword(s):  
Integrable Case ◽  
Completely Integrable
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