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.

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 Moving energies as first integrals of nonholonomic systems with affine constraints

Nonlinearity ◽  
2018 ◽  
Vol 31 (3) ◽  
pp. 755-782 ◽  
Author(s):  
Francesco Fassò ◽  
Luis C García-Naranjo ◽  
Nicola Sansonetto
Keyword(s):  
Nonholonomic Systems ◽  
First Integrals ◽  
Affine Constraints

Saturn's E, G and F rings: modulated by the plasma sheet

1984 ◽  
Vol 75 ◽  
pp. 597
Author(s):  
E. Grün ◽  
G.E. Morfill ◽  
T.V. Johnson ◽  
G.H. Schwehm
Keyword(s):  
Solar Wind ◽  
Direct Contact ◽  
Transport Processes ◽  
Time Variable ◽  
Dust Particles ◽  
Spatial Diffusion ◽  
Drag Forces ◽  
Orbit Perturbation ◽  
Time Variations ◽  
F Ring

ABSTRACTSaturn's broad E ring, the narrow G ring and the structured and apparently time variable F ring(s), contain many micron and sub-micron sized particles, which make up the “visible” component. These rings (or ring systems) are in direct contact with magnetospheric plasma. Fluctuations in the plasma density and/or mean energy, due to magnetospheric and solar wind processes, may induce stochastic charge variations on the dust particles, which in turn lead to an orbit perturbation and spatial diffusion. It is suggested that the extent of the E ring and the braided, kinky structure of certain portions of the F rings as well as possible time variations are a result of plasma induced electromagnetic perturbations and drag forces. The G ring, in this scenario, requires some form of shepherding and should be akin to the F ring in structure. Sputtering of micron-sized dust particles in the E ring by magnetospheric ions yields lifetimes of 102to 104years. This effect as well as the plasma induced transport processes require an active source for the E ring, probably Enceladus.

Microdiffraction Patterns of Small Metallic Particles II; Theoretical Analysis

1982 ◽  
Vol 40 ◽  
pp. 668-669
Author(s):  
A. Gómez ◽  
P. Schabes-Retchkiman ◽  
M. José-Yacamán ◽  
T. Ocaña
Keyword(s):  
Experimental Data ◽  
Electron Diffraction ◽  
Theoretical Analysis ◽  
Size Range ◽  
Dynamical Theory ◽  
Metallic Particles ◽  
Splitting Effect

The splitting effect that is observed in microdiffraction pat-terns of small metallic particles in the size range 50-500 Å can be understood using the dynamical theory of electron diffraction for the case of a crystal containing a finite wedge. For the experimental data we refer to part I of this work in these proceedings.

Theoretical analysis of a monopole antenna with conducting flat disk above the earth

2001 ◽  
Vol 84 (7) ◽  
pp. 27-36
Author(s):  
Aki Yuasa ◽  
Daisuke Itatsu ◽  
Naoki Inagaki ◽  
Nobuyoshi Kikuma
Keyword(s):  
Theoretical Analysis ◽  
Monopole Antenna ◽  
The Earth ◽  
Flat Disk

Context Aversion, Pavlovian Conditioning, and the Psychological Side Effects of Chemotherapy

1997 ◽  
Vol 2 (2) ◽  
pp. 118-124
Author(s):  
Geoffrey Hall
Keyword(s):  
Animal Model ◽  
Side Effects ◽  
Theoretical Analysis ◽  
Conditioned Response ◽  
Behavioral Strategies ◽  
Contextual Cues ◽  
Anticipatory Nausea ◽  
Laboratory Rats ◽  
Anticipatory Nausea And Vomiting ◽  
Parallel Case

Patients who have undergone several sessions of chemotherapy for cancer will sometimes develop anticipatory nausea and vomiting (ANV), these unpleasant side effects occurring as the patients return to the clinic for a further session of treatment. Pavlov's analysis of learning allows that previously neutral cues, such as those that characterize a given place or context, can become associated with events that occur in that context. ANV could thus constitute an example of a conditioned response elicited by the contextual cues of the clinic. In order to investigate this proposal we have begun an experimental analysis of a parallel case in which laboratory rats are given a nausea-inducing treatment in a novel context. We have developed a robust procedure for assessing the acquisition of context aversion in rats given such training, a procedure that shows promise as a possible animal model of ANV. Theoretical analysis of the conditioning processes involved in the formation of context aversions in animals suggests possible behavioral strategies that might be used in the alleviation of ANV, and we report a preliminary experimental test of one of these.

Sign in / Sign up

Export Citation Format

Share Document