scholarly journals Kinetic effects on the stability properties of field-reversed configurations. II. Nonlinear evolution

2004 ◽  
Vol 11 (5) ◽  
pp. 2523-2531 ◽  
Author(s):  
Elena V. Belova ◽  
Ronald C. Davidson ◽  
Hantao Ji ◽  
Masaaki Yamada
Keyword(s):  
Nonlinear Evolution ◽  
Stability Properties ◽  
Kinetic Effects ◽  
The Stability ◽  
Field Reversed Configurations

scholarly journals Kinetic effects on the stability properties of field-reversed configurations. I. Linear stability

2003 ◽  
Vol 10 (6) ◽  
pp. 2361-2371 ◽  
Author(s):  
Elena V. Belova ◽  
Ronald C. Davidson ◽  
Hantao Ji ◽  
Masaaki Yamada
Keyword(s):  
Linear Stability ◽  
Stability Properties ◽  
Kinetic Effects ◽  
The Stability ◽  
Field Reversed Configurations

scholarly journals The stability and nonlinear evolution of quasi-geostrophic toroidal vortices

2019 ◽  
Vol 863 ◽  
pp. 60-78 ◽  
Author(s):  
Jean N. Reinaud ◽  
David G. Dritschel
Keyword(s):  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Azimuthal Mode ◽  
Stability Properties ◽  
Central Vortex ◽  
Minor Radius ◽  
Toroidal Vortices ◽  
The Stability ◽  
Major Radius ◽  
Vortex Array

We investigate the linear stability and nonlinear evolution of a three-dimensional toroidal vortex of uniform potential vorticity under the quasi-geostrophic approximation. The torus can undergo a primary instability leading to the formation of a circular array of vortices, whose radius is approximately the same as the major radius of the torus. This occurs for azimuthal instability mode numbers $m\geqslant 3$, on sufficiently thin tori. The number of vortices corresponds to the azimuthal mode number of the most unstable mode growing on the torus. This value of $m$ depends on the ratio of the torus’ major radius to its minor radius, with thin tori favouring high mode $m$ values. The resulting array is stable when $m=4$ and $m=5$ and unstable when $m=3$ and $m\geqslant 6$. When $m=3$ the array has barely formed before it collapses towards its centre with the ejection of filamentary debris. When $m=6$ the vortices exhibit oscillatory staggering, and when $m\geqslant 7$ they exhibit irregular staggering followed by substantial vortex migration, e.g. of one vortex to the centre when $m=7$. We also investigate the effect of an additional vortex located at the centre of the torus. This vortex alters the stability properties of the torus as well as the stability properties of the circular vortex array formed from the primary toroidal instability. We show that a like-signed central vortex may stabilise a circular $m$-vortex array with $m\geqslant 6$.

The Stability of Radiatively Cooling Jets. II. Nonlinear Evolution

1997 ◽  
Vol 483 (1) ◽  
pp. 136-147 ◽  
Author(s):  
James M. Stone ◽  
Jianjun Xu ◽  
Philip E. Hardee
Keyword(s):  
Nonlinear Evolution ◽  
The Stability

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability
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