scholarly journals Superbrane actions and geometrical approach

2007 ◽  
pp. 79-91 ◽  
Author(s):  
I. Bandos ◽  
P. Pasti ◽  
D. Sorokin ◽  
M. Tonin
Keyword(s):  
Geometrical Approach

Studies on Isotropy of Planar 5-Bar Linkages

2004 ◽  
Author(s):  
C. Amarnath ◽  
K. N. Umesh
Keyword(s):  
Geometric Approach ◽  
Geometrical Approach ◽  
End Effector ◽  
Isotropic Point ◽  
Important Requirement ◽  
Point To Point

The ability to move at reasonable ease in all directions is an important requirement in the design of manipulators. The degree of ease of mobility varies from point to point in the workspace of the manipulator’s end effector. Maximum ease of mobility is obtained at an isotropic point, and the minimum occurs at singularities. An attempt has been made here to use a geometric approach for determining the isotropic points in the workspace of planar 5-bar linkages. The geometrical approach leads to interesting observations on the location of isotropic points in the workspace. The procedure also yields a technique for the synthesis of 5-bar linkages and associated coupler points exhibiting isotropic behaviour. Additionally it has been shown that coupler points exhibiting isotropic mobility occur in pairs.

Integrating nutrition: a geometrical approach

1999 ◽  
Vol 91 (1) ◽  
pp. 67-82 ◽  
Author(s):  
D. Raubenheimer ◽  
S.J. Simpson
Keyword(s):  
Geometrical Approach

scholarly journals Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum

2001 ◽  
Vol 435 ◽  
pp. 103-144 ◽  
Author(s):  
M. RIEUTORD ◽  
B. GEORGEOT ◽  
L. VALDETTARO
Keyword(s):  
Lyapunov Exponent ◽  
Velocity Field ◽  
Spherical Shell ◽  
Asymptotic Properties ◽  
Analytical Form ◽  
Shear Layers ◽  
Three Dimensions ◽  
Geometrical Approach ◽  
Steady Flows ◽  
Whole Space

We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic equation (Poincaré's equation) satisfied by inviscid solutions. Characteristics are straight lines in a meridional section of the shell, and the mapping shows that, generically, these lines converge towards a periodic orbit which acts like an attractor (the associated Lyapunov exponent is always negative or zero). We show that these attractors exist in bands of frequencies the size of which decreases with the number of reflection points of the attractor. At the bounding frequencies the associated Lyapunov exponent is generically either zero or minus infinity. We further show that for a given frequency the number of coexisting attractors is finite.We then examine the relation between this characteristic path and eigensolutions of the inviscid problem and show that in a purely two-dimensional problem, convergence towards an attractor means that the associated velocity field is not square-integrable. We give arguments which generalize this result to three dimensions. Then, using a sphere immersed in a fluid filling the whole space, we study the critical latitude singularity and show that the velocity field diverges as 1/√d, d being the distance to the characteristic grazing the inner sphere.We then consider the viscous problem and show how viscosity transforms singularities into internal shear layers which in general reveal an attractor expected at the eigenfrequency of the mode. Investigating the structure of these shear layers, we find that they are nested layers, the thinnest and most internal layer scaling with E1/3, E being the Ekman number; for this latter layer, we give its analytical form and show its similarity to vertical 1/3-shear layers of steady flows. Using an inertial wave packet travelling around an attractor, we give a lower bound on the thickness of shear layers and show how eigenfrequencies can be computed in principle. Finally, we show that as viscosity decreases, eigenfrequencies tend towards a set of values which is not dense in [0, 2Ω], contrary to the case of the full sphere (Ω is the angular velocity of the system).Hence, our geometrical approach opens the possibility of describing the eigenmodes and eigenvalues for astrophysical/geophysical Ekman numbers (10−10–10−20), which are out of reach numerically, and this for a wide class of containers.

scholarly journals Frequency-Domain Robust Performance Condition for Controller Uncertainty in SISO LTI Systems: A Geometric Approach

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Vahid Raissi Dehkordi ◽  
Benoit Boulet
Keyword(s):  
Frequency Domain ◽  
Linear Time ◽  
Order Reduction ◽  
Geometric Approach ◽  
Geometrical Approach ◽  
Robust Performance ◽  
Linear Time Invariant ◽  
Additive Perturbation ◽  
Plant Uncertainty ◽  
Invariant Control

This paper deals with the robust performance problem of a linear time-invariant control system in the presence of robust controller uncertainty. Assuming that plant uncertainty is modeled as an additive perturbation, a geometrical approach is followed in order to find a necessary and sufficient condition for robust performance in the form of a bound on the magnitude of controller uncertainty. This frequency domain bound is derived by converting the problem into an optimization problem, whose solution is shown to be more time-efficient than a conventional structured singular value calculation. The bound on controller uncertainty can be used in controller order reduction and implementation problems.

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