scholarly journals AnLp-Lq-Version of Morgan's Theorem for then-Dimensional Euclidean Motion Group

2007 ◽  
Vol 2007 ◽  
pp. 1-9
Author(s):  
Sihem Ayadi ◽  
Kamel Mokni
Keyword(s):  
Fourier Transform ◽  
Motion Group ◽  
Euclidean Motion Group ◽  
Euclidean Motion ◽  
Group Fourier Transform

We establish anLp-Lq-version of Morgan's theorem for the group Fourier transform on then-dimensional Euclidean motion groupM(n).

Numerical Synthesis of Binary Manipulator Workspaces Using the Fourier Transform on the Euclidean Motion Group

1998 ◽  
Author(s):  
Alexander Kyatkin ◽  
Gregory S. Chirikjian
Keyword(s):  
Fourier Transform ◽  
Analytical Form ◽  
Convolution Product ◽  
Generalized Convolution ◽  
Motion Group ◽  
Euclidean Motion Group ◽  
Linear Inverse Problems ◽  
Euclidean Motion ◽  
The Fourier Transform ◽  
Fitting Parameters

Abstract In this paper we apply the Fourier transform on the Euclidean motion group to solve problems in kinematic design of binary manipulators. We begin by reviewing how the workspace of a binary manipulator can be viewed as a function on the motion group, and how it can be generated as a generalized convolution product. We perform the convolution of manipulator densities, which results in the total workspace density of a manipulator composed of double the number of modules. We suggest an anzatz function which approximates the manipulator’s density in analytical form and has few free fitting parameters. Using the anzatz functions and Fourier methods on the motion group, linear and non-linear inverse problems (i. e. problems of finding the manipulator’s parameters which produce the total desired workspace density) are solved.

Synthesis of Binary Manipulators Using the Fourier Transform on the Euclidean Group

1999 ◽  
Vol 121 (1) ◽  
pp. 9-14 ◽  
Author(s):  
A. B. Kyatkin ◽  
G. S. Chirikjian
Keyword(s):  
Fourier Transform ◽  
Inverse Problems ◽  
Analytical Form ◽  
Convolution Product ◽  
Euclidean Group ◽  
Motion Group ◽  
Euclidean Motion Group ◽  
Linear Inverse Problems ◽  
Euclidean Motion ◽  
The Fourier Transform

In this paper we apply the Fourier transform on the Euclidean motion group to solve problems in kinematic design of binary manipulators. In recent papers it has been shown that the workspace of a binary manipulator can be viewed as a function on the motion group, and it can be generated as a generalized convolution product. The new contribution of this paper is the numerical solution of mathematical inverse problems associated with the design of binary manipulators. We suggest an anzatz function which approximates the manipulator’s density in analytical form and has few free fitting parameters. Using the anzatz functions and Fourier methods on the motion group, linear and non-linear inverse problems (i.e., problems of finding the manipulator’s parameters which produce the total desired workspace density) are solved.

The Stochastic Resonance of Noise Frequency Modulation Signal Using Motion-Group Fourier Transform

2015 ◽  
Vol 713-715 ◽  
pp. 1452-1455
Author(s):  
Jing Bo He ◽  
Sheng Liang Hu
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Stochastic Resonance ◽  
Frequency Modulation ◽  
Planck Equation ◽  
Motion Group ◽  
Noise Frequency ◽  
Modulation Signal ◽  
Group Fourier Transform ◽  
Linear Differential

In this paper stochastic resonance was studied in radar driven by noise frequency modulation signal. According to the intrinsic relations between the stochastic differential and the radar jamming signal processing, the stochastic calculus was used in the radar jamming signal processing in this paper. The noise frequency modulation signal was particularly analyzed. The Fokker-Planck equation of noise frequency modulation was presented and the Motion-Group Fourier Transform was used by converting the partial differential equation into the variable coefficient homogenous linear differential equations. Then the solutions were given.

On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras

2006 ◽  
Vol 49 (2) ◽  
pp. 213-225
Author(s):  
Andrew J. Dean
Keyword(s):  
Dynamical Systems ◽  
Inductive Limit ◽  
Unitary Representations ◽  
Motion Group ◽  
Direct Sums ◽  
Euclidean Motion Group ◽  
Euclidean Motion

AbstractAn invariant is presented which classifies, up to equivariant isomorphism, C*-dynamical systems arising as limits from inductive systems of elementary C*-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.

scholarly journals Applications of the Exponential Function of the Euclidean Motion Group to the Theory of Gearing

2014 ◽  
Vol 6 ◽  
pp. 869580
Author(s):  
Baozhen Lei ◽  
Harald Löwe ◽  
Xunwei Wang
Keyword(s):  
Differential Geometry ◽  
Exponential Function ◽  
Machine Tools ◽  
Basic Equation ◽  
Time Parameter ◽  
Motion Group ◽  
New Approach ◽  
Euclidean Motion Group ◽  
Special Machine ◽  
Euclidean Motion

The present paper provides a first step to a new approach to the theory of gearing, which uses modern differential geometry in order to ensure a strict and coordinate-independent formulation. Here, we are mainly concerned with a basic equation, namely, the equation of meshing, of two rotating surfaces in mesh. Since we are able to solve this equation by the time parameter, we derive parameterizations of the mating pinion from a bevel gear as well as a parameterization for gears produced by special machine tools.

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