scholarly journals On Closed-Form Formulas for the 3-D Nearest Rotation Matrix Problem

2020 ◽  
Vol 36 (4) ◽  
pp. 1333-1339
Author(s):  
Soheil Sarabandi ◽  
Arya Shabani ◽  
Josep M. Porta ◽  
Federico Thomas
Keyword(s):  
Closed Form ◽  
Rotation Matrix ◽  
Matrix Problem

On the closed form of Wigner rotation matrix elements

1996 ◽  
Vol 19 (2) ◽  
pp. 131-145 ◽  
Author(s):  
Shan-Tao Lai ◽  
P. Palting ◽  
Ying-Nan Chiu
Keyword(s):  
Closed Form ◽  
Rotation Matrix ◽  
Matrix Elements ◽  
Wigner Rotation ◽  
Rotation Matrix Elements

Synthesis of a Spherical Cycloidal Mechanism

1976 ◽  
Vol 98 (4) ◽  
pp. 1342-1346
Author(s):  
R. Mayo ◽  
A. H. Soni
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Unit Sphere ◽  
Rotation Matrix ◽  
Fourth Degree ◽  
Rotational Displacement ◽  
Synthesis Technique ◽  
Moving Points ◽  
Crank Mechanism

Using rotational displacement matrices to describe spherical motions, closed-form synthesis equations are derived for two rotation matrix mechanisms. These equations are used to calculate the linkage parameters of a spherical cycloidal crank mechanism so that it will guide a rigid body through five finitely separated positions lying on the surface of a unit sphere. It is shown that the synthesis equation for calculating the coordinates of the fixed and moving points lying on the unit sphere is of fourth degree. This indicates that a maximum of four unique solutions of the mechanism are possible when five finitely separated positions are specified. A synthesis example is presented illustrating the proposed synthesis technique using a spherical cycloidal crank mechanism to guide a rigid body.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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