scholarly journals Analytic Solutions of the Teukolsky Equation and Their Properties

1997 ◽  
Vol 97 (2) ◽  
pp. 213-232 ◽  
Author(s):  
M. Shuhei ◽  
T. Eiichi
Keyword(s):  
Analytic Solutions ◽  
Teukolsky Equation

scholarly journals Analytic Solutions of the Teukolsky Equation in Kerr-de Sitter and Kerr-Newman-de Sitter Geometries

1999 ◽  
Vol 102 (2) ◽  
pp. 253-272 ◽  
Author(s):  
Hisao Suzuki ◽  
Eiichi Takasugi ◽  
Hiroshi Umetsu
Keyword(s):  
Analytic Solutions ◽  
De Sitter ◽  
Teukolsky Equation

scholarly journals Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions

1996 ◽  
Vol 95 (6) ◽  
pp. 1079-1096 ◽  
Author(s):  
S. Mano ◽  
H. Suzuki ◽  
E. Takasugi
Keyword(s):  
Low Frequency ◽  
Analytic Solutions ◽  
Teukolsky Equation

Analytic Solutions to the Closed Bomb

1988 ◽  
Author(s):  
Frederick W. Robbins ◽  
Franz R. Lynn
Keyword(s):  
Analytic Solutions

scholarly journals Type Synthesis of 1T2R Parallel Mechanisms Using Structure Coupling-Reducing Method

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Haitao Liu ◽  
Ke Xu ◽  
Huiping Shen ◽  
Xianlei Shan ◽  
Tingli Yang
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Analytic Solutions ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Real Time Control ◽  
Time Control ◽  
Topological Characteristics ◽  
Zero Coupling

Abstract Direct kinematics with analytic solutions is critical to the real-time control of parallel mechanisms. Therefore, the type synthesis of a mechanism having explicit form of forward kinematics has become a topic of interest. Based on this purpose, this paper deals with the type synthesis of 1T2R parallel mechanisms by investigating the topological structure coupling-reducing of the 3UPS&UP parallel mechanism. With the aid of the theory of mechanism topology, the analysis of the topological characteristics of the 3UPS&UP parallel mechanism is presented, which shows that there are highly coupled motions and constraints amongst the limbs of the mechanism. Three methods for structure coupling-reducing of the 3UPS&UP parallel mechanism are proposed, resulting in eight new types of 1T2R parallel mechanisms with one or zero coupling degree. One obtained parallel mechanism is taken as an example to demonstrate that a mechanism with zero coupling degree has an explicit form for forward kinematics. The process of type synthesis is in the order of permutation and combination; therefore, there are no omissions. This method is also applicable to other configurations, and novel topological structures having simple forward kinematics can be obtained from an original mechanism via this method.

scholarly journals Singularity analysis and analytic solutions for the Benney–Gjevik equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon ◽  
P. G. L. Leach
Keyword(s):  
Evolution Equations ◽  
Singularity Analysis ◽  
Analytic Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Painlevé Test ◽  
Wave Solutions ◽  
Algebraic Solutions

Abstract We apply the Painlevé test for the Benney and the Benney–Gjevik equations, which describe waves in falling liquids. We prove that these two nonlinear 1 + 1 evolution equations pass the singularity test for the travelling-wave solutions. The algebraic solutions in terms of Laurent expansions are presented.

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