Rigorous Three-Dimensional Vector Characteristic Wave Analysis Of Holographic Gratings Diffraction

1990 ◽  
Author(s):  
B. C. Chernov ◽  
E. I. .. Krupitsky
Keyword(s):  
Three Dimensional ◽  
Dimensional Vector ◽  
Wave Analysis ◽  
Holographic Gratings ◽  
Characteristic Wave ◽  
Vector Characteristic

Three-dimensional coupled wave study for finite-sized anisotropic volume holographic gratings under ultrashort pulsed beam readout

2007 ◽  
Vol 24 (6) ◽  
pp. 1799 ◽  
Author(s):  
Chunhua Wang ◽  
Liren Liu ◽  
Aimin Yan ◽  
Dean Liu ◽  
Yu Zhou ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Holographic Gratings ◽  
Coupled Wave

Solutions to the Vector Tetrahedron Equation

1965 ◽  
Vol 87 (2) ◽  
pp. 228-234 ◽  
Author(s):  
Milton A. Chace
Keyword(s):  
Closed Form ◽  
Digital Computer ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Spherical Coordinates ◽  
Tetrahedron Equation ◽  
Position Determination ◽  
Closed Form Solutions

A set of nine closed-form solutions are presented to the single, three-dimensional vector tetrahedron equation, sum of vectors equals zero. The set represents all possible combinations of unknown spherical coordinates among the vectors, assuming the coordinates are functionally independent. Optimum use is made of symmetry. The solutions are interpretable and can be evaluated reliably by digital computer in milliseconds. They have been successfully applied to position determination of many three-dimensional mechanisms.

scholarly journals Identities Generalizing the Theorems of Pappus and Desargues

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1382
Author(s):  
Roger D. Maddux
Keyword(s):  
Projective Plane ◽  
Vector Space ◽  
Invariant Theory ◽  
Lattice Theory ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Dimensional Vector Space

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

Error Sensitivity Analysis for Machine Tool Based on Three-Dimensional Vector Chain

2013 ◽  
Vol 457-458 ◽  
pp. 1562-1565
Author(s):  
Qiang Huang ◽  
Chan Jun Gao
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Three Dimensional ◽  
Error Modeling ◽  
Dimensional Vector ◽  
Modeling And Analysis ◽  
Vector Operation ◽  
Error Sensitivity ◽  
Space Error ◽  
Error Sensitivity Analysis

Error modeling and analysis can provide some important direction to the machining precision control. According to the characteristics of topology structure on machine tool, a space error model of machine tool and detailed modeling method are presented in this paper, which are based on three-dimensional vector chain. Taking a lathe as an example, the application method of this model in error sensitivity analysis is introduced. By this model, the relationship between the relative error of workpiece-tool and each source error can be solved by ordinary vector operation, and the analysis efficiency should be enhanced greatly.

Three-dimensional vector potential analysis for machine field problems

1982 ◽  
Vol 18 (2) ◽  
pp. 436-446 ◽  
Author(s):  
M. Chari ◽  
A. Konrad ◽  
M. Palmo ◽  
J. D'Angelo
Keyword(s):  
Vector Potential ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Potential Analysis
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