Optimal control of the electrical mode of an arc furnace on the basis of the three-dimensional vector of phase currents

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.

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Identities Generalizing the Theorems of Pappus and Desargues

Symmetry ◽

10.3390/sym13081382 ◽

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.

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Three-dimensional vector field visualization based on tensor decomposition

Journal of Computer Science and Technology ◽

10.1007/bf02947212 ◽

1996 ◽

Vol 11 (5) ◽

pp. 452-460

Author(s):

Xundong Liang ◽

Bin Li ◽

Shenquan Liu

Keyword(s):

Vector Field ◽

Three Dimensional ◽

Tensor Decomposition ◽

Dimensional Vector ◽

Vector Field Visualization ◽

Three Dimensional Vector Field

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Optimal control of three-dimensional steamflooding processes

International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts ◽

10.1016/0148-9062(95)90146-9 ◽

1995 ◽

Vol 32 (1) ◽

pp. A20

Keyword(s):

Optimal Control ◽

Three Dimensional

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.457-458.1562 ◽

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.

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