Origins of Geometric Algebra

2002 ◽  
pp. 1-38
Keyword(s):  
Geometric Algebra

scholarly journals Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1259
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán Roldán Pérez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Operation Conditions ◽  
Multiple Phase ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

scholarly journals Invariants of Space Line Element Structure Based on Projective Geometric Algebra

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 62610-62618 ◽  
Author(s):  
Zhang Youzheng ◽  
Mui Yanping
Keyword(s):  
Geometric Algebra ◽  
Line Element ◽  
Space Line

scholarly journals GAPPCO: An Easy to Configure Geometric Algebra Coprocessor Based on GAPP Programs

2017 ◽  
Vol 27 (3) ◽  
pp. 2115-2132 ◽  
Author(s):  
D. Hildenbrand ◽  
S. Franchini ◽  
A. Gentile ◽  
G. Vassallo ◽  
S. Vitabile
Keyword(s):  
Geometric Algebra

G 6,3 Geometric Algebra; Description and Implementation

2014 ◽  
Vol 24 (2) ◽  
pp. 493-514 ◽  
Author(s):  
Julio Zamora-Esquivel
Keyword(s):  
Geometric Algebra

Geometric Algebra of Singular Ruled Surfaces

2021 ◽  
Vol 31 (2) ◽  
Author(s):  
Yanlin Li ◽  
Zhigang Wang ◽  
Tiehong Zhao
Keyword(s):  
Geometric Algebra ◽  
Ruled Surfaces

scholarly journals Chirality in Geometric Algebra

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1521
Author(s):  
Michel Petitjean
Keyword(s):  
Geometric Algebra ◽  
Orthogonal Group ◽  
Matrix Representation ◽  
Quadratic Space ◽  
Complex Numbers ◽  
Chiral Algebra

We define chirality in the context of chiral algebra. We show that it coincides with the more general chirality definition that appears in the literature, which does not require the existence of a quadratic space. Neither matrix representation of the orthogonal group nor complex numbers are used.

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