Results 11 to 20 of about 251 (170)
Development of the Method of Averaging in Clifford Geometric Algebras
Mathematics, 2023 We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras.
Dmitry Shirokov
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Geometric Clifford Algebra Networks
CoRR, 2023 We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group.
David Ruhe +4 more
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Exponentials of general multivector in 3D Clifford algebras
Nonlinear Analysis, 2022 Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Clp;q are presented for n = p + q = 3.
Adolfas Dargys, Artūras Acus
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UAV’s Agricultural Image Segmentation Predicated by Clifford Geometric Algebra
IEEE Access, 2019 Image segmentation is widely used in the field of agriculture to improve the yields and protecting them from pests, herbs, shrubs, and weeds. Precision agriculture is also contributing to the inter and intra crop monitoring.
Prince Waqas Khan +4 more
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IEEE Access, 2022 This article presents a revisited proposal for the formulation of objects and geometric relations and constraints in the conformal space. For modeling, graphics engineering, kinematics, and dynamics, the solution of problems using only points and lines ...
Eduardo Jose Bayro-Corrochano +4 more
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Algebraic programming of geometrical calculus and clifford algebra
Journal of Symbolic Computation, 1989 The basic concepts of geometrical calculus have been implemented in an algebraic programming language. In this paper, we describe how our program performs fundamental operations on multivectors.
Ph. Tombal, A. Moussiaux
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Logarithm of multivector in real 3D Clifford algebras
Nonlinear Analysis, 2023 Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3.
Artūras Acus, Adolfas Dargys
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Relativity in Clifford's Geometric Algebras of Space and Spacetime [PDF]
International Journal of Theoretical Physics, 2004 Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cl{1,3} of Minkowski space, and in the ...
Baylis, William E., Sobczyk, Garret
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A new derivation of the Minkowski metric
Journal of Physics Communications, 2023 The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws.
James M Chappell +5 more
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Time as a geometric property of space
Frontiers in Physics, 2016 The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}.
James Michael Chappell +4 more
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