Exponentials of general multivector in 3D Clifford algebras
Adolfas Dargys
Center for Physical Sciences and Technology
Artūras Acus
Vilnius University
Published 2022-01-01


Clifford (geometric) algebra
exponentials of Clifford numbers
computer-aided theory

How to Cite

Dargys A. and Acus A. (2022) “Exponentials of general multivector in 3D Clifford algebras”, Nonlinear Analysis: Modelling and Control, 27(1), pp. 179-197. doi: 10.15388/namc.2022.27.24476.


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. The obtained exponential formulas were applied to find exact GA trigonometric and hyperbolic functions of MV argument. We have verified that the presented exact formulas are in accord with series expansion of MV hyperbolic and trigonometric functions. The exponentials may be applied to solve GA differential equations, in signal and image processing, automatic control and robotics.

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