Exponentials of general multivector (MV) in 3D Clifford algebras
Abstract
Closed form expressions to calculate the exponential of a general multivector (MV) in Clifford geometric algebras (GAs) Cl(p,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.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 DOI:
 10.48550/arXiv.2104.01905
 arXiv:
 arXiv:2104.01905
 Bibcode:
 2021arXiv210401905D
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematical Physics;
 15A18;
 15A66
 EPrint:
 19p, 2fig