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Coordinate-free exponentials of general multivector in Cl(p,q) algebras for p+q=3
  • Arturas Acus,
  • Adolfas Dargys
Arturas Acus
Vilnius University

Corresponding Author:[email protected]

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Adolfas Dargys
State Research Institute Center for Physical Sciences and Technology
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Closed form expressions in real Clifford geometric algebras Cl(0,3), Cl(3,0), Cl(1,2), and Cl(2,1) are presented in a coordinate-free form for exponential function when the exponent is a general multivector. The main difficulty in solving the problem is connected with an entanglement (or mixing) of vector and bivector components ai and ajk in a form (ai-ajk)2, i≠ j≠ k . After disentanglement, the obtained formulas simplify to the well-known Moivre-type trigonometric/hyperbolic function for vector or bivector exponentials. The presented formulas may find wide application in solving GA differential equations, in signal processing, automatic control and robotics.
04 Oct 2021Submitted to Mathematical Methods in the Applied Sciences
05 Oct 2021Submission Checks Completed
05 Oct 2021Assigned to Editor
10 Oct 2021Reviewer(s) Assigned
10 Jan 2022Review(s) Completed, Editorial Evaluation Pending
12 Jan 2022Editorial Decision: Revise Major
30 Jan 20221st Revision Received
31 Jan 2022Assigned to Editor
31 Jan 2022Submission Checks Completed
31 Jan 2022Reviewer(s) Assigned
17 Feb 2022Review(s) Completed, Editorial Evaluation Pending
18 Feb 2022Editorial Decision: Revise Minor
08 Mar 20222nd Revision Received
08 Mar 2022Submission Checks Completed
08 Mar 2022Assigned to Editor
10 Mar 2022Reviewer(s) Assigned
15 Jun 2022Review(s) Completed, Editorial Evaluation Pending
16 Jun 2022Editorial Decision: Accept
Jul 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8529