Coordinate‐free exponentials of general multivector in <i>Cl</i>_<i>p,q</i> algebras for <i>p+q=3</i>

Abstract

Closed form expressions in real Clifford geometric algebras , and 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 and in a form . After disentanglement, the obtained formulas simplify to the well‐known de 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.