A decoupled solution to the generalized Euler decomposition problem in \(\mathbb R^3\) and \(\mathbb R^{2, 1}\). (English) Zbl 1305.70013

Summary: We suggest a new method, partially based on earlier works, that resolves the generalized Euler decomposition problem (about arbitrary axes) using a system of quadratic equations. The main contribution made here is that we manage to decouple this system and express the solutions independently in a compact covariant form. We apply the same technique to the Lorentz group in \(2+1\) dimensions and discuss certain complications related to the presence of isotropic directions in \(\mathbb R^{2, 1}\).


70E15 Free motion of a rigid body
15A75 Exterior algebra, Grassmann algebras