## 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 $$\mathbb R^{2, 1}$$.

### MSC:

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