The Solution ofSO(3) through a Single Parameter ODE

In many applications we need to solve an orthogonal transformationtensor Q∈SO(3) from a tensorial equation Q˙ = WQ under a given spin history W. In this paper, we address some interesting issues about this equation. A general solution of Q isobtained by transforming the governing equation into a new one in the space of ℝP3. Then, we develop a novel method to solve Q in terms ofa single parameter, whose governing equation is a single nonlinearordinary differential equation (ODE)