The Solution of SO(3)‎ through a Single Parameter ODE

Abstract EN

In many applications we need to solve an orthogonal transformation tensor 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 is obtained 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 of a single parameter, whose governing equation is a single nonlinear ordinary differential equation (ODE).