Colloquium: Christian Peterson
Christian Peterson Department of Physics and Astrophysics University of North Dakota Grand Forks, ND Euler’s Rotation Equations for a Freely Rotating Object and the Dzhanibekov Effect
Euler’s rotation equations, a set of non-linear coupled ODE’s, are solved analytically in the non-inertial or body frame of reference in terms of Jacobi’s Elliptic functions. The solution constructs a transformation between the stationary and rotating frames by giving the time dependence of the Euler angles, ϕ, θ, and ψ that define three factors of the rotation matrix.A computer animation of the elliptic function solution is then applied to explain the flipping motion of a spinning T-handle in zero gravity, known as the Dzhanibekov effect, seen in several famous videos on the internet.