During motion, both the energy and angular momentum-squared are conserved, thus we have two conserved quantities: { 2 E = ∑ ∑ i I i ω ω i 2 L 2 = ∑ ∑ i I i 2 ω ω i 2 and so for any initial condition ω ω ( 0 ) , the trajectory of ω ω ( t ) must stay on the intersection curve between two ellipsoids defined by { ∑ ∑ i I i ω ω i 2 = ∑ ∑ i I i ω ω i ( 0 ) 2 ∑ ∑ i I i 2 ω ω i 2 = ∑ ∑ i I i 2 ω ω i ( 0 ) 2 This is shown on the animation to the left.