Motion of rigid bodies using Eulers equations?

my question is:

using

A(d/dt w_1) = (B-C)w_2w_3

B(d/dt w_2) = (C-A)w_3w_1

C(d/dt w_3) = (A-B)w_1w_2

where A%26gt;B%26gt;C are real constants, and w=omega, solve:

A body is symmetric about the e_1 (basis vector) axis, so that B=C. Show that w_1 stays constant, while w_2 and w_3 perform simple harmonic motion on a circle (w_2)^2 + (w_3)^2 = constant, a form of motion known as precession. What i the period of these oscillations?

Motion of rigid bodies using Eulers equations?chicago theater

If B=C then equation "A(d/dt w_1) = (B-C)w_2w_3" becomes "d/dt w1=0" and since d/dt(w1) tells you how much w1 changes with time this means that w1 does not change and is thus constant.