A spinning top (a rigid body of revolution) is in general motion with its vertex (a particle on the axis of symmetry) fixed at the origin O. Let a(t) be the unit vector pointing along the axis of symmetry and let ω(t) be the angular velocity of the top. (In general, ω does not point along the axis of symmetry.)
By considering the velocities of particles of the top that lie on the axis of symmetry, show that a satisfies the equation
a· = ω X a.
Deduce that the most general form ω can have is
ω = a X a· + λa,
where λ is a scalar function of the time.
[This formula is needed in the theory of the spinning top.]