We can
**analyze the motion of a spinning top** using the Lagrange equations for the Euler angles.
Let us assume that the top has its lowest point (tip) fixed on a surface.
We will
**use the fixed point as the origin**.
The rotation about the origin will be described by the Euler angles so that
**all the kinetic energy
is contained in the rotation**.

So and are constants of the motion and we can solve the equations for and .

There is a
**third** Lagrange equation but it will be easier to understand the motion of the top by using the
**total energy equation**, along with the two conserved momenta.

This is very much
**like a central force problem** with the mass oscillating back and forth in the potential.
goes to zero at the limits.
The motion will be limited between the some angles
and
at which
.
This oscillation of
as the angular momentum precesses is called
**nutation**.

Jim Branson 2012-10-21