Euler's equations

If , and the body rotates about an arbitrary axis, then

For example, sphere can keep rotating without any moment. This is not true for other bodies in general.

(5) Steady rotation of an assymetric body:

From the Euler's equation, it can be seen that steady rotation of an assymetric body is possible, only if

This requires that at least two of the components of angular velocity be zero, i.e, angular velocity is along only one of the principal axes.

(6) Translation of a rigid body

For a translating body . In that case, Euler equations are automatically satisfied. The motion can be studied by applying Newton's equation.