| dλ | − rν + qν = L, |
| dt |
| dμ | − pν + rλ = M, |
| dt |
| dν | − qλ + pν = N. |
| dt |
(1)
These equations are applicable to any dynamical system whatever. If we now apply them to the case of a rigid body moving about a fixed point O, and make Ox, Oy, Oz coincide with the principal axes of inertia at O, we have λ, μ, ν = Ap, Bq, Cr, whence
| A | dp | − (B − C) qr = L, |
| dt |
| B | dq | − (C − A) rp = M, |
| C | dr | − (A − B) pq = N. |
| dt |
(2)
If we multiply these by p, q, r and add, we get