The Lagrangian formalism and the balance law of angular momentum for a rigid body

In this paper we derive Lagrange's equations for a rigid body rotating about its centre of gravity. We base our calculations on the balance law of angular momentum and refrain from the use of the customary and deficient model in which a rigid body is regarded as a limiting case of a rigid system of mass points. After some kinematical preliminaries we proceed in two ways. First we apply coordinates to achieve our goal, and in a second approach we do without them. The latter analysis is seen to be very simple