Equations of motion in lagrangian form are established for a rigid body with a fixed point, by using an expression of the angular velocity previously introduced by the Author in the kinematics of finite deformations. This form of the equations, in which the components of a vector $\bf{q}$ are used in describing the angular motion, instead of Eulerian angles, constitute a normal system of second order in which the coefficients of the quadratic terms in $\dot{q}^{h}$ are rational functions of $q^{h}$. Moreover a simple relationship is given between the angular momentum and the momentum conjugate to $\bf{q}$.