Non-inertial torques and the Euler equation

The key equation describing the rotational dynamics of a rigid body is \({\vec \tau } = \text{d}{\vec L} / dt\) which can be understood based on Newton’s second and third laws motion together with assumption mutual centrality internal forces valid in an inertial coordinate system. While this written down by observer, for practical purposes, it efficiently worked out within non-inertial rotating ancillary system along principle axes body. This results famous Euler rotation bodies. We show that also possible to describe from point view observer (rotating system), provided torques are taken into account. explicitly calculate express them terms physical characteristics resulting dynamical equations exactly recover equation.