On the Euler and Lagrange's Points of View in Rigid Body Mechanics

Abstract

In this work we take Lagrange's and Euler's important concepts from fluid mechanics and apply them to the movement of a rigid body. By means of two examples, namely motion around a fixed axis and around a fixed point, Lagrangian and Eulerian formulations of the problems are discussed. It is shown that Euler's approach suits better the description of rigid body kinematics, since the linearized equations of motion are simpler than the ones obtained by Lagrange's formulation. This topic is rarely discussed in undergraduate courses on mechanics but it can provide students with a deeper comprehension of the movement of a rigid body and, at the same time, establish a connection with the scope of fluid mechanics.