Discovery of a new principle of mechanics
In this paper, Euler begins work on the motion of a general rigid body. Among other things, he finds necessary and sufficient conditions for permanent rotation, though he does not look for a solution. He also argues that a body cannot rotate freely unless the products of the inertias vanish. As a result of his research in hydraulics during the 1740s, Euler is able to present here a fundamentally different approach to mechanics, and this paper has dominated the mechanics of extended bodies ever since. It is in this paper that the so-called Newton equation F = ma appears, marking the first appearance of this equation in a general form. Moreover, Euler discusses how to use this equation to find differential equations for the general motion of a rigid body (in particular, three-dimensional rigid bodies). For this application, he assumes that any internal forces that may be within the body can be ignored in the determination of torque since such forces cannot change the shape of the body. Thus, Euler arrives at "the Euler equations" of rigid dynamics, with the angular velocity vector and the tensor of inertia appearing as necessary incidentals. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances and his introduction to Opera Omnia Series II, Volume 12.)
Original Source Citation
Mémoires de l'académie des sciences de Berlin, Volume 6, pp. 185-217.
Opera Omnia Citation
Series 2, Volume 5, pp.81-108.