E177 -- Decouverte d'un nouveau principe de Mecanique

(Discovery of a new principle in Mechanics)

(based on Clifford A. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances and his introduction to Opera Omnia Series II, Volume 12)
In this paper, Euler begins work on the general 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 researches in hydraulics during the 1740s, Euler is able, in this paper, to present 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's equations f = ma in rectangular coordinates appears, marking the first appearance of these equations in a general form since when they are expressed in terms of volume elements, they can be used for any type of body. Moreover, Euler discusses how to use this equation to solve the problem of finding 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.


According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on September 3, 1750.

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