## E177 -- Decouverte d'un nouveau principe de Mecanique

(Discovery of a new principle in Mechanics)

**Summary:**
##### (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* = *m**a* 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.

a.s.

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

**Publication:**
- Originally published in
*Mémoires de l'académie des sciences de Berlin* 6, 1752, pp. 185-217
*Opera Omnia*: Series 2, Volume 5, pp. 81 - 108

**Documents Available:**
- Original publication: E177
- E177 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
- E177 was reprinted in Gentlemen's Magazine: E177a
- English translation (Stacy Langton): E177

- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E177 include:
- de Boer R., “Theory of porous media - past and present.” Zeitschrift fur Angewandte Mathematik und Mechanik, 78 (7), pp. 441-466 (1998).
- Fraser C., “Lagrange, J. L. early contributions to the principles and methods of mechanics.” Archive for History of Exact Sciences, 28 (3), pp. 197-241 (1983).
- Harman PM., “Newton to Maxwell - the 'Principia' and British physics.” Notes and Records of the Royal Society of London, 42 (1), pp. 75-96 (Jan 1988).
- Maltese G., “On the relativity of motion in Leonhard Euler's science.” Archive for History of Exact Sciences, 54 (4), pp. 319-348 (2000).
- Sander J, Hutter K., “On the development of the theory of the solitary wave - a historical essay.” Acta Mechanica, 86 (1-4), pp. 111-152 (1991).
- Whitrow GJ., “Presidential address - laws of motion.” British Journal for the History of Science, 5 (19), pp. 217-234 (1971).
- A paper about lax representations for systems of S. Kowalevskaya Type here
in
.pdf format

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