EULER, Leonhard. Theoria Motus Corporum Solidorum seu Rigidorum ex primis nostrae cognitione principiis stabilita et ad omnes motus qui in huiusmodi corpora cadere possunt accomodata.Rostoch e Gryphiswald, Roese, 1765

4to, mm. 220x170; contemporary half vellum binding, gold title on the back; pp. 32 not numbered , 520; 15 folded copper plates out text.

First edition. Roberts & Trent: “Although published some thirty years later, Theoria Motus complements the Mechanica... In the introduction Euler gives a new exposition of analytical mechanics, following Maclaurin\'s example of projecting the forces into the axes of a fixed orthogonal system. The first part deals with the motion of a point mass, and the second discusses the movement of solid bodies; in a supplement, he discusses the issue of friction.” Gautschi: “Euler’s program for mechanics progressed steadily but slowly, as he tried to develop a theory of the motion of solids. Major technical difficulties had to be overcome, and were gradually dealt with in a series of memoirs. These, in 1765, eventually led to his great treatise Theoria motus corporum, also called the Second mechanics, which crowned Euler’s work on mechanics. In addition to an improved exposition of his earlier mechanics of mass points, it now contains the differential equations (Euler’s equations) of motion of a rigid body subject to external forces. Here, Euler introduces the original idea of employing two coordinate systems—one fixed, the other moving, attached to the body—and deriving differential equations for the angles between the respective coordinate axes, now called the Euler angles. The intriguing motion of the spinning top is one of many examples worked out by Euler in detail.” DSB: “Establishing that the instantaneous motion of a solid body might be regarded as composed of rectilinear translation and instant rotation, Euler devoted special attention to the study of rotatory motion. Euler thus laid the mathematical foundation of the numerous studies on variational principles of mechanics and physics which are still being carried out.”

Roberts & Trent, p. 105; D.S.B. IV, 480; W. Gautschi, Leonhard Euler, p. 22.

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