404] 
135 
404. 
REPRODUCTION OF EULER’S MEMOIR OF 1758 ON THE 
ROTATION OF A SOLID BODY. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. ix. (1868), 
pp. 361—373.] 
Euler’s Memoir “Du mouvement de rotation des corps solides autour d’un axe 
variable,” Mem. de Berlin, 1758, pp. 154—193 (printed in 1765), seems to have been 
written subsequently to the memoir with a similar title in the Berlin Memoirs for 
1760, and to the “ Theoria Motus Corporum Solidorum &c.,” Rostock, 1765, and there 
are contained in the first-mentioned memoir some very interesting results which appear 
to have escaped the notice of later writers on the subject; viz. Euler succeeds in 
integrating the equations of motion without the assistance furnished by the consideration 
of the invariable plane. In reproducing these results I make the following alterations 
in Euler’s notation, viz. instead of x, y, z I write p, q, r; instead of Ma 2 , Mb 2 , Me 2 
(where M is the mass) I write A, B, G, these quantities denoting the principal 
moments, and in some equations where the omission or insertion of the factor M is 
really immaterial I write A, B, G in the place of a 2 , b 2 , c 2 ; moreover instead of Euler’s 
A, B, C (which denote respectively 
b 2 — c 2 c 2 — a 2 a 2 — b 2 
a 2 ’ b 2 ’ c 2 
other respects Euler’s notation is preserved. The equations of motion are 
Adp + (C — B) qrdt = 0, 
Bclq +{A — G) rpdt = 0, 
Gdr +(B —A)pqdt = 0 ; 
I write L, M, N; but in 
so that putting for shortness 
L = 
B-G 
m G ~ A 
N = 
A-B 
C