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2. On the Motion of Free Solids through a Liquid

Published online by Cambridge University Press:  15 September 2014

William Thomson
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Extract

This paper commences with the following extract from the author's private journal, of date January 6, 1858:—

“Let be rectangular components of an impulsive force and an impulsive couple applied to a solid of invariable shape, with or without inertia of its own, in a perfect liquid, and let u, ν, ω, ѽ, ρ, σ, be the components of linear and angular velocity generated.

Type
Proceedings 1870-71
Information
Proceedings of the Royal Society of Edinburgh , Volume 7 , 1872 , pp. 384 - 390
Copyright
Copyright © Royal Society of Edinburgh 1872

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References

page 384 note * Henceforth T, instead of ½ Q, is used to denote the “mechanical value,” or, as it is now called, the “kinetic energy” of the motion.

page 385 note * These equations will be very conveniently called the Eulerian equations of the motion. They correspond precisely to Euler's equations for the rotation of a rigid body, and include them as a particular case. As Euler seems to have been the first to give equations of motion in terms of coordinate components of velocity and force referred to lines fixed relatively to the moving body, it will be not only convenient, but just, to designate as “Eulerian equations” any equations of motion in which the lines of reference, whether for position, or velocity, or moment of momentum, or force, or couple, move with the body. or the bodies whose motion is the subject.

page 386 note * See “Vortex Motion,” §6, Trans. Roy. Soc. Edin. (1868).