Mathematical and Physical Papers, Vol. 2 (Classic Reprint)

From the Cambridge aiid Dublin Mathematical Journal, Vol. iii. p. 121, March, 1848.] Notes on Hydrodynamics. III. On theD ynamical Equations. In reducing to calculation the motion of a system of rigid bodies, or of material points, there are two sorts of equations with which we are concerned; the one expressing the geometrical connexions of the bodies or particles with one another, or with curves or surfaces external to the system, the other expressing the relations between the changes of motion which take place in the system and the forces producing such changes. The equations belonging to these two classes may be called respectively the geometrical, and the dynamical equations. Precisely the same remarks apply to the motion of fluids. The geometrical equations which occur inT he series of notes on Hydrodynamics which are printed in Vols, ii., in. and IV. of the Cambridge arid Dublin Mathematical Journal, were written by agreement betweenS ir WiU iam Thomson and myself mainly for the use of Students. As far as my own share in the series is concerned, there is httle contained in the notes which may not be found elsewhere. Acting however upon the general advice of my friends, I have included my share of the series in the present reprint. It may be convenient to give here the references to the whole series. I. On theE quation of Continuity (T homson), Vol. ii. p. 282. n. On theE quation of theB ounding Surface (T homson), Vol. in. p. 89. III. (S tokes) as above. IV. Demonstration of a Fundamental Theorem (S tokes), Vol. in. p. 209. V. On the Vis Viva of a Liquid in motion (T homson), Vol. rv. p. 90. VI. Ore Waves (S tokes), Vol. iv. p. 219. S. II.
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