A Treatise on the Theory of Screws

Forfatter: Sir Robert Stawell Ball

År: 1900

Forlag: The University Press

Sted: Cambride

Sider: 544

UDK: 531.1

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286] DEVELOPMENTS OF THE DYNAMICAL THEORY. 305 Multiplying similarly by/jj/Si, ...pnßn, and adding, H u> qß ~~ • Eliminating H, we find WaaS’øi) — Ua1 +pßj-, ... 9n = Xan +pßn. Substituting these in the two previous equations, we get 4- p^^ß = 0 ; Xuaa + puaß = 0 ; whence, as before, Uaat^ßv ~ Uapttfay = 0. 286. Twist Velocity acquired by an Impulse. From the fact that the twist velocity ä acquired by a free body in consequence of an impulsive wrench of unit intensity on a screw y is expressed (§ 280) by the equation cos (at)) a —-------- Pa we see that the second of the two formulae of § 281 may be expressed thus:— ß^ßn = The proof thus given of this expression has assumed that the body is quite free. It is however a remarkable fact that this formula holds good whatever be the constraints to which the body is submitted. If the body receive the unit impulsive wrench on a screw t), the body will commence to twist about b. 20