This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ...zPy, zPx-xPz, xPy--yPx. The advantage of this representation is that the resulting effect of any number of forces is found by ...Read MoreThis historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 edition. Excerpt: ...zPy, zPx-xPz, xPy--yPx. The advantage of this representation is that the resulting effect of any number of forces is found by adding their several corresponding components. If we wish to represent the line of action of the force apart from the force itself, we may regard the straight line as the seat of some force of given magnitude, and suppose the line itself determined by the six components of this chosen force. Let (I, m, n) be the direction cosines of the straight line, (x, y, z) the coordinates of any point on it. Then, if the force chosen is a unit, the six components or coordinates of the line are I, m, n, --yn--zm, f i = zl--xn, v = xm--yl, with the obvious relation l + mfi + nv = 0 (1). If a force P act along this straight line, its six components or coordinates are PI, Pm, Pn; PX, Pfi, Pv. If we compound several forces together, the six components become X = 2.PI, Y= tPm, Z=ZPn; L = 2P, M = Xpfm, N = 2Pv, but the relation XL + YM+ZN = 0 (2) is not necessarily true. 261. We have seen in Art. 257 that all these forces may be joined together so as to make a single force R and a couple G. This combination of a force and a couple has been called by Plucker a dyname. The six quantities X, Y, Z, L, M, N are the components of the dyname. The three former components are multiples of some unit force, the three latter of some unit couple. It will be shown further on that when the coordinates of the dyname satisfy the condition (2), either the force R or the couple G of the dyname is zero. 262. Ex. 1. The six components of a force are 1, 2, 7; 4, 5, -2. Show that the magnitude of the force is 54, and that the equations to its line of action are (7y-2z)/4=(z-7s)/5 = (2s-y)/(-2) = 1. Ex. 2. The six components of a dyname are 1, 2, 3; 4, 5, 6. Show that tRead Less
Good/ No dustwrapper. 407 pages Volume 1 only Previous owners small name in ink on half title page Unsightly water or damp stain on top edge corner which has gone onto margins of first 20 or so page-corners bumped and bit of fraying to spine-text block solid clean and tight 407 pages.
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