An Elementary Treatise on Theoretical Mechanics Volume N . 1 by Alexander Ziwet
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Author: Alexander Ziwet
Number of Pages: 42 pages
Published Date: 21 May 2012
Publisher: Rarebooksclub.com
Publication Country: Miami Fl, United States
Language: English
Format: Pdf
ISBN: 9781236430045
Download Link: an elementary treatise on theoretical mechanics volume n . 1
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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. 1893 Excerpt: ... the forward and backward strokes. Find the point at which steam will be cut off in the two strokes. Also when the obliquity of the connecting rod is neglected. 3. ACCELERATION IN CURVILINEAR MOTION. 155. Let the velocity of a moving point be represented by the vector v = PTat the time t, and by the vector v' = P'T at the time t+At (Fig. 37). Then, drawing from any point O OV and OV respectively equal and parallel to PT and P'T, the vector VV represents the geometrical difference between v' and v; in other words, VV is the velocity which, geometrically added to v, produces v'. The vector VV approaches the limit 0 at the same time with At and PP'. This limit of VV for an infinitely small time dt may be called the geometrical differential or vector differential, of v. Dividing this infinitesimal vector by dt, we obtain in general a finite magnitude UnLO the geometrical derivative of the dt velocity with respect to the time, and that is what we call the acceleration at the time t or at the point P. We represent it geometrically by a vector j drawn from P parallel to the direction of lim VV. It will be noticed that the sense of the acceleration will be towards that side of the tangent of the curve on which the centre of curvature is situated. 156. Suppose a point P to move along a curve PxP2P3... with variable velocity v (Fig. 38). From any fixed origin 0 draw a vector OVx = vv equal and parallel to the velocity vxd Fig. 38. Pv and repeat this construction for every position of the moving point P. The ends Vv V2, V3, ... of all these radii vectores drawn from O will form a continuous curve VxV2V3... which is called the hodograph of the motion of P. If we imagine a point V describing this curve VxVV%--at the same time that P describes the curve PxP2P3 it is evide..
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