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Elements of Dynamic Volume 1, Bks. 1-3; An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies

Elements of Dynamic Volume 1, Bks. 1-3; An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies


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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. 1878 Excerpt: ...-mbsm0, along oX, oY. The sum of their resolved parts along OP = "5racos0. cos0 + OT&sin0. sin0 = Ot (acos20 + 6sin20). The sum of their resolved parts perpendicular to OP = era cos 0. sin 0--.sr&'sin 0. cos 0--tss a--b) sin 20. The latter part shifts the axis OP parallel to itself in a direction perpendicular to the plane through a distance k, = i(a-b) sin 20. The former part shews that the pitch of the resultant twist p, = a cos2 0 + b sin2 0. Now let a circle be drawn through o and two points A, B on oXand o Y equidistant from o. The centre c is the middle point of A B. Then since 0 is the angle at the circumference AoP, 20 is the angle at the centre AcP, and sin 20 = Pm: cA. If a cylinder be drawn upon this circle, a plane through AB and a point vertically over C at a distance J a--b) will cut the cylinder in an ellipse, and if Q be the point of the ellipse vertically over P we shall have PQ = k. For and Cd=i (a--b), whence PQ--a--b) sin 20 = k. Hence zQ, parallel to oP, is the axis of the resultant twist. The angle 0 depends upon the magnitude of the component twists, not at all upon their pitches. By varying this angle then, we shall obtain the screws of all twists which can be got by compounding twists upon the given screws. If 0 varies uniformly, the line zQ, which is parallel to OP, turns round uniformly, being always perpendicular to oZ; while the point z has a simple harmonic motion up and down oZ, whose period is equal to that of P in the circle. The surface traced out by the line zQ is called a cylindroid. It is clear that if we cut the cylindroid by a circular cylinder having oZ for axis, the section will be the bent oval previously obtained by wrapping round the cylinder two waves of a harmonic curve (p. 35), The line oZ is calle...


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Product Details
  • ISBN-13: 9781231964934
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 72
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1231964936
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 145 gr


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Elements of Dynamic Volume 1, Bks. 1-3; An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies
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