Treatise on Natural Philosophy Volume 1

Treatise on Natural Philosophy Volume 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. 1886 edition. Excerpt: include all the particles of the any sJ'stem system. This may be called the indeterminate, or the variational, equation of motion. Lagrange used it as the foundation of his whole kinetic system, deriving from it all the common equations of motion, and his own remarkable equations in generalized co-ordi-nates (presently to be given). We may write it otherwise as follows: 2m (xSx + ySy + z&s) = 2 XSx + YSy + ZBz) (2), where the first member denotes the work done by forces equal to those required to produce the real accelerations, acting through the spaces of the arbitrary displacements; and the second member the work done by the actual forced through these imagined spaces. If the moving bodies constitute a conservative system, and if V denote its potential energy in the configuration specified by (x, y, z, etc.), we have of course ( 241, 273) SV=-2 (XSx + YSy ZSz) (3), and therefore the indeterminate equation of motion becomes 2m (a&B + yhj + zfy =-&V (4), ofoonserva-where SVdenotes the excess of the potential energy in the con tive system. figuration (x + Sx, y + Sy, z + Sz, etc.) above that in the configuration (x, y, z, etc.). One immediate particular result must of course be the common equation of energy, which must be obtained by supposing Sx, Sy, Sz, etc., to be the actual variations of the co-ordinates in an infinitely small time St. Thus if we take Sx = xSt, etc., and divide both members by St, we have 2 (Xx +Yy + Z) = %mxx + yy + zi) (5). Equation of Here the first member is composed of Newton's Actiones Aqentium; energy... .... with his Reactwnes Resistentium so far as friction, gravity, and molecular forces are concerned, subtracted: and the second consists of the portion of the Reactiones due to...
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Product details

  • Paperback | 166 pages
  • 189 x 246 x 9mm | 308g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236566211
  • 9781236566218