A Treatise on Dynamics of a Particle
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A Treatise on Dynamics of a Particle

A Treatise on Dynamics of a Particle


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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. 1898 Excerpt: ...projected from P in the same direction, with equal velocities, acted on by the same forces, describing different paths; which is impossible; Art. 243. We notice that a change in the direction of projection PT affects the size of the circle described, but not the fact that the path is a circle. Ex. 2. A particle moves in a circle about a centre of force in the circumference, the force being attractive and equal to /xrn. Prove that the resistance of the medium in which the particle moves is Jj (n + 5)?, tlsin 0, where cos 0--rj2a. Use the normal and tangential resolutions. Coll. Ex. Ex. 3. A particle of unit mass describes a circle about a given centre of force 0 situated on the circumference. If the particle at any point P is acted on by an impulse 2v cos 0 in a direction making an angle ir-j with the direction of motion PT, show that the new orbit is also a circle and prove that the ratio of the radii is cos 20 + sin 20 cot 0, where 0 is the angle OPT. Ex. 4. The force being F--jjlu5, a particle when projected from a point P with an initial velocity V, equal to that from infinity, describes the circle r=2acos0; investigate the path when the initial velocity is F(l + 7), where y is so small that its square can be neglected. Proceeding as in Art. 317, we find--( )'+H-, +a The conditions of the question give where c--l/2a and 0--a initially. Putting u=csec0 + cr and neglecting the squares of 77 and y?)ve arrive at ART. 320. VARIOUS ORBITS. 205 Each side being a perfect differential, we find cos2 0 y / /c + YCotfl-fcotfl + ffl + isinflcos), and K is determined from the condition that Tj = 0 when 0 = a; y.'. K= 7C0taH-j-(cota + f a + sin a cos a). Putting u=ljr9 we have r=2a cos 0 (1-n cos 0), .-.--= cos 0-/c sin 0-7 cos 0--------(cos 0 + 1-0 sin 0-H...


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Product Details
  • ISBN-13: 9781231144022
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 154
  • Spine Width: 8 mm
  • Width: 189 mm
  • ISBN-10: 1231144025
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 286 gr


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