Philosophical Transactions of the Royal Society of London Volume 170

Philosophical Transactions of the Royal Society of London Volume 170

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1880 edition. Excerpt: ...of inertia. In forming the equations of motion we are met 'by a difficulty, because the axes A, B, C are neither principal axes, nor can they rigorously be said to be fixed in the earth. But M. LIOUVILLE has given the equations of motion of a body which is changing its shape, using any set of rectangular axes which move in any way with reference to the body, except that the origin always remains at the centre of inertia. If A, B, C, D, E, F be the moments and products of inertia of the body about these axes of reference at any time; H1, H2, H3 the moments of momentum of the motion of all the parts of the body relative to the axes; m1, m2, (03 the component angular velocities of the axes about their instantaneous positions, the equations may be written and two other equations found from this by cyclical changes of letters and sufiixes. Now in the case to be considered here the axes A, B, C always occupy the average position of the same line of particles, and they move with very nearly an ordinary uniform precessional motion. Also the moments and products of inertia may be wiitten A+a', B+b', C---c', d', e', f', where a', b', c', d', e', f' are small periodic functions of the time and a'+b'----c'=O, and where A, B, C are the principal moments of inertia of the undisturbed earth, so that B is equal to A. Now the quantities a', b', &c., have in effect been already determined, as may be shown as follows: By the ordinary formulat the force function of the moon's action on But the first three terms of I only give rise to the ordinary precessional couples, and a comparison of the last six with (11) and (13) shows that Also in the small terms we may ascribe to 001, ...show more

Product details

  • Paperback | 280 pages
  • 189 x 246 x 15mm | 503g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236792688
  • 9781236792686