ISBN: 9781231008683

RareBooksClub.com. Paperback. New. This item is printed on demand. Paperback. 194 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.This historic book may have numerous typos and missing text.… Plus…

RareBooksClub.com. Paperback. New. This item is printed on demand. Paperback. 194 pages. Dimensions: 9.7in. x 7.4in. x 0.4in.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. 1877 Excerpt: . . . contracting from loss of heat in course of time, the vis viva will not be constant, for the same reason as before. The increase of angular velocity produced by this contraction can be easily found by the conservation of areas. 337. Let gravity be the only force acting on the system. Let the axis of z be vertical, then we have. Y 0, Y0, Z-g. Hence the equation of vis viva becomes Imv1-2w! -2 Jig (z-z). Thus the vis viva of the system depends only on the altitude of-the centre of gravity. If any horizontal plane be drawn, the vis viva of the system is the same whenever the centre of gravity passes through the plane. 338. The equation of Virtual Velocities in Statics is known to contain in one formula all the conditions of equilibrium. In the same way the general equation 2m (J Bx g By g and ) 2m (XBx YBy ZBz), may be made to give all the equations of motion by properly choosing the arbitrary displacements Bx, By, Bz. In Article 334 we made one choice of these displacementsand thus obtained an equation in an integrable form. If we give the whole system a displacement parallel to the axis of a we have Bx 0, By 0, and Bz is arbitrary. The equals tion then becomes 2m-A 2mZ, which represents any one of the at three first general equations of motion in Art. 71. If we give the whole system a displacement round the axis of of z through an angle Bd, we have Bx --yB9, By xBd, Bz 0. The equation then becomes 2 m x--y J 2m (xY--yX), which represents any one of the three last general equations of motion in Art. 71. 339. The principle of Vis Viva was first used by Huyghens in his determination of the centre of oscillation of a body, but in a form different from that now used. See the note to page 69. The principle was extended by John B. . . This item ships from La Vergne,TN., RareBooksClub.com<

2012, ISBN: 9781231008683

General Books LLC , May-2012. softcover. New. pp. 194, General Books LLC