The Elementary Part of a Treatise On the Dynamics of a System of Rigid Bodies B

Cover The Elementary Part of a Treatise On the Dynamics of a System of Rigid Bodies B
The Elementary Part of a Treatise On the Dynamics of a System of Rigid Bodies B
Edward John Routh
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The equation (13) can be solved by separating the variables.
We get L I (S 9 cos - pP) p = (#o sin - qQ)*, where a is an arbitrary constant. At the beginning of the motion ART. 324. ] IMPACT OF ROUGH ELASTIC ELLIPSOIDS. 261 P and Q are zero, hence we have sin - \ ( S cos I \ S sin which may also be written fS0$ = /8jm6\j }> or This equation gives the relation between the direction and the velocity of sliding.
322. If the direction of sliding does not change during the impact, must be constant a
...nd equal to . We see from (16) that, if p = q, then = ; and that conversely if 0=0 > & is constant unless p = q. Also, if sin or cos # be zero, S must be zero or infinite unless 6 = B . The necessary and sufficient condition that the direction of friction should not change during the impact is therefore p = q or sin 20 = 0. The former of these two conditions, by (12), leads to If this condition holds, we have by (13) P = Qcot6 and therefore by (14) P = //jftcos0, Q = /AJRsin0 (19).
It follows from these equations that, when the friction is limiting, the representative point T moves along a straight line making an angle tan" 1 //, with the axis of R, in such a direction as to meet the straight line of no sliding.


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