34 Prof. Maxwell on the Collision of 



Let M, and M 2 be the centres 

 of gravity of the two bodies. M, X t , 

 Mj Y„ and M, Z, the principal axes 

 of the first; and M 2 X 2 , M 2 , Y 2J 

 and M 2 Z 2 those of the second. 

 Let I be the point of impact, and 

 H , 1 R , the line of impact. 



Let the coordinates of I with 

 respect to Mj be x x y x z v and with 

 respect to M 2 let them be x 2 y 2 z 2 . 



Let the direction-cosines of the line of impact R, I It 2 be 



l x m l n i with respect to M„ and Z 2 m 2 w 2 with respect to M 2 . 



Let Mj and M 2 be the masses, and Aj^Bj C, and A 2 B 2 C 2 the 

 moments of inertia of the bodies about their principal axes. 



Let the velocities of the centres of gravity, resolved in the 

 direction of the principal axes of each body, be 



Ui V, W, and U 2 V 2 W 2 before impact, 

 and 



U'j V^ W\ and U' 2 V 2 W 2 after impact. 



Let the angular velocities round the same axes be 



Pi 9i r i an d Pz 02 r a before impact, 

 and 



P'\ tfi ^i an( * P ! 2 Q 1 * ^2 a ^ ter impact. 



Let R be the impulsive force between the bodies, measured by 

 the momentum it produces in each. 



Then, for the velocities of the centres of gravity, we have the 

 following equations : 



U'.-U. + g, U' 2 =U 2 -g*, .... '(62) 



1 2 



with two other pairs of equations in V and W. The equations 

 for the angular velocities are 



T» T» 



yi=Pi + j- to**i~'A& p'^p*- a" (yf 1 *-**™*)' ( 63 ) 



with two other pairs of equations for q and r. 



The condition of perfect elasticity is that the whole vis viva 

 shall be the same after impact as before, which gives the equation 



M,(U'?-U?) + M 2 (U'?-U^+A 1 ( P '?-^) + A 2 (y 2 -^)+&c.=0. 



The terms relating to the axis of x are here given ; those relating 

 to y and z may be easily written down. 



Substituting the values of these terms, as given by equations 



