322 VII. DYNAMICS OF ROTATING BODIES. 



These are linear equations with constant coefficients , and may readily 

 be integrated. As a simple example let us consider the effect of the 

 earth's rotation on a railway train moving with constant velocity. 

 A railway train running with a velocity v is urged to the right 



with a force 



d^n 

 m -j~ = 2mQv sin cp. 



The acceleration experienced by a train running 50 miles per hour 

 in latitude 45 would be 



. .-o 4 TTX 50 x 160,933 cm A OOAX cm 0.2305 



Sln45 86,164.1x3600 1& = ' 2305 ^ r W 



of its weight. 



Secondly consider a body falling freely. We shall assume that 

 the body is dropped from a point in the -axis with no initial 

 velocity. Then integrating the first of equations 244) we obtain 



Integrating the third 



Substituting this in the second 



3JF."* 2&{2&sin 2 g? y -gtcosy 



Integrating this, making the assumption that & 2 may be neglected, 

 we have 



gt 2 . 

 Integrating again, 



and inserting this value in ? 



Consequently we have finally 



d 2 ~ 9 . 



- = 8? sm cp cos cp - gt*, 



to this order of approximation. We have 



_ &cosg> -i/8 ( - ) 3 

 ^ ~ ~3 V ~ g 



