CHAPTER III. 

 HAMILTON'S PRINCIPLE. 



GENERALIZED EQUATIONS OF MOTION. CYCLIC SYSTEMS. 

 60. Hamilton's Principle. If in d'Alembert's equation 



we consider &, Sy, z variations consistent with the equations of 

 condition, we have 



d?x -, _ d fdx \ dx dx 



dt* ~dt(~di dx ~ 



_ d fdx ~\ dx dx 

 ~~di(dt )~di ~dt 



d (dx j, \ ., 1 /dso 



= Ba: - 



Treating each term in this manner, 

 dy ~ dz 



s+ 



If there is a force function U we have 



hence the right-hand member of (1) is 



ST+SU. 



82 



