" ! T 

 94, 95] APPLICATION OF JACOBFS METHOD. 297 



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95. Top Equations deduced by Jacotai's Method. We will 

 conclude the treatment of the top by deducing the equations of 

 motion by the method of Jacobi, 41. Since we have for the kinetic 

 energy, 



77) T= 



and for the momenta 



p# = Aft', py = J.sin 2 # ^' 4- C cos 0- (9' 

 p (p = C(<p' + cos #?/;'), 

 we obtain at once 



151) 



Forming the sum of products of corresponding velocities and momenta, 

 we obtain the energy, and also the Hamiltonian function, 



152) H=T + W^ 



From this we form the Hamiltonian equation 41, 99), 



^ov dS . i(i/0S\a. 1 

 lo3 ) W + + 



-f 



We find, as in the problems of 41, that this is satisfied by a linear 

 function of t, y>, ty, plus a function & of -9-, which we will determine. 

 We shall obtain the result in the notation of 90 if we, put 



154) S=-ht + A(bg> + ^ + ). 



nserting in the differential equation 153), we obtain 

 155) 



from which 

 156) 



Accordingly we have the solution, 

 157) S = --ht + A (by + ^ 



The integrals are obtained by differentiating by the arbitrary constants, 

 *, 6, ft, 



