[F (6.) - F (0.)]' 

 ■- V 1 OV 1 



dU 1 



2A,cos 26. cos 



+ 2B,sin 20. cos 9. + 2C,c6s 6. 

 1 1 1 1 1 



+ 2 D.cos^ 6. + 2E,sin ' 

 111 



- 2F (6.) cos 0. = (A27) 



OV 1 1 



[F (0.) - F (0.)]2 



"- V 1 OV 1 



„„ = 2A,cos 20. sin 6. sin 8. 



dt 1 1 1 ' i' 



+ 2B sin 20. sin 0. Isin 6. 

 1 1 1 ' 1 



+ 2C,sin 6. Isin 6. I 

 1 1 ' 1 ' 



+ 2D, cos 0. sin 0. Isin 0. I 



+ 2E, (sin 6. Isin 6. h^ 

 1 1 ' 1 ' 



- 2F (6.) sin 6. sin 6. = . CA28) 



OV 1 1 ' 1 ' 



For an even number of equally spaced time intervals, 0., summed over 

 a complete wave cycle, many of the terms cancel out due to the symmetry 

 of these sinusoidal functions. Thus, 



I cos 0. = (A29) 



i=l 



I cos 26. = (A30) 



i=l ^ 



n 



.\ sin 20. - (A31) 



1=1 1 



V sin sin 0. = (A32) 



I i ' i' 



i=l 



V cos 0. cos 20. =0 (A33) 



1=1 



130 



