APPENDIX 

 MATHEMATICAL DETAILS 



Substituting directly from Equation (21) into Equation (6) yields 



2 - - 2- 2 _ 



0^ = [cos a - t(f +f ) sin a cos a + t f sin a] = 9^^g^^(t,H) (49a) 



*^12 " ^11 t(l~t^f^) sin a cos a + tf^ cos^a - tf^ sin a] E e^^g^2(t'H) ('^9b) 



2- - 2 - 2 _ 



0„-. = 9,, [ (1-t f ) sin a cos a + tf, cos a - tf, sin a] = 0^^g2-,(t,H) (49c) 



2 - - 2- 2 _ 



0„„ = 0^ [sin a + t(f,+f„) sin a cos a + t f^ cos a] = 0,-,g22(t,H) (49d) 



A = (H cos a - tf sin a) = h (t,H) (49e) 



A = 0^^ (H sin a + tf^ cos a) E 0^^h2(t,H) (49f) 



The momentum integral Equations (3) can then be written 



11 + fl _!ii ^^ 4- fl _!ii ^ + p 11 



and 



'11 9£, 11 8t 9£^ 11 9H 9£^ ^12 9£, 



^ ^11 ^ li -^ ^11 ^ f: = Ci(eii'^'«) (^0-) 



^11 . „ ^§21 3t . ^ 9g21 9H . ^^11 



"*" °11 Cn- CiO "*" °1 1 'liu ao §' 



'21 dl^ 11 9t 9£, 11 9H 9£^ ^22 9£ 



'22 9t . . '^22 9H =, (0„,t,H) (50b) 



11 9t 9£^ 11 9H dir. 2' 11' 



where 



63 



