Savitsky 



Evaluating bH/boi from (12) and using the condition H = 

 leads to a determination of the Lagrange multipliers. 



^ 8C . 



C cos a + -g— sin ex 



V (C cos Q- +-S^ sin a) + C^ 



(15) 



8C ^ . 



•jr — COS Of - C sin Of 



. _ 8Q^ 



V ~ a/"* 2 



VJC COS <^ +^ sin or) +C 



The remaining differential equations are employed and, after 

 extensive algebraic manipulations (which will not be reproduced 

 herein), the following expression for Q'(t) , the angular trajectory 

 for minimum travel tinne, is obtained. 



8C . 2„ 



•8 — sin a 

 da 



2 aVu, > x-2 a^c ^r- 9C ac 



+ C ^ sin a cos a + C ^^^ cos a - 2C ^^ cos a 



^ av^ ac 2 ^ aVj./ac\ ^. ^ ^^^ ^ + ^2 8C 



- ^ "Sr -5^ ''"^ "" ■ frl^y ^'"^ ^ cos or + C ^ cos or 



^2 a^c , -^ ac ac . „. ^ r-2av^^^^2^ 



- C -K— K— sin a + 2C -k— -stt si^ o; + C -jjf-Bcos a 



SySa Oy aof ay 



The partial derivatives of C and V^ contained in Eq. (16) 

 are obtained from the definition of C and V^ as follows: 



C = 2 [Co + Vc| + 4V^o cos a J 

 Vjx,y) = (0.45 - 0.0074X) ekp[ - ( l . ^7 /q. 0062x ) ] 



428 



