Multisegmented optimal trajectories
T. L. S. Vincent · NASA Technical Reports Server (NASA) · 1968
energy per u n i t mass f c o n s t a n t F f u n c t i o n a l form defined on p.1 g f u n c t i o n a l form defined on p.1, p.3, a c c e l e r a t i o n due t o g r a v i t y .G f u n c t i o n a l form defined on p.4, u n i v e r s a l g r a v i t a t i o n a l c o n s t a n t G' remainder o f G h length coordinate (Fig. 3 .1 ) angular momentum per u n i t mass.H f u n c t i o n a l form defined on p.4 k length coordinate (Fig. 3.1), c o n s t a n t defined on p. 20.. l length coordinate (Fig. 3 .1 ) m i n t e g e r , mass M mass o f e a r t h n i n t e g e r P mass o f payload r r a d i u s from c e n t e r of e a r t h t independent v a r i a b l e , time T t h r u s t u c o n t r o l v a r i a b l e , x component of v e l o c i t y v v e l o c i t y , y component of v e l o c i t y V .exhaust v e l o c i t y X s t e e r i n g angle (Fig. 3.4 and Fig. 3.5) y s t a t e v a r i a b l e z* f u n c t i o n a l form defined on p . 4 .e y t r a j e c t o r y angle (Fig. 3.1 and Fig. 3.4) 1 Lagrange m u l t i p l i e r p Lagrange m u l t i p l i e r (d f u n c t i o n a l form defined on p . 1 , polar a n g l e (Fig. 3.4) f u n c t i o n a l form defined on p.1.Subscript s e l . . .v 5 2n + 2 f f i n a l point h 1...2n i l . . .n j 1. . .n k 1. ..m .i ?l . . .p 5 f ( n + 1) a 1, 3, 5 ... 2 , 4, 6 ... 1, 2 , 3, ... value o f quanti-ty a t various p o i n t s V Superscripts no non-optimal controal o optimal control q 1 ... f / 2 1,2,3 value o f quantity along f i r s t , second, and third subarc.