By Chairman, Professor A. M. Letov, Dr. Charles Draper, Professor A. I. Lur’e (auth.), John A. Aseltine (eds.)

ISBN-10: 1489962034

ISBN-13: 9781489962034

ISBN-10: 1489964118

ISBN-13: 9781489964113

**Read or Download Peaceful Uses of Automation in Outer Space: Proceedings of the First IFAC Symposium on Automatic Control in the Peaceful Uses of Space, held June 21–24, 1965, in Stavanger, Norway PDF**

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**Example text**

Cl:: ~I<'~, : AO(L ' J. 31), which we have used often above. 19) 1 where is some Lagrange multiplier. 4), . /( r ... 2) All of the remaining conditions remain the same. 2 or, of course, the scalar integral H~ does not change). 3, are colinear. 28). 2 The differential equations of spherical motion. ; + Oc; O(t. cit2. 3 Spherical motion with w • const (devices of the first type• In order to simplify the notation, we introduce the dimensionless variables JJ~ ~~ '~1>t:">1f=r:' IV~"-,. 10) Here ~ is the ratio of the velocity v • k/r to the velocity on a circular Kepleristic orbit of the same radius, n is the angular velocity on such an orbit, and ~ is the ratio of the force of gravity to the thrust ("overload")*.

Of course, it is doubtful whether it is possible to trust such solutions in practice. 1) This result may be obtained by direct statement of the variational problem of minimizing the total fuel consumption. 1). ;.. e... 2). where .. C. f~' ~ + dr3-(' I dJ: o - I ( .. 4), the problem reduces to finding Ritz method for dete~ination of the vector r. 4) 3 to third order, inclusive, that satisfy the boundary 0 conditions of the problem. 5) t, t, system of s finite equations. r\s(cr+ are given and t1 is fixed, it is easTer to choose e r•an appropriate expression for r; this case of where A denotes the total variation.

I. r-~ - ('1.. 5) leads to the following expression for the variation: t, & •I " . 1\1 I!! 15) it follows from (6,12) that 2 V'L; 11, r3 {1- 3w~ cf') ' zr= - 3r3 seA-.. ). 16), we find that (6. ,'f This is the previously introduced quantity H >. 2) for 'A= const and I')= o. 2) for ?.. = const. >- which represents the result of eliminating q(t) from the equations of motion. x -e. 11) (2,20), e:.

### Peaceful Uses of Automation in Outer Space: Proceedings of the First IFAC Symposium on Automatic Control in the Peaceful Uses of Space, held June 21–24, 1965, in Stavanger, Norway by Chairman, Professor A. M. Letov, Dr. Charles Draper, Professor A. I. Lur’e (auth.), John A. Aseltine (eds.)

by Daniel

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