In David Vallado's book 'Fundamental of Astrodynamics and Applications', chapter 6.7. ("Continuous-Thrust Transfers") there is an algorithm #47: Low Thrust Transfer. In this algorithm a part of code is not fully revealed, and instead of this there is remark: "Find λ (need to iterate)". I understood that under λ Vallado meant Lagrange multiplier λi from control hamiltonian. But for me is absolutely unclear, what should I iterate to calculate a value of this multiplier.

  • $\begingroup$ Is it mentioned in the section that $\lambda_i$ is a constant ? From google books preview, it appears that author is referring to techniques used in "Bryson and Ho" text book on optimal control. $\endgroup$
    – AJN
    Jan 11, 2022 at 12:26
  • $\begingroup$ Yes, λi is constant, but, for a single solution. I.e., in each exact case of calculation it will be different. For calculations I need it's value. The book from link from Google Books looks like a kind of previous edition. I'm using 4-th edition of Vallado's book. Yes, author mentioned Bryson and Ho textbook, written at 1987. But I didn't found it in internet, there is only Bryson and Ho book from 1975 (like this: e.guigon.free.fr/rsc/book/BrysonHo75.pdf), which looks like not that Vallado meant. $\endgroup$ Jan 11, 2022 at 14:53
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    $\begingroup$ Typically one needs to iterate when a closed form solution to a problem doesn't exist. It would help a lot if you summarized Vallado's algorithm #47. (There are many at this site who are reluctant to shell out over \$300 US for a paperback.) Also note: Vallado's Fundamental of Astrodynamics and Applications is almost as widely criticized as Numerical Recipes for inaccuracies and lousy algorithms. $\endgroup$ Jan 11, 2022 at 15:26


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