# Please explain a way of calculation of Lagrange multiplier in algorithm of low thrust transfer

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.

• 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.
– AJN
Jan 11, 2022 at 12:26
• 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. Jan 11, 2022 at 14:53
• 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. Jan 11, 2022 at 15:26