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Comment by antegamisou | Hacker News Reader

This type of learning material, lacking any desperate 'ELI5' oversimplifications and laying out the proper amount definitions and equations without having to resort to fancy animations to keep the -quite often indolent- reader engaged, is unfortunately scarce in today's web, as is evident from the website's layout.

Here are two favorite readings for anyone willing to delve more into the subject:

    Orbital Mechanics for Engineering Students by Howard D. Curtis

https://www.amazon.com/Orbital-Mechanics-Engineering-Student...

    Fundamentals of Astrodynamics (aka BMW) by  Roger R. Bate, Donald D. Mueller, Jerry E. White, William W. Saylor

https://www.amazon.com/Fundamentals-Astrodynamics-Second-Dov...

Another great textbook as suggested by musgravepeter in the comments is

    Fundamentals of Astrodynamics and Applications by David A. Vallado, Wayne D. McClain

https://www.amazon.com/Fundamentals-Astrodynamics-Applicatio...

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Better yet, keep proper definitions and equations and then drive interesting animations from "real deal" code!

I've been working for a couple of years on a computer algebra system written in Clojure (named "Emmy") designed for writing this like. It's a port of Gerald Sussman's scmutils library, plugged in to a bunch of modern graphics libraries.

Here are a few examples, shamefully lacking exposition since much of this is JUST working and I was powering through demos for a talk:

- particle in a quartic potential well: https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

- Phase Portrait of the Pendulum: https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

- Colin's torus geodesics: https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

- Taylor Series https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

- (p, q) torus knot: https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

- Dual Number Visualization: https://sritchie.github.io/clojure-conj-2023/notebooks/conj/...

I'd love a textbook like the one you link above with figures that feel almost like Kerbal games, powered by the real code in the book that is ALSO generating the math you see.

See https://github.com/mentat-collective/emmy for more information if this is interesting.

That's really cool work you've done there !!

Indeed the key to efficient learning is to provide the user the ability to have some sort of parameters play around interaction to better understand the underlying complicated equations involved in the examples you posted.

Projects like Manim are cool, don't get me wrong, but I've observed that since 3B1B's skyrocketing popularity, similar channels are in a way misusing it to only create fancier videos without necessarily containing the respective high-quality material imperative to convey concepts.

Hopefully Emmy gains the traction it deserves which should be high even going by the preliminary demos you've shared.

Both these books are on my book shelf and are very good. Bate et. al. especially since it is a Dover book and very affordable.

The book that is always on my DESK is "Fundamentals of Astrodynamics and Applications" by Vallado. There is also a website with code from the book for Hohmann and Lambert transfers among other things. <self-promotion>This has been indispensable in creating my Unity Asset "Gravity Engine".</self-promotion>

Apologies if this is in the books you linked, but there's something I've always been curious about and can't seem to find good resources on anywhere: how do you actually plan and optimize the trajectory of a rocket?

I understand orbital mechanics at a basic level and there are lots of resources out there to get a better understanding of those, but then to put them into practice in Kerbal Space Program, I just kind of drag the sliders and nodes around until the line goes where I want it to. Obviously NASA had nothing like that in the 60s, so I've always wondered how they actually calculated when the launch windows were and so on.

I've been trying to dive into this myself and there are a paucity of good resources on the subject. One that I found really good though was Longuski's Optimal Control with Aerospace Application. It has a good balance of math and application, even some MATLAB code at the end to implement some of it.

One note I'll make is that usually there's 2 separate optimization programs for a rocket. The first stage runs on "open-loop" guidance, i.e. a trajectory is created beforehand (and by trajectory I mean something like a pitch-velocity lookup table - when you are at this velocity, pitch by this amount) and the rocket flies this trajectory without optimizing it in real time.

After stage separation the upper stage will run closed loop guidance (typically something like Powered Explicit Guidance or PEG) that actually takes into account orbital parameters and fixes error in inclination, RAAN, apogree, perigee, etc. that may have been introduced by the first stage.

I've worked at one aerospace company where I know they follow this pattern, and I believe others do as well though can't confirm from personal experience.

Longuski's book mostly deals with the latter part of things. I haven't found a good reference for how to create an optimized first stage trajectory.

> How do you actually plan and optimize the trajectory of a rocket?

You're looking into Control Theory and specifically the field of Optimal Control.

If you have some college Math {1,2}XX literacy, I remember

    Optimal Control Theory: An Introduction by Donald E. Kirk

https://www.amazon.com/Optimal-Control-Theory-Introduction-E...

having some chapter or two dedicated to trajectory optimization. Although it's not an easy reading by any means, it greatly serves its purpose as the title states; an adequate optimal control introductory. You really want a good grasp of optimal control's fundamentals before you go into trajectory/path optimization so it's advised you start from the very beginning.

However in case you want an alternative to the book and wonder what trajectory optimization is about here's the relevant chapter of MIT's Underactuated Robotics course

https://underactuated.mit.edu/trajopt.html

whose parts are also good alternatives to the Kirk book.

There is also a little simplified web version of the Howard's book: https://orbital-mechanics.space/intro.html

Whats wrong with this? https://ciechanow.ski/gps/

I do really enjoy interactive content. Lets you experiment and get practical... oh, I'm the practical guy.

I don't see how poor mobile-hostile web design helps education.

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