4 ms·

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

by rdlw 3y ago

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.

antegamisou 3y ago
> 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-Engineering/dp/0486434842 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 https://underactuated.mit.edu/trajopt.html whose parts are also good alternatives to the Kirk book.
actinium226 3y ago
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.

by rdlw 3y ago

antegamisou 3y ago

> 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-Engineering/dp/0486434842 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 https://underactuated.mit.edu/trajopt.html whose parts are also good alternatives to the Kirk book.

actinium226 3y ago

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.