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I understand how the Brachistochrone Problem works, and do understand how the friction is added to it, however I am unsure of how to use the Brachistochrone Problem for use in spacecraft.

We know that one solution to the Brachistochrone Problem is the following:

$$x=a(\theta - \sin\theta)$$

$$y=a(1 - \cos\theta).$$

Now, to further explore that idea, I'd like to ask how one could add the thrust force of a spacecraft into the equation for the optimal path taken for it to go into its orbit.

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  • $\begingroup$ Do you have a good formalism in mind for what this thrust might look like? Can it go in any direction or just, say, forward, or just, say upwards. Either way this'll be an interesting question, though, the answer will be cool to know $\endgroup$
    – Cade Reinberger
    Commented Jul 27, 2019 at 18:03
  • $\begingroup$ Hey, yes I was thinking of the thrust going basically just upward, which should make it a little easier $\endgroup$
    – TryingMyBestPlsBearWithMe
    Commented Jul 27, 2019 at 18:22

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