Discussion on question by satellites: apply forces such that satellite reaches a given point in space

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14:31

Q: apply forces such that satellite reaches a given point in space

I'd like to find out a strategy for solving the following simplified problem. A small spherical craft at $t=0$ has a position and velocity vectors $\mathbf{x_0}, \mathbf{v_0}$ in a zero gravity environment. It has one outward-pointing thruster that can vector in any direction by rotating it's ...

satellites

Ok, max_acceleration = 0.0085m/s^2 and v_max = 1m/s^2.

Yes, I know the attitude, but I don't think I have to worry too much about it. You can consider the satellite to be spherical, if it simplifies the problem.

Yes, these are the only constraints.

Yes, I think it would be useful.

Nathan Tuggy

@uhoh: The SPHERES satellites have 12 thrusters, per WP article.

satellites

Just one thruster that can point in any direction.

You can watch a simulation here: zerorobotics.mit.edu/ide/simulation/3524531 Not my code, but a good enough one. Mine works too, but is slower because I'm using predefined functions. If I want to make it work properly I have to solve all the physics myself.

JCRM

"and stops" ... errr.... what's your frame of reference.

satellites

Because the satellites run on ISS, we consider the ISS to be my frame of reference.

leftaroundabout

14:31

Can the craft vector its attitude fast enough so two sequential pulses can have arbitrary different direction? (I don't think that would be necessary for fastest-time, but might be relevant to know.)

satellites

@leftaroundabout, yes.

leftaroundabout

And, are the pulses effectively infinitesimally small (i.e., smaller than the required precision in final velocity), or is it necessary to time the last pulse so it exactly cancels the remaining speed (à la suicide burn)?

uhoh

@leftaroundabout that's a very good point! Maybe just stop within $\pm 1 \Delta v$?

satellites

The first one. The pulses are small enough.

uhoh

In that case, maybe you can just drop the 1 pulse per second and make the thrust continuous.

satellites

14:31

Yeah, you can approximate the thrust like that. I'm so grateful you're helping me out!!

uhoh

when you're ready, go ahead and modify the question to reflect all of this, and Welcome to Space!

and once you have done so, it's best to clean up most of your old comments.

satellites

I'll do it in a few minutes.

I thought a bit about the problem, and finally edited it. The pulses are not infinitesimally small, but the craft must be moving with a speed (absolute value, not directional velocity) less than $\mathbf{v_m}$ at the position $\mathbf{x_1}$.

Does it make any sense? What else do you think I should edit?

leftaroundabout

It makes sense, just it would have been much easier if the pulses could have been assumed as infinitesimal.

satellites

Ok, you can consider them to be infinitesimal. It would be really helpful if you could help me.

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