3 ms·

This is great write up, thanks for the explanation. I've studied physics in undergrad but I still made the mistake you describe in your last paragraph. The Gra

This is great write up, thanks for the explanation. I've studied physics in undergrad but I still made the mistake you describe in your last paragraph. The Grasshopper intuitively feels dynamically like an inverted pendulum but even harder because all you have are rockets at the bottom and you can adjust their rotation (I assume?). On the other hand, there is no fixed pivot point around which you get torque, is this what the difference comes down to? Do you happen to have any pointers to some articles that discuss this, and how difficult it is to balance? How does the wind affect things? What are the biggest challenges?

deleted 13y ago
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mikeash 13y ago
I think that yes, it's the lack of a fixed pivot point. The inverted pendulum case (as approximated when balancing a pencil on its tip) can be reduced to a single object resting on the surface of a frictionless sphere, under the influence of gravity. At the precise top of the sphere, it can stay stationary. Perturb it even slightly, and it begins to accelerate away. With the rocket, the object is essentially resting on a flat frictionless plane. If you tilt it a bit, then it begins to slide away, but the acceleration is always proportional to the initial perturbation. This is because the rocket always remains in the same orientation, and so the force always comes from the same direction. That, in turn, is because the rocket engine moves along with the rest of the rocket, rather than being a fixed point in space. Think about it another way: without external support, and ignoring the influence of the atmosphere, a rocket is in free fall. The fact that it's accelerating to counter the force of gravity doesn't change that fact. Again ignoring the atmosphere, a rocket firing with 1g of thrust counteracting gravity behaves the same as a rocket firing with 1g of thrust in empty space. The second case is obviously not unstable (what would it be unstable with respect to?) and so the first case isn't either. Adding the atmosphere back in, I could be way off here, but I think what little effect it would have at low speeds would be beneficial. Since the goal is not to move, the drag from the atmosphere will help make sure that happens. Since the rocket is more or less of a uniform shape, that drag shouldn't end up applying much of a torque either. Edit: forgot to mention, I'm afraid I don't have pointers to articles. I've collected this stuff through various readings and thought over the years and don't have anything specific to point to. I think I first learned about Goddard's pendulum mistake in high school physics, for example.
sehugg 13y ago
Here's a good article on Lunar Module stability, which is a similar problem with the exception that the Grasshopper has a much longer longitudinal axis, and relies solely on gimbaling (thrust vectoring) with no separate attitude control thrusters. http://www.clavius.org/techlmstab.html http://www.clavius.org/techlmstab.html

deleted 13y ago

[deleted]

mikeash 13y ago

I think that yes, it's the lack of a fixed pivot point. The inverted pendulum case (as approximated when balancing a pencil on its tip) can be reduced to a single object resting on the surface of a frictionless sphere, under the influence of gravity. At the precise top of the sphere, it can stay stationary. Perturb it even slightly, and it begins to accelerate away. With the rocket, the object is essentially resting on a flat frictionless plane. If you tilt it a bit, then it begins to slide away, but the acceleration is always proportional to the initial perturbation. This is because the rocket always remains in the same orientation, and so the force always comes from the same direction. That, in turn, is because the rocket engine moves along with the rest of the rocket, rather than being a fixed point in space. Think about it another way: without external support, and ignoring the influence of the atmosphere, a rocket is in free fall. The fact that it's accelerating to counter the force of gravity doesn't change that fact. Again ignoring the atmosphere, a rocket firing with 1g of thrust counteracting gravity behaves the same as a rocket firing with 1g of thrust in empty space. The second case is obviously not unstable (what would it be unstable with respect to?) and so the first case isn't either. Adding the atmosphere back in, I could be way off here, but I think what little effect it would have at low speeds would be beneficial. Since the goal is not to move, the drag from the atmosphere will help make sure that happens. Since the rocket is more or less of a uniform shape, that drag shouldn't end up applying much of a torque either. Edit: forgot to mention, I'm afraid I don't have pointers to articles. I've collected this stuff through various readings and thought over the years and don't have anything specific to point to. I think I first learned about Goddard's pendulum mistake in high school physics, for example.

sehugg 13y ago

Here's a good article on Lunar Module stability, which is a similar problem with the exception that the Grasshopper has a much longer longitudinal axis, and relies solely on gimbaling (thrust vectoring) with no separate attitude control thrusters. http://www.clavius.org/techlmstab.html http://www.clavius.org/techlmstab.html