Yeah, I’m familiar with the meaning in DEs, which is exactly why it seemed weird: the DEs version is the sort of thing which should basically-never happen, because it’s extremely sensitive. Change the parameters even the slightest bit, and we either get two equilibria (one stable, one unstable) or no equilibrium.
Yeah, I think that’s right if we are considering a fast system and are being precise about the zero-velocity point. But the process of deceleration approaching zero at the limit could take a long time, and the forces that risk pushing us to the other side may be rare enough that we can often find objects at or near the equilibrium point.
Yeah, I’m familiar with the meaning in DEs, which is exactly why it seemed weird: the DEs version is the sort of thing which should basically-never happen, because it’s extremely sensitive. Change the parameters even the slightest bit, and we either get two equilibria (one stable, one unstable) or no equilibrium.
Yeah, I think that’s right if we are considering a fast system and are being precise about the zero-velocity point. But the process of deceleration approaching zero at the limit could take a long time, and the forces that risk pushing us to the other side may be rare enough that we can often find objects at or near the equilibrium point.