That’s very kind of you! Thanks also for pointing out the edit—fixed! Incidentally, this example is taken directly from my differential equations textbook, which describes asymptotically stable, unstable, and semistable equilibrium points.
You may already be familiar with these concepts if you’ve studied this subject. If not, an asymptotically stable equilibrium point is a point at which velocity is zero, and that nearby velocities on both sides of the point move us closer to the equilibrium point (they are attractive). This tracks with your “stable equilibrium” frame. Unstable equilibrium points have zero velocity at the point, but a velocity that moves us away from the point on both sides (they are repulsive). Because of this, objects are rarely found at unstable equilibrium points, since any disturbance from that point will cause repulsion from it. An example might be a coin standing on its edge.
A semistable equilibrium point is a place at which velocity is zero, and where velocity tends to move us closer to the point on one side (attraction) and away from it on the other side (repulsion).
That’s very kind of you! Thanks also for pointing out the edit—fixed! Incidentally, this example is taken directly from my differential equations textbook, which describes asymptotically stable, unstable, and semistable equilibrium points.
You may already be familiar with these concepts if you’ve studied this subject. If not, an asymptotically stable equilibrium point is a point at which velocity is zero, and that nearby velocities on both sides of the point move us closer to the equilibrium point (they are attractive). This tracks with your “stable equilibrium” frame. Unstable equilibrium points have zero velocity at the point, but a velocity that moves us away from the point on both sides (they are repulsive). Because of this, objects are rarely found at unstable equilibrium points, since any disturbance from that point will cause repulsion from it. An example might be a coin standing on its edge.
A semistable equilibrium point is a place at which velocity is zero, and where velocity tends to move us closer to the point on one side (attraction) and away from it on the other side (repulsion).
This is where the name comes from.