What's the system that's clearly up and up stable but

it's not asymptotically stable, right?

That's the next one we're going to.

Mariel do you remember mechanical animals?

>> [INAUDIBLE] >> Well yeah we're not quite to

asymptotic yet.

So what, Chip.

>> Spring mass system.

>> Spring mass system and even for a linear system spring mass is kind of just

marginal, they call it marginal stable.

There are roots of the characteristic equations, imaginary axis.

It's just going to oscillate.

So with stability we always talk about small departures,

you can say well my domain of attraction is zero, have to be on it.

Now you just have an equilibrium, that's not a stability.

Stability is always you've departed, there's some epsilon, no matter how small

but there's some find the epsilon that you bump it what's the use of that?

And that's kind of the challenge.

So, as soon as you take the spring master system and you detour it ever so

slightly it's just going to keep on wiggling.

You can make them wiggle as small as you wish.

So if your mission says I have to be within one art session

you can just bump it very, very lightly.

If any mechanical thing move the fuels wiggles a little bit.

We might be exceeding it already.

So, that now dictates other things in your,

what are the disturbance torques acting on the spacecraft?

If your good to within one degree, well now you can actually, and

you have the optimal stability.

You can bump it quite a bit more, obviously.

And stay within one degree then one arc second.

So there's that kind of stability.

So, Andrew, what's the next level of stability, beyond Lyapunov stable?

>> Asymptotic?

>> Asymptotic stability, right?

So now, that final neighborhood has gone to zero.

Does it do this for any initial conditions, Tony, or only for

local initial conditions, if you say it's asymptotically stable?