Hank Walker wrote:
>> What's state-space?
>> I'm cross-posting to be safe, I'm not sure what it is, but be easy
> on me -- I'm just a Linguistics undergrad, and I've come across
> state-space (and other stuff, too) in a chapter on harmonic
> phonology and other chapters and articles yet to be read (like
> stuff on 'attractors' by KP Mohanan).
[...]
If you have some kind of system (let's say: the solar system), it can
usually be described completely by a finite set of parameters:
*the masses of the sun, the planets and the moons
*the positions of all the bodies (three coordinates each)
*the velocities of all the bodies (again, three coordinates each)
If we are to calcutate orbits, the masses won't change, so these can be
regarded as constants.
Let's say we only account for the sun, mercury, venus, earth, the moon,
mars and it's two moons.
That 's 8 bodies, 6 parameters each (pos. and veloc.), together 48
parameters.
Note that, using these 48 parameters and the masses, we can calculate
the gravitational forces acting on each body, which allows us to
calculate the change of velocity. The velocity in turn, determines how
the positions change.
In other words, if we know the 48 parameters at a certain moment, we can
calculate (or at least try to approximate) the values of those
parameters at another moment. These 48 parameters determine the state of
the system.
If we write those parameters between brackets, we get something that
looks awfully much like a point in a 48 dimensional space. That way, the
state of a system becomes a point in some 48-dim. space - the
state-space of the system !
Note that in time, the state of the system changes. This gives us
trajectories in state-space.
Hope this helps,
Nils