QUERY What is a Dynamic System (SD6510)

[SDMAIL Mabel Fong]

Posted by  Mabel Fong <may_belle_66 at yahoo.com>

Hi All,

I am embroiled in a discussion about what does and does not
constitute a dynamic system as such might be described by SD. Perhaps you might
comment on my reasoning. (I will express myself in difference equations because
of the textural limits of email.)

* * *

Case 1. The first dynamic machine I learned was a clock:

TIME(t+dt) = TIME(t) + dt

Though trivial, I understand this mechanism to be ?dynamic
in the Forrestonian sense? because it ?finds it own way? across a span of time.

* * *

Case 2. Using the time-radiant generated by such a clock, I
will delineate a span of time with a sign wave:

SIGNAL(TIME) = AMPLITUDE x sine (FREQUENCY x TIME)

Though the sign wave generated vivifies the time span, this
machine is not an ?SD dynamic? because the signal is merely ?riding the time
radiant? generated by the clock, rather than ?finding its own way? across the
span of time.

* * *

Case 3. To delineate a span of time with a sine wave by way
of a ?Forrestonian mechanism? one might build a wave generator by emulating a
simple pendulum with a system of first-order difference equations.

Let P = the position of the pendulum mass; V = the velocity
of that mass; and A its acceleration. Compute the natural frequency FREQ of the
pendulum as the square root of GRAVITY/LENGTH. This machine would then be constructed
as follows:

V(t+dt) = V(t) + A(t) x dt 
P(t+dt) = P(t) + V(t) x dt
A(t+dt) = - FREQ x P(t+dt)

* * *

My reasoning is to contrast Case 2 with Case 3: the former
is not an instance of SD because the machine is merely ?riding a time-radiant?;
while the latter is an instance of SD because the machine is generating a
sequence by which a time is delineated.

Have I got it right?

Mabel
Posted by  Mabel Fong <may_belle_66 at yahoo.com>
posting date  Fri, 27 Jul 2007 10:25:01 -0700 (PDT)