Re: Fun with C

["Nasser M. Abbasi" <nma@12000.org>]

On 4/25/2011 11:18 PM, Dmitry A. Kazakov wrote:
> On Mon, 25 Apr 2011 13:46:40 -0700 (PDT), Maciej Sobczak wrote:
>
>> On Apr 25, 9:09 am, "Dmitry A. Kazakov"<mail...@dmitry-kazakov.de>
>> wrote:
>>
>>> No, it is a catastrophic approximation because linear system cannot
>>> oscillate.
>>
>> What? A simple hanging spring can oscillate while being purely linear.
>

> That system is not linear.
>

One should really attribute linearity or not to the equations that
describes the motion of the system.

The pendulum itself is just the pendulum, and saying that
the pendulum itself is not linear, I do not think is very exact,
but I know you meant the equation of motion when you said that.

So, now lets talk then about the equation of motion.

Again, under small angle approximation, the equation of motion
of the pendulum can be approximated to linear one.  When
the angle is large, then the  approximation is not a good one,
and one must use the non-linear equation of motion to make
better prediction of its motion.

So, we back to square one. We make a mathematical model
of the physical problem, and if the approximation we make
to this model seems to give good results for our needs, then
that is the model we should use.

One can use GR equations (10 highly non-linear coupled PDE's [1])
to describe the equation of motion of the pendulum, and
after making all the approximations needed to account for
slow motion of the pendulum blob (relative to speed of light :),
its small mass (relative to earth) hence small space-time curvature,
and after numerically solving them, one will get the same results
within a tolerance of error that can be ignored for all
practical reasons, as the one we get with a simple model based
on F=ma and small angle approximation.

So, you can use GR to solve the pendulum problem, and I can
use F=ma, and in the end, we will get the same results
for all practical reason, except I used a very simplified
model, and you used a very complicated model, of the same
physical problem. What matter is if the result of the model
agrees well to the observed behavior.

Any way, this is how engineers look at things :)

--Nasser
[1]http://en.wikipedia.org/wiki/Einstein_field_equations