sci.physics

On Fri, 31 Aug 2007 03:40:40 +0100, "JM Albuquerque"
wrote:

>
>"Eric Gisse" < @ > escreveu na mensagem
>news:scted3hh4le23s7a2k43pqbl8bqa5qetrp@ ...
>> On Fri, 31 Aug 2007 02:47:08 +0100, "JM Albuquerque"
>> wrote:
>
>
>>>Solutions exist?
>>>Solved?
>>
>> Read a book and not look stupid?
>>
>>>
>>>Is the gyroscope solved? Where? How? By Whom?
>>
>> Page 454, Symon. "The symmetrical top".
>>
>> Consider studying some classical mechanics.
>>
>>>
>>>I'm gonna repeat again:
>>>Those three differential equations are non-linear and are dependent
>>>one from each other.
>>
>> So?
>>
>> Nonlinearity does not mean "unsolvable". Did you know GR is highly
>> nonlinear?
>
>The problem is not the nonlinearity.
>The problem is that they are dependent one from each other,
>which renders it impossible to solve mathematically.

Is this system of differential equations impossible to solve?

dx/dt + y = 0
dy/dt + x = 0

>
>
>>>Without any major assumption (simplification) they don't
>>>have a solution. That's the point.
>>
>> ...and it is idiotic. So what if no analytic solutions exist in the
>> full nonlinearized set of equations? You can solve them numerically.
>
>Numerically is no good for my standards.

Who cares?

*Real* scientists use numerical solutions almost exclusively.

>I've told you that what really counts is understanding.

Talk to a computational physicist some time. It will be enlightening.

>
>
>> The solutions exist in the mathematically-proven-to-exist type of
>> existence. Numerical methods for ODEs are rather simple - I can
>> program them myself or I could use one of many prepackaged methods.
>>
>> The three body problem is analyitically unsolvable, but that does not
>> mean it is useless. Ditto for quantum chemistry, and such.
>
>Now you say the three body problem is analytically unsolvable.
>If you haven't notice, Euler's equations of motion talk about
>3 inertia moments that undergo rotation around principal axis.
>
>
>>>If they have a solution one should be able to describe
>>>the motion of a gyroscope where torque is applied in its
>>>both precession axis and also motion exists in its both
>>>precession axis, besides the constant spin of the gyroscopic
>>>mass.
>>
>> Yea - Symon, page 454. Consider reading it. Extending the example to
>> include torque is trivial by inclusion of the relevant generalized
>> forces into Lagrange's equations.
>
>Thank you, I already have all that I need.
>I bet torque was tossed out, didn't it?

Yep, but as I said extending it to include torque is trivial. That
situation is one of the homework exercises in Symon.

>
>
>> You can use Euler's equations by tossing on the torque into the right
>> hand side of the equations but that makes the huge assumption that you
>> will be able to do it. The principle inertial axis might not be the
>> best one.
>
>I don't want to toss on the torque.
>Torque must be applied, always.

That's nice.

>An due to torque (on both precession axis, motion also
>exists on both precession axis).
>
>
>>>Now I have a question for you, smartass:
>>>You have a school gyroscope where you place a gravity mass
>>>and starts precessing. The mass doesn't fall as you know
>>>and the gyroscope undergo precession. Trivial.
>>
>> The analysis is most certainly not trivial.
>
>For sure.
>I took about one Year, full time, 12 hours a day, 365 days
>a Year.

Hm, the analysis took a few days of lecture time and is 7 pages in
Symon.

Perhaps physics isn't for you?

>
>
>>>Where does the precession kinetic energy came from?
>>>I mean, the gyroscope is precessing, so it has kinetic
>>>energy on its precession motion. The question is:
>>>Where did the required energy came from?
>>
>> From the initial rotation of the body.
>
>Wrong!
>Try again.

Your welcome to prove otherwise.

>
>The rotation of the gyroscopic spinning mass is done
>over bearings and in no way there is a redution on
>the main spinning mass to acount for the required energy.

Why?

Spend a few minutes playing with a compound pendulum.

>
>
>
>> I hope you will extend your misunderstanding of classical mechanics by
>> saying that the energy came from nowhere and that you could build a
>> perpetual motion machine from the spinning top.
>
>Nope.
>The gyroscope works based on the energy conservation law.

Define energy in terms of the system.

>No power can be dissipated on a gyroscope.
>What goes in must come out.
>
>
>>
>>>
>>>[snip remaining]
>>>
>