lagrangian

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a.s. Cult. Micene - 29 Dec 2006 17:18 GMT

Hi all,
i need to write the lagrangian for a mechanical system (simple like a
mass-spring-damper system) in the proper reference frame and in the
coordinate reference frame, because i want to write the motion equations of
the system in both of the frames. in particular the aim of the work is to
yield the spring constant and the damper factor in the proper case and in
the coordinate one.

can someone help me?
thanks

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Luca

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sal - 29 Dec 2006 19:18 GMT

> Hi all,
> i need to write the lagrangian for a mechanical system (simple like a
[quoted text clipped - 5 lines]
>
> can someone help me?

I have a question or two and a suggestion.

Just to confirm that you are saying what I think you're saying, you want
a relativistically correct Lagrangian for a mass on a spring, _including_
_friction_ -- right? (The "damper" is frictional, right?)

Do you get to pick the form of the friction function? I.e., can you use
viscous damping, F ~ v, rather than the uglier but often more realistic
constant friction F ~ -v/|v|? (The former is what a bubble rising through
a bottle of shampoo feels; the latter is what happens when you press on
the brake peddle in a car.)

I can't give you a Lagrangian for such a case and I seriously doubt there
are more than half a dozen regulars here (even counting lurkers) who could.

My suggestion, if you come up dry in this newsgroup, is to try
www.physicsforums.com. There are more posters over there who are
knowledgeable, and it's moderated so the signal to noise ratio is a
whole lot better than it is here.

> thanks

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a.s. Cult. Micene - 30 Dec 2006 00:58 GMT

>> Hi all,
>> i need to write the lagrangian for a mechanical system (simple like a
[quoted text clipped - 16 lines]
> a bottle of shampoo feels; the latter is what happens when you press on
> the brake peddle in a car.)

I would like writing the lagrangian of a sping-mass-damper (viscous damping)
both in the proper frame (the same frame of the system and of the spacecraft
where the system is) and in the coordinate frame (at rest on the earth). the
two lagrangians are to derive the motion equations in both the cases.
This mechanical system is parallel to the direction of the spacecraft flight
(constant velocity respect to the terrestrial frame) in the first case and
perpendicular in the second case.

> I can't give you a Lagrangian for such a case and I seriously doubt there
> are more than half a dozen regulars here (even counting lurkers) who
[quoted text clipped - 4 lines]
> knowledgeable, and it's moderated so the signal to noise ratio is a
> whole lot better than it is here.

anyway thank you very much!!!
Luca

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Natural Science Forum / Physics / Relativity / December 2006

lagrangian