Hyperbolics

let x = 0 be the lowest point on the string and let the points where it is attached be +-A, can you write A in terms of something you know?

let the length of the string be l now we can find l in terms of A and c using the arc length integral which is int((1+(y')^2)^0.5) where y'=dy/dx

so u should be able to write l in terms of A and c, and A in terms of d(distance apart) so you can solve for c.

Hope that helps.

theres a thread about this already i think.

[edited by - vivi2k on April 16, 2003 2:49:11 PM]

a uniform string to with no forces are applied except its own gravity and the points on witch it is suspended is a parabol in the form aX^2+bX+c. under any circumstance.

you might wanna look at http://mathworld.wolfram.com/Catenary.html

and also the other thread
http://www.gamedev.net/community/forums/topic.asp?topic_id=150521

Thanks for the links. But the as yet unanswered question, is what is c given y and x?

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I tried to guide you through the solution in my first post but if its just a formula your after you can get it as far as

2sinh(d/2c)=lc

with d the sepertion distance and l the rope length. as far as i know this has to be solved numeriacally.

quote:

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Original post by walkingcarcass
I promise this isn''t homework!

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But it does sound like a homework problem. I would greatly appreciate it if you were to show us your own work on this one!

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

I''m just one of those people who sees a problem like this and can''t rest until it''s solved!

My own work went as far as getting length in terms of Sinh and getting some simultaneous equations like cSinhx/c and x/cCoshc or something like that, all I can remember is I couldn''t solve them.

This sort of thing happens every week or two and I come here since a fair few of you know some pretty advanced stuff. Trouble is I was getting accused of dumping homework (who gets this kind of proof problem as homework?) so I figured a disclaimer was in order.

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quote:

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Original post by walkingcarcass
I''m just one of those people who sees a problem like this and can''t rest until it''s solved!

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Thats great!

quote:

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Original post by walkingcarcass
My own work went as far as getting length in terms of Sinh and getting some simultaneous equations like cSinhx/c and x/cCoshc or something like that, all I can remember is I couldn''t solve them.

This sort of thing happens every week or two and I come here since a fair few of you know some pretty advanced stuff. Trouble is I was getting accused of dumping homework (who gets this kind of proof problem as homework?) so I figured a disclaimer was in order.

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This sort of problem might very well be given in a freshman-level college math class, or even in some high schools (AP calculus class for example).

Actually, a disclaimer isn''t really what needs to happen here. Please read the forum FAQ, which gives guidelines for how to post homework-like questions appropriately.

Forum FAQ

I really do want to see evidence that problems such as this have been seriously attempted by the poster. Its just too easy for folks who, unlike yourself, are indeed trying to get homework answers to just throw in a disclaimer and try to get away with it. So a disclaimer isn''t really enough. In the future, please show some work. Show me your math. By the way, your explanation of getting some simultaneous equations that you couldn''t solve is not at all evidence that you''ve worked the problem. Type the equations that you derived, and show us specifically where you had a problem. And also do not expect an answer to this type of problem, but merely advise on how to get yourself unstuck.

I hope you understand. You may very well be an honest person, but some folks here are out to cheat and I have to treat all similar threads as equally as possible.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Its also interesting to note that this question is almost identical to another post that was also stated in a homework-like fashion. Please, folks, read the forum FAQ. Follow the forum rules if you''re going to post questions that sound like homework. I don''t mind theoretical math discussions, but things that have concrete, definite answers that sound like end-of-chapter homework problems do not really belong here.

Forum FAQ

There, I''m done with my rant!

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

y=c*Cosh(x/c)
=> x=c*arcCosh(y/c)
endpoints at (x,y) and (-x,y)

length from centre to end = L=d*Sinh(x/d) where d=2c

so length between endpoints = 2*c*Sinh(arcCosh(y/c)/2)

but what is c? L and y are known

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