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I'm thinking about a project to tackle, and I'd like to make a simulation that allows the user to define a rope or chain of length L, pin it at arbitrary points r1, r2.... etc. and draw the resulting curve in real time.

Also, I'd like the user to be able to alter the field that the rope exists in, for example more complex vector fields than just a straight gravitational field. This is a bonus, however, and I'd like to get the basic example working.

Could you recommend some resources, preferably free/online, for me to learn the physics involved (I'm not exactly sure what to CALL this area of classical mechanics)? I learn through concepts and then math so a resource that is concept-heavy would be nice.


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I made a simulation of a bungee jumper on a chain (in order to graph acceleration) there's source code linked in the description, but I must warn you: It's in [a variant of] BASIC, and I didn't spend a huge time on physical accuracy. (the method used to solve it is simple. Take a bunch of particles with position/velocity, have some function apply a force to the particles based on their relative positions and what-not, and then integrate. There're elasticity and damping forces.) – NeuroFuzzy Jan 12 '13 at 23:05
Oh jeez, "asked may 30 '11"... my bad. (well, other answerer's bad x) – NeuroFuzzy Jan 12 '13 at 23:08
up vote 2 down vote accepted

Looks like what you are trying to simulate is a Catenary. And this comes under statics - a part of Classical Mechanics. This paper (so does the Wikipedia article) introduces to the basics of catenary analysis. Also see a similar question on MathOverflow.

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A catenary is the correct shape in a constant field, but the problem asks for a bit more than that. – dmckee May 30 '11 at 20:07
Link to the paper seems to be dead. Any idea where to find it? – Daniel Jour Feb 16 at 18:41

Catenary-like curves which solve the above problem in the case of a parallel field which is proportional to a power of $y$ are introduced in the arXiv article 1102.1579 of which yours truly is the author. They are called MacLaurin catenaries and the article displays explicit parametrisations which could, presumably, be used for your project.

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