Hyperbolic Triginometry

Thread Starter

Danielsix-five

Joined Dec 6, 2005
20
Learning about hyperbolic trig functions in calc class. It seems really interesting, and I would like to study it in-depth. Anybody got any info??

-Daniel
 

Thread Starter

Danielsix-five

Joined Dec 6, 2005
20
Here's an idea. If a catinary is created by suspending a wire between two posts, then its shape must result from gravity. So why doesn't a ball thrown in the air, which is also acted upon by gravity, form a path of a catinary. (Is that the right grammar?)
 

Papabravo

Joined Feb 24, 2006
13,548
Originally posted by Danielsix-five@Feb 7 2006, 05:35 PM
Here's an idea. If a catinary is created by suspending a wire between two posts, then its shape must result from gravity. So why doesn't a ball thrown in the air, which is also acted upon by gravity, form a path of a catinary. (Is that the right grammar?)
[post=13902]Quoted post[/post]​
I'll give it a try. The ball is like a point mass and it's shape does not change appreciably under the force of gravity while it is in motion. This changes of course if the ball hits something.

Now the cable is a different story. It is like a distributed mass, and each mass element along the cable is under tension. This effect changes the shape of the hanging cable. The equilibrium shape of such a system can be shown to be a catenary.
 
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