What is the physical interpretation of hyperbolic functions?

[Lord Loh.]

Hyperbolic Functions

http://www.math.com/tables/trig/hyperbolics.htm

What is the physical interpretation of hyperbolic functions? sinh cosh tanh etc.

Just the way in a right angled triangle,

sin x= opp/hyp
cos x=adj/hyp
tan x=opp/adj

etc..

Thanks in advance.

 

[neoaspilet11]

Re: Hyperbolic Functions

There is none. They can't be represented as a ratio of sides af a triangle. Becaus e by definition,

sinh(x) = (e^x - e^-x) /2
cosh(x) = (e^x + e^-x) /2

(It is interesting enough that if x is a pure imaginary number, the function becomes a trigonometric function sin x and cos x)

I think they are purely mathematical concept and has no physical representation.

 

[hamidr_karami]

Re: Hyperbolic Functions

hi
this functions is very useful inpresentation
for example in the partial diffrential equation you can show
A*e^(a*x)+B*e^(b*x) equal to C*sinh(a*x)+D*cosh(b*x).

 

[cheng]

Re: Hyperbolic Functions

Surely there is.

Think of the exponent as damped sin or cos. (when x is complex).
To represent damped sin or cos the hyperbolic stuff is just the complex representation of a physical process that has such behaviour. The network analysis with its complex representation is another example.
The fact that the hyp. fun is solution to certain PDEs is secondary. That is, the sum or difference of exponent is representing incidence and reflection phenomena. Had there not been for damped magnitude the solution would be pure sin and cos.


Hope it helps.

 

[papu]

Hyperbolic Functions

hyperbolic functions are mainly used in complex analysis.....

 

[LouisSheffield]

Re: Hyperbolic Functions

There is a physical interpretation
(from https://en.wikipedia.org/wiki/Hyperbolic_functions)



Just as the points (cos t, sin t) define a circle, the points (cosh t, sinh t) define the right half of the equilateral hyperbola x² - y² = 1. This is based on the easily verified identity ......


Read freely - they are also used in coordinate transforms in SAR imagery

 

[LouisSheffield]

Hyperbolic Functions

... and have a look here too ...
https://oregonstate.edu/~drayt/talks/WOUpub.pdf
(special relativity & hyperbolic rotations - gotta love 'em)

 

[jackpiper]

Hyperbolic Functions

try taking arc sines and arc cosines for triangles on the surface of a sphere - even the three angles of the triangle don't add upto 180 degrees.

 

[jc_bock]

Re: Hyperbolic Functions

Perhaps an explanation from answers.com will help clear things up..
**broken link removed**