Elliptic functions are inverses of the elliptic integrals. Here's an elliptic integral:
Alright, let's take the inverse of that function, that is, for some value of with fixed , figure out what has to be. Well, that's easy, it's the elliptic function ( ):
One application of elliptic functions is in the solution of the non-linear equation for a pendulum:
When you solve this equation, you'll get an elliptic integral in terms of which of course you'll want to solve for right? Well, you'll have to ``invert'' the expression by taking the inverse of that integral and that results in the elliptic function. The solution is then:
Where is a constant created in the calculations.