Solving Differential - Equation of Motion

1. Jan 30, 2013

aerowenn

Let's say I have the equation:

$\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn$

It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ${\theta}(t)$ and y(t) are equations of t. J and Jn are just constants.

I'm wanting to solve for ${\theta}(t)$, $\dot {\theta}(t)$, and $\ddot {\theta}(t)$ as a function of time. These will correspond to position, velocity, and acceleration around an axis.

${\theta}(t)$ = (equation of t)

Any help would be greatly appreciated!

2. Jan 31, 2013

Staff: Mentor

have you tried using e^iat style functions for theta(t)?

I ask because its sometimes used when you periodic motion which in your case is rotating about an axis.

3. Jan 31, 2013

HallsofIvy

That's not a differential equation. Is one of those "+" signs supposed to be an "=" sign? Or is the whole formula equal to something, say "0"?

4. Jan 31, 2013

aerowenn

Terribly sorry about that, you are correct. All of that is equal to 0.

As for the other response, I thought of that, but I'm not sure the general solution to second order differential equations applies here. Both functions are dependent on "t".