# Archived Nonlinear Dynamics and Chaos, Strogatz: 2.1.5

1. Jun 3, 2013

### Niteo

1. The problem statement, all variables and given/known data
a) Find a mechanical system that is approximately governed by $\dot{x}=sin(x)$
b) Using your physical intuition, explain why it now becomes obvious that x*=0 is an unstable fixed point and x*=$\pi$ is stable.

2. Relevant equations

$\dot{x}=sin(x)$ (?)

3. The attempt at a solution
I'm thinking a pendulum can be used as a mechanical system that varies with sinθ, but I'm not sure how to solidify my answer.

Could it possibly be an inverted pendulum in a very viscous medium?

Last edited: Jun 3, 2013
2. Feb 5, 2016

### haruspex

Consider a particle sliding over terrain y=f(x). Assuming conservation of energy (and some convenient total) what is the PE at x? What does that yield for f?

3. Feb 6, 2016

### epenguin

Question of understanding what they want. I think all you need to do is draw a diagram of the given function (familiar!) extending a little further on both sides than the points mentioned; xdot is the ordinate, but more important, with little horizontal arrows show which way x Is moving on each side of the named points, and you will soon see what they mean about stability/instability. Just explain this in your own words.

Last edited: Feb 7, 2016
4. Jan 5, 2017

### velkhaliliB

Immerse your pendulum in honey and evolve your equations. When you finish, you're gonna get a second order differencial equation. At this point, you gotta be audacious and destroy the second order term. Voilà.

5. Jan 5, 2017

### haruspex

The OP never came back, and this is years old.
But for what it's worth, I believe my suggestion in post #2 gives a very easy model, no approximations needed.