## SNE # 0. Stochastic inverse pendulum

This is the first installment of “Small Numerical Experiments” (SNE), a section where I upload and comment (briefly) some small numerical example. The purpose is to prove a point to myself, test some code, ideas, etc.

In this first post I will explore the response of a *stochastic inverse
pendulum.* What I mean in this case is an inverse pendulum (shown left)
with a random initial condition. The purpose is to obtain the
time-evolving probability density function (PDF) of the pendulum’s
position. I will be doing Monte-Carlo simulations to obtain an
approximation to this PDF.

The response of the …