Example of Stochastic DE for elementary physics?

[Stephen Tashi]

Are there any tutorials that apply stochastic differential equations to the settings of elementary physics problems ? - for example, an object sliding down a not-frictionless ramp.

The ramps of everyday life don't have a constant coefficient of friction. A better model for them would be that the friction coefficient is a stochastic process that takes place over the distance of the ramp. An imitation of an elementary physics scenario would be to specify that process as a "given", along with the slope of the ramp and the mass of the object. The task would be to solve for the stochastic process that describes the distance the object has traveled down the ramp..

 

[Jhero]

A good tutorial for this type of problem can be found here: https://www.quantamagazine.org/stochastic-differential-equations-tutorial-20160912/ This tutorial provides a thorough explanation of how to solve stochastic differential equations, along with several examples from physics. The tutorial also includes references to other helpful resources.