ball-bouncing-uneven-street-HC-method.ipynb

[moorepants]

From Peter:

I tried to simulatel a homogenious ball dropping on an uneven street.
I noticed this:

Here building the model is fast, less than 100,000 operations in the force vektor, but numerical calculation takes a long time.
This is mostly so, because I had to set the parameter max_step in ivp_solve to a very small value, otherwise the integration misses the points of impact.

From the ball's perspective, the street is concave. I modeled this by simply making R_2, the osculating radius of the street to be negative. (This radius is needed in the Hunt-Crossley formula, given in the article you gave me a while back)

• I have no idea, whether whether this is stretching the formula beyod its range.
• to get the effective R_2, I simply averaged the osculating radii in the X and Z direction.

Getting the speed right before the impact (this is needed in formula of the article, I guess in your lecture, you encorporated this dependency into the collision factor) was tricky.
I can only get it during the numerical integration, and it took me a while to get it rght - I hope.

I got a system of nonlinear equations to numerically determine the point of contact. This has to be solved at each step of the integration, slowing it down further.

The numerical integration seems very sensitive to initial conditions.
I also observed this:
Running a cell, say to get the energy of the system, an error message would come that an invalid value was encountered, but it still finished running.
When I simply ran it again, ther would be no error message...
This sort of thing makes me believe this simulation is quite a challenge to numerical integration - at least the way I set it up.