CONSULTING WORK

From time to time people come to me with requests for the solution of a mathematical problem. Provided the problem falls within my area of competence, I am happy to engage in such work. The problems I have been called upon to solve range from simple ones such as computing the capacity of a truck bed or the coordinates for a row of holes to be drilled in a machine part, through intermediate-level problems like the four you can find by following the links below, to rather sophisticated problems involving more arcane parts of harmonic analysis. (Unfortunately, the consulting engineer who came to me with the best of these problems required me to promise confidentiality to protect the commercial value of his work.) In the fourth of the problems below, I probably answered more than the questioner (a geology student) asked, but the problem was interesting. It is just my analysis of what should be a standard problem in classical physics: a particle sliding over a surface under the influence of gravity and subject to friction. I would have thought it could be found in any standard physics book, but I couldn't find it anywhere. For any reasonable landscape-like surface at all, the equations are too complicated for any closed-form solution to work, so I had to resort to Mathematica to get the solution pictured here. The Mathematica notebook I used is also included.

Here are the intermediate-level problems mentioned above:

1. Adjusting the position of a sundial.

2. Finding the position of a molecule in a lattice.

3. A proposed angle trisection.

4. Migration of a pebble over a landscape: the physical model and a Mathematica notebook solving the differential equations.