Project

A portion of your grade will be assigned based on a quarter long project involving analysis of the dynamics of a multibody system using Kane's method and SymPy/PyDy. You must select a reasonably complex system (including possibly significant damping and other interesting dynamic components). This is an ideal opportunity to get started on the dynamic analysis of a thesis topic (with free consulting!). Next you must suggest a set of well-posed questions about the system which the simulation can help you to answer, derive the differential equations of motion, study the system by simulating the system dynamics, and present you results in a well formatted written report in the form of a Jupyter notebook (or set of) including whatever charts, tables, figures, and visualizations you may need to clearly communicate your results.

Many students believe that once the equations are written and the simulation is completed, the job is finished. Actually, the task has only begun. Dynamic simulations are merely a tool to learn about the possible dynamic behaviors that a system can exhibit and how these dynamics depend on other parameters. They must be used cleverly and resourcefully to elucidate the behavior of the system. This involves asking the right questions about the system and understanding which parametric dependencies are of interest. Usually this will come from some engineering job requirements and specifications or from some scientific question which one would like answered (e.g. "Design an antenna deployment system for a communication satellite which works in the near earth orbit, deploys in less that 10 sec, ..., etc." or "What are the important parameters which limit the maximum range of achievable in a throw of the discus and how should it be launched optimally?"). In this project you will be responsible for generating this project requirement before writing the simulation to help you answer the question you have asked. A good, precise statement of an interesting question is every bit as important as good answer. Indeed, poorly defined or worded questions are often impossible to answer in a satisfying and fulfilling way.

Your grade will be based on the following aspects:

1. Sophistication, interest, and difficulty of system and the questions(s) you will ask about it
2. Correctness of equations/analysis and interpretation
3. The cleverness and resourcefulness with which you use the simulation to learn about the dynamics of the system and answer the questions posed
4. Your written discussion of the system and the presentation of the results of your study/interpretation.
5. Clarity, coherence and general organization of your report