Thoughts on Dynamics

Friday was Expo, the last day of the semester. I’m more than a third of the way through college, which feels a little weird.

For some reason this semester didn’t feel like it was ending until the very end. Midway through the semester, I still caught myself thinking that it was just the beginning. I’m not sure why this was; I was definitely learning, so in general it wasn’t that I didn’t think we had covered enough material for it to be that far into the semester.

The class in which I learned the most this semester was Dynamics, which is a mechanical engineering requirement. It was also the class into which I put by far the most time. Below the fold are my thoughts on Dynamics.

Dynamics is mostly about the movement of rigid bodies, with a focus on rotational motion, and near the end it also covers vibrations and the response of linear systems. With the current professor, it has a reputation for being difficult and an enormous amount of work. The semester started out very slowly. We went over the physics of projectile motion and coded it in MATLAB, which we had all done in ModSim. Adding in drag wasn’t new, either. Then we coded a simple Design Nature hopper model, but that was also very similar to a problem we had done in ModSim. At first, none of us could understand why Dynamics had such a fierce reputation. It didn’t seem that bad at all.

It ramped up very quickly. Soon, all the material was new, and what wasn’t new was presented much more formally. For example, most of us had seen mass moment of inertia in a previous physics class, but most of us hadn’t seen inertia in the form of a three by three matrix, which is how we treated it in Dynamics.

Class periods were usually at least half lecture. Chris, the professor, does board lectures, and generally I thought the lectures were effective, but Chris had a tendency to move quickly, and a lot of people weren’t comfortable interrupting him to ask a question. They would ask him (or a NINJA or friend) afterwards, but if someone got lost early in the class, it was easy to fall very behind. 

Olin’s normal solutions for people really needing help in a class are to recommend going to NINJA hours, the prof’s office hours, and to get a peer tutor. The Dynamics NINJAs put in a lot of hours, but there were three of them for forty students in a difficult and time-consuming class, so getting personal help could be hard. There also weren’t enough peer tutors for everyone who requested one. At one point in the semester someone told me there was an eight person waitlist for Dynamics tutors. Chris also put in a lot of time helping individual students, but again, he’s only one person.

The non-lecture part of class we usually spent working on in-class exercises that Chris posted to the course folder. These were simpler than the problems on the homework assignments. They were generally meant to be more straightforward applications of whatever we had learned. I do wish we had discussed some of these more in class, though. We would work on them for a while but usually not finish, and Chris would post solutions on the course folder later, but I think it would have been useful to go over a few more of them in class. Doing the homework assignments was more important than finishing the in-class exercises after class was over (homework was graded, exercises weren’t), so lots of the time we just didn’t ever finish the in-class exercises, and thoroughly understanding them would have helped on the homework. The lectures didn’t include example problems very often, I think because of the in-class exercises, so just in general seeing the full process we would have to go through on homework, even for a simpler problem, would have been nice.

We had an assignment most weeks, and assignments generally took me 12 hours, sometimes more. The assignments were long, involved, and usually had at least one very challenging problem. The problems focused on finding equations of motion for systems and then on simulating that motion in MATLAB. Some of the derivations were pretty straightforward if you understood the material, but others were just messy no matter what. The structure of the MATLAB code didn't change from assignment to assignment, so I just had to change the parts of the code that corresponded to the specific equations. That meant that how well my code functioned was generally a good sign as to whether my equations were correct. It was often frustrating for the assignments to take so long, but I thought the assignments helped me learn by integrating previous concepts with the new ones and solidifying everything.  I sometimes thought the messiness of the equation derivations got in the way of the learning, but some of the nastiest equations of motion were for the double pendulum, and that’s a really important system. (Side note: a lot of the ugly problems are a lot nicer if done with Lagrangian method. I have no idea why we never did this.)

We had two exams and a final in this course, and I really liked the format. They were basically like assignments, but the only person from whom we could ask help was the professor, and while the exam was open book and open notes, it was closed internet. The similarity to assignments made the exams much less stressful. Like with the assignments, I thought I learned from the exams, and I also figured out what I still didn’t completely understand and needed to go over again. What was a little odd was the disparity in how much time I spent on the exams: eight hours on the first, fifteen on the second, and then four on the final (which was written to be about half the length of the previous ones). 

The class also had a final project, but it was a pretty simple one. We worked in pairs and chose a system for which the equations of motion were well-known. Then we collected data, modeled the system in MATLAB, and wrote a report. My final project was about trifilar pendulums, which rotate back and forth and can be used to measure the mass moments of inertia of objects. My partner and I built two trifilar pendulums, used some objects with known moments of inertia to test the pendulums, and then we found the moments of inertia of less standard objects, like pointe shoes and pliers. I liked the project because most of the class had been theoretical, but it had come up on several occasions that some things have to be done empirically, so actually doing the experimental work was cool.

For a lot of the semester, if you had asked me if I liked Dynamics, my first response would have been somewhere between “Ehh” and “Ugh, no.” Now, I think I would say that yes, I liked it. I like being able to look back and see that I learned so much over the course of a semester, and now I’m comfortable thinking about mechanical systems with fewer assumptions and simplifications. Whether or not I actually liked it, though, Dynamics was definitely an effective course for me.