One of my areas of interest is classical mechanics. Here is a list of some of my works in this area.
This is a treatment of heavy symmetric top using Euler's equations. Although the idea here - that of using Euler's equation to do a problem other than free top - is good, the treatment is in hindsight cumbersome. I completed the work in 2012. The journal reference is American Journal of Physics 81 (7), 518-526 (2013), but the paper has primarily archival value.
Top in Euler angles
Here is a more sophisitcated application of Euler's equations to inhomogeneous rigid body motion. This is the first nonlinear equation of motion of a motorcycle. This simple but non-trivial model predicts/explains most features of real motorcycle motion, including calculation of lean angle, calculation of stability on straight and in turn, and dynamics of transition from straight to turning state. I completed the work in October 2016 and it is in submission in journals.
Mobikes remain stable primarily due to the wonders of rotational mechanics. Another stability miracle is that of train - what keeps them on the track ? Many people believe it's rolling without slipping - in that case, does a wheel slip incident produce threat of a derailment ? Can you cause a train accident just by greasing the track ? This paper shows that in fact the primary stabilizer is the normal reaction from the tracks - the friction plays only a secondary role. I completed this work in November 2015. The journal reference is American Journal of Physics 85 (3), 178-184 (2017).
It is a common experience that the blades of a helicopter droop when they are static but become nearly straight when they are rotating. A simple cantilever model can help us to understand why this is so. I completed this work in June 2018. The journal reference is European Journal of Physics 40 (2), 025001 (2019). This is also one of the Tutorials in DELTA (T068).
Helicopter blade shape