Motors and Magnetic Levitation

My first published paper was regarding a simple model of an induction motor. Here is a version of it. I completed the work in April 2011. The below version is my orignal manuscript and the typesetting quality matches the naivete of the analysis. The journal reference is American Journal of Physics 80 (1), 43-46 (2012), a citation which I can still rattle off the top of my head (after all, one's first paper is always worth something).
Basic motor model

Here is a considerable extension of the above work to the case where the dynamic motor model is derived. Some references for it are Proceedings of Progress in Electromagnetics Research Symposium, Moscow, 482-486 (2012) and "The Electromagnetism of the Induction Motor," Lambert Acacemic Publishing, (2013). While the 2012 conference was a very happy occasion for me owing to its being my first conference presentation and the full scale funding I received from IITK (my sincere gratitude to DRPG Professor MANINDRA AGRAWAL for this), unfortunately, the derivation I have included in these works is in hindsight cumbersome. The version below, although (obviously) unpublished, does the derivation much more cleanly and can be used as a starting point for more complicated eddy current problems. Approximate date of this version is February 2015.
Advanced motor model

Here is something more recent, a potential new design of a magnetic levitator which can achieve stable permanent magnet confinement with zero active control. Stability uses the BROUWER saddle mechanism i.e. the result that a particle in the centre of a rotating saddle is stable. Simulations indicate the effectivity of the proposed design. I completed this work in February 2017. Here is a short version showing the physics behind the rigid body trap. The journal reference is EPL (Europhysics Letters) 118, 45002 (2017).
Ring trap short
And here is a longer version with the mathematical and simulational details.
Ring trap long


High frequency can sometimes be a game-changer. For example in an inverted pendulum, if you shake the base slowly, nothing happens. But vibrate it fast enough and the inverted position becomes stable. It turns out that a similar phenomenon happens in electromagnetism. If you have a slowly oscillating (magnetostatic) dipole suspended above a metal sheet, the lift force it feels varies as 1/h^4 where h is height. But if the frequency is high (radiative) then the lift is 1/h^2. As a side benefit, this calculation also shows us how to obtain a radiation field by directly solving the wave equation - no retarded potential. This dates from July 2018. Journal reference is Physics Letters A 383 (13), 1381-1384 (2019)
Rapidly oscillating dipole