Simulated motion of an oblate and prolate spinning spheroid

[Russ Edmonds]

TL;DR

Equations of motion for a spinning spheroid where implemented in a Blender Python script and a video displaying the motion was made.

Equations of motion for a spinning spheroid [1] where implemented in a Blender Python script.

1. H. K. Moffatt, Y. Shimomura and M. Branicki 2004 Dynamics of an axisymmetric body spinning on a horizontal surface I. Stability and the gyroscopic approximation.

 

[yisyelkencisi]

hi,

i have a question regarding the "gyroscopic approximation" mentioned in the video. since friction (μ = 0.2) is present, the angular velocity will inevitably decrease over time. at what point does this approximation lose its validity?

specifically, once the rotation drops below a certain critical speed, should we expect a bifurcation or a transition into more erratic motion (like tumbling) depending on the geometry (oblate vs. prolate), or does the system tend to maintain stable precession until it comes to a rest? i'm curious how the script handles the physics as the "gyroscopic dominance" fades away. does the simulation switch to a more complete rigid body integrator to handle the low-speed dynamics, or does it stay within the approximation until the very end?

thanks in advance for any insights!

(i understand the physics intuitively, but i'm not very well-versed in the formal math behind it. i'd love a simplified explanation if possible.)