Simulated motion of an oblate and prolate spinning spheroid

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SUMMARY

The discussion centers on implementing the equations of motion for spinning oblate and prolate spheroids using a Blender Python script based on the 2004 study by Moffatt, Shimomura, and Branicki. The key focus is the validity of the gyroscopic approximation under friction (μ = 0.2) as angular velocity decreases. It is established that below a critical rotational speed, the gyroscopic approximation loses validity, leading to potential bifurcations or transitions to tumbling motion depending on the spheroid's geometry. The simulation must transition from the gyroscopic approximation to a full rigid body dynamics integrator to accurately capture low-speed behavior and stability changes.

PREREQUISITES

  • Gyroscopic approximation in rigid body dynamics
  • Equations of motion for axisymmetric spinning bodies
  • Blender Python scripting for physics simulation
  • Friction modeling with coefficient of friction (μ) in dynamics

NEXT STEPS

  • Study full rigid body integrators for low angular velocity regimes
  • Analyze bifurcation theory in spinning spheroids with varying geometry
  • Implement frictional torque models in Blender physics simulations
  • Explore stability criteria for oblate vs. prolate spheroids under friction

USEFUL FOR

Physicists, computational modelers, and Blender developers simulating rigid body dynamics of spinning spheroids, especially those interested in transitions from gyroscopic stability to tumbling under frictional effects.

Russ Edmonds
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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.

 
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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.)
 

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