Spinning Top — How can you visualize gyroscopic precession?

Questions
, , , ,
1

I never forgot the youtube clip demonstrating the simulation of a Schwerer Kreisel in Matlab. In Engrish, that should be a Lagrange top i guess, it doesn’t matter. I assume that the visual simulation of the gyroscopic precession of a Lagrange top could be done in SystemModeler but the question is if an animation output exactly like the youtube clip could be done in Mathematica too? And if yes, would it be a straight-forward or rather awkward coding thing to do in Mathematica? And would it be a challenging expansive project, what do you think?

Feel free to assume any simplified conditions:

  • gravitational gravity is constant, pointing downwards
  • the spinning rod (rotational axis) is a 1-D line without mass and its end is (seemingly) fixed on the table
  • the initial location of the top’s centroid is given
  • the initial angular speed (re rotational axis) is given
  • the angular speed seems to slow down during the course of the simulation, maybe due to friction on the table
  • this is a real simulation, starting at t=0 and letting nature determine the course and end of the run; the simulation could end as soon as the brim of the top touches the table
  • any further simplified conditions to reduce the complexity of the problem

I am totally new to programming and have no imagination how this could be implemented in Mathematica (not SystemModeler), the building blocks/steps. I can only guess that the most outer bracket in the program would be an Animate[] wrapper? Inside of Animate[], would you need several and/or nested DynamicModule[] and Dynamic[] statements? For sure one would need one NDSolve[] and one Graphics3D[] statement, what else?

Anyhow i find the video very intriguing and impressive. Would love to see the implementation in Mathematica! Would be worth another Staff Pick, no doubt!!

2

Look at arrow / vertex graphics examples in the Mathematica book. putting arrows on things or showing vector fields is exampled.

Precession, minus some tedious calculous representation, is extremely simple to represent.

Arrows are tangent to the cone (due to spin). Because the spin isn’t perfect and because there is some down arrow (due to natural instability of a small base, a tall neck, and wide top).

The top begins to fall just as if it were not spinning at all but because of the forces of it’s spin it does not fall quickly, it falls slowly and the direction of fall “walks around” with the spin. so if it’s fallen half way down and the top still spins, the result is the top “walks around” the center trying to conserve the energy of the spin (which looses, eventually g pulls it all the way down).

The two arrows were tangential and downward (plus instability that is not represented).

The resulting arrow is tangential and a little downward. If I remember correctly :slight_smile: