spin_top

What Keeps Spinning Tops Upright?

Goal: To simulate and animate the behavior of a spinning top using Mathematica software.

Project Objectives:

  • Develop a mathematical model to simulate behavior of spinning top using lagrangian mechanics
  • Deduce the precession and nutation behavior of the top, in turn answering the classic question – ‘What keeps spinning tops upright?’
  • Generate a 3D graphics model in Mathematica
  • Use Mathematica to animate the 3D model to illustrate various behaviors of spinning top

Precession refers to revolution of top about vertical axis.
Nutation refers to changes in lean angle of top (bobbing up and down)

Drawing of system:

top-system

To keep the project feasible, following assumptions were made:

  • Top modelled as a ‘heavy’ top that remains fixed to the ground
  • Geometry of top simplified; it is modelled as a wheel on a thin stem as shown in above figure

Results Summary:

Here I present animation of top and the resulting trajectory for 3 different cases:

A. Initial precession rate is equal to zero:

Animation:

top001
Trajectory:

 

top0001
B. Initial precession rate is greater than zero

Animation:

top002

Trajectory:

top0002

 

C. Initial precession rate is less than zero

Animation:

top003

Trajectory:

top0003


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