Wolfram Computation Meets Knowledge

Mechanical Engineering

Use System Modeler to model and simulate dynamics problems including mechanisms and machinery with kinematic, dynamic, and thermal behaviors. Study and solve vibration problems.

Tennis Racket Theorem (Dzhanibekov Effect)

The tennis racket theorem or the Dzhanibekov effect states that for a rigid body with three unique moments of inertia, rotation about the intermediate axis is unstable, while rotation about the other two axes is stable. You can see this theorem in action in this wing nut example.

To run this example, you'll need

The latest versions of System Modeler and Mathematica.

Please make a selection:

Get a
free trial
Continue
with download

The Model

Import or create a CAD model of the wing nut and create a SystemModel with the CAD data (including the physical properties).

Use CreateSystemModel functionality to create SystemModels.

Visualization

The wing nut is initialized with a linear velocity and an angular velocity in a zero gravity environment. You can see in the following video that the wing nut flips during its motion.

Instant animation

Automatically create 3D animations for models.

Demonstration of tennis racket theorem using a wing nut.

Programmatically create models

Create rigid body components using your CAD data.