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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.

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The Model

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

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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.

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Demonstration of tennis racket theorem using a wing nut.

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