Why a rectangular box refuses to tumble around its middle axis
In short: If you toss a box with three different side lengths into the air, its rotation follows a predictable but strange pattern. This video explores why certain axes remain stable while others inevitably fail.
Using a model of angular momentum, instructor Cleve Moler demonstrates how a rectangular object, like a cereal box, behaves in flight. The system is defined by a nonlinear set of three differential equations.
The physics reveals six critical points: rotation around the longest and shortest axes is stable, but the two points corresponding to the middle axis are unstable.
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Sources
- Summary by Intellect · source: Tumbling Box
- Also: Tumbling Box | Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler | Mathematics | MIT OpenCourseWare
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