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Let $K$ be a convex body in $\mathbb{R}^3$. Suppose $K$ is held at some position and orientation on an inclined plane, and released. Let there be sufficient friction so that it rolls without slippage. ...

A gömböc is a $3$-dimensional convex body (having uniform density) which has exactly one stable and one instable equilbrium position (see https://en.wikipedia.org/wiki/G%C3%B6mb%C3%B6c). Such a convex ...

Domokos, Papadopulos, and Ruina showed that there does not exist a convex planar rigid body of uniform density which has only one orientation of stable equilibrium and one orientation of unstable ...