Non-Determinism in Classical Mechanics: Norton's Dome and the Space Invader
2025-02-15
Classical mechanics harbors some famously non-deterministic cases. The article first introduces Norton's Dome, where the derivative of the force is undefined at a specific point, leading to non-unique solutions. A more bizarre example is the 'Space Invader,' experiencing unbounded acceleration in finite time, reaching infinity at t=π/2. Painlevé non-collision singularities are also mentioned, such as a five-body gravitational problem where a particle reaches infinity in finite time. These examples challenge the deterministic assumptions of classical mechanics.
Read more