A Note on Norton's Dome

Abstract

"Norton's Dome" is an example of a Newtonian system that violates the Lipschitz condition at a single point, leading to non-unique solutions (indeterminism). Here we reformulate this problem into a "weak" form (in the sense of distributions). In our description the indeterminism manifests through the problematic interpretation of initial conditions, since distributions (as linear functionals on the space of test functions) do not have values at individual points.