From the 1 of 5 linked papers with an AI index.
4 citations · 4 across the 1 of their papers we have counts for
5 papers
The Maxwell Conjecture is False
Philip Arathoon, Gavin Ball, Matthew D. Kvalheim
The authors present a configuration of five point charges that yields at least 24 non‑degenerate critical points of the electrostatic potential, disproving Maxwell's conjecture abo…
Linearizability of flows by embeddings
Matthew D. Kvalheim, Philip Arathoon
We consider the problem of determining the class of continuous-time dynamical systems that can be globally linearized in the sense of admitting an embedding into a linear system on…
Integrable sub-Riemannian geodesic flows on the special orthogonal group
Alejandro Bravo-Doddoli, Philip Arathoon, Anthony M. Bloch
We analyse the geometry of the rubber-rolling distribution on the special orthogonal group and show that almost all the normal geodesics of any right-invariant sub-Riemannian metri…
Real Forms of Holomorphic Hamiltonian Systems
Philip Arathoon, Marine Fontaine
By complexifying a Hamiltonian system one obtains dynamics on a holomorphic symplectic manifold. To invert this construction we present a theory of real forms which not only recove…
Relative Equilibria of Mechanical Systems with Rotational Symmetry
Philip Arathoon
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class whic…