7 citations · 37 across the 15 of their papers we have counts for
6 papers · 1 filter
A look at endemic equilibria of compartmental epidemiological models and model control via vaccination and mitigation
Monique Chyba, Taylor Klotz, Yuriy Mileyko +1
Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the class…
An introduction to the Kepler-Heisenberg problem
Corey Shanbrom
Here we provide an overview of what is known, and what is not known, about an interesting dynamical system known as the Kepler-Heisenberg problem. The main idea is to pose a versio…
Multi-agent systems for quadcopters
Richard Carney, Monique Chyba, Chris Gray +2
Unmanned Aerial Vehicles (UAVs) have been increasingly used in the context of remote sensing missions such as target search and tracking, mapping, or surveillance monitoring. In th…
Self-similarity in the Kepler-Heisenberg problem
Victor Dods, Corey Shanbrom
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the Heisenberg group, thought of as a three-dimensional sub-Riemannian manifold. The sub…
Periodic Orbits in the Kepler-Heisenberg Problem
Corey Shanbrom
One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our…
Keplerian Dynamics on the Heisenberg Group and Elsewhere
Richard Montgomery, Corey Shanbrom
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamenta…