1 citations · 1 across the 7 of their papers we have counts for
Showing 2021Show all
3 papers · 1 filter
math.OC2021
A Geometric Approach to Optimal Control of Hybrid and Impulsive Systems
William Clark, Maria Oprea, Andrew J. Graven
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory is applied to these systems and a hybrid…
math.SG2021
An Elementary Proof of Poincaré's Last Geometric Theorem
Andrew J. Graven, John H. Hubbard
It is shown that the Poincaré-Birkhoff fixed point theorem may be proven by extending the geometric approach originally devised by Henri Poincaré himself, along with several result…
astro-ph.EP2021
A Rapid Method For Orbital Coverage Statistics With Using Ergodic Theory
Andrew J. Graven, Alan H. Barr, Martin W. Lo
Quantifying long-term statistical properties of satellite trajectories typically entails time-consuming trajectory propagation. We present a fast, ergodic\cite{Arnold} method of an…