4 papers
Universal Birkhoff Method for Computing Extremals in the Elliptic Restricted Three-Body Problem
Michael J. Dixon, Isaac M. Ross
The computation of finite-thrust extremal arcs in the elliptic restricted three-body trajectory optimization problem is considered. Libration-point orbits are approximated to near-…
On The Mathematics of the Natural Physics of Optimization
I. M. Ross
A number of optimization algorithms have been inspired by the physics of Newtonian motion. Here, we ask the question: do algorithms themselves obey some ``natural laws of motion,''…
Hessians in Birkhoff-Theoretic Trajectory Optimization
I. M. Ross
This paper derives various Hessians associated with Birkhoff-theoretic methods for trajectory optimization. According to a theorem proved in this paper, approximately 80% of the ei…
A Universal Birkhoff Theory for Fast Trajectory Optimization
I. M. Ross
Over the last two decades, pseudospectral methods based on Lagrange interpolants have flourished in solving trajectory optimization problems and their flight implementations. In a…