@inproceedings{59134d28e8e842e69fc47167e8e00022,
title = "Canonical transformations via a sparse approximation-based collocation method for dynamical systems",
abstract = "Semi-analytical approaches to solve the Hamilton-Jacobi Partial Differential Equation that governs the transformation of coordinates to rectify the motion of a dynamical system are proposed in this paper. It is shown that recent advances in sparse approximation can be utilized to develop a collocation method to approximate the generating function for which closed-form solution to the HJ equation may not be obtained. By utilizing a family of trajectories in the domain of the relevant phase volume, the sparse approximation problem for the coefficients of the generating function is formulated and solved efficiently, for arbitrary choice of basis function sets.",
author = "Eapen, {Roshan T.} and Manoranjan Majji and Alfriend, {Kyle T.} and Puneet Singla",
note = "Funding Information: This research described in this paper was carried out at and supported by the Department of Aerospace Engineering, Texas A&M University, College Station, TX. This material is based upon the work jointly supported by the U.S. Air Force Office of Scientific Research (FA9550-15-1-0313 and FA9550-17-1-0088), and by the National Science Foundation under Award No. NSF CMMI-1634590. Publisher Copyright: {\textcopyright} 2020, Univelt Inc. All rights reserved.; AAS/AIAA Astrodynamics Specialist Conference, 2019 ; Conference date: 11-08-2019 Through 15-08-2019",
year = "2020",
language = "English (US)",
isbn = "9780877036654",
series = "Advances in the Astronautical Sciences",
publisher = "Univelt Inc.",
pages = "1171--1190",
editor = "Horneman, {Kenneth R.} and Christopher Scott and Hansen, {Brian W.} and Hussein, {Islam I.}",
booktitle = "AAS/AIAA Astrodynamics Specialist Conference, 2019",
address = "United States",
}