Canonical transformations via a sparse approximation-based collocation method for dynamical systems

Roshan T. Eapen, Manoranjan Majji, Kyle T. Alfriend, Puneet Singla

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationAAS/AIAA Astrodynamics Specialist Conference, 2019
EditorsKenneth R. Horneman, Christopher Scott, Brian W. Hansen, Islam I. Hussein
PublisherUnivelt Inc.
Pages1171-1190
Number of pages20
ISBN (Print)9780877036654
StatePublished - 2020
EventAAS/AIAA Astrodynamics Specialist Conference, 2019 - Portland, United States
Duration: Aug 11 2019Aug 15 2019

Publication series

NameAdvances in the Astronautical Sciences
Volume171
ISSN (Print)0065-3438

Conference

ConferenceAAS/AIAA Astrodynamics Specialist Conference, 2019
CountryUnited States
CityPortland
Period8/11/198/15/19

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

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