Approximation of probability density functions propagated through the perturbed two-body problem

Michael Mercurio, Reza Mandankan, Puneet Singla, Manoranjan Majji

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

Abstract

This paper presents the details associated with the development of approximate probability density function (PDF) expressions for its evolution along a batch of trajectories. The exact value of the PDF is determined using the transformation of variables formula, in conjunction with the Abel's identity for the evolution of the determinant of the state transition matrix along the trajectory of the dynamical system of interest. Global Local Orthogonal MAPping (GLO-MAP) process is employed to construct the approximate PDFs from the exact values that are scattered in the phase fluid. The methodology is applied to representative dynamical systems, including the perturbed two body problem to demonstrate the effectiveness of the tools developed in this paper.

Original languageEnglish (US)
Title of host publicationAstrodynamics 2013 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Astrodynamics Specialist Conference
PublisherUnivelt Inc.
Pages2457-2468
Number of pages12
ISBN (Print)9780877036050
StatePublished - Jan 1 2014
Event2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 - Hilton Head Island, SC, United States
Duration: Aug 11 2013Aug 15 2013

Publication series

NameAdvances in the Astronautical Sciences
Volume150
ISSN (Print)0065-3438

Other

Other2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013
CountryUnited States
CityHilton Head Island, SC
Period8/11/138/15/13

Fingerprint

two body problem
probability density function
probability density functions
dynamical systems
Probability density function
Dynamical systems
trajectory
Trajectories
trajectories
approximation
determinants
methodology
matrix
Fluids
fluid
fluids

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Mercurio, M., Mandankan, R., Singla, P., & Majji, M. (2014). Approximation of probability density functions propagated through the perturbed two-body problem. In Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference (pp. 2457-2468). (Advances in the Astronautical Sciences; Vol. 150). Univelt Inc..
Mercurio, Michael ; Mandankan, Reza ; Singla, Puneet ; Majji, Manoranjan. / Approximation of probability density functions propagated through the perturbed two-body problem. Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc., 2014. pp. 2457-2468 (Advances in the Astronautical Sciences).
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Mercurio, M, Mandankan, R, Singla, P & Majji, M 2014, Approximation of probability density functions propagated through the perturbed two-body problem. in Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Advances in the Astronautical Sciences, vol. 150, Univelt Inc., pp. 2457-2468, 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013, Hilton Head Island, SC, United States, 8/11/13.

Approximation of probability density functions propagated through the perturbed two-body problem. / Mercurio, Michael; Mandankan, Reza; Singla, Puneet; Majji, Manoranjan.

Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc., 2014. p. 2457-2468 (Advances in the Astronautical Sciences; Vol. 150).

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

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Mercurio M, Mandankan R, Singla P, Majji M. Approximation of probability density functions propagated through the perturbed two-body problem. In Astrodynamics 2013 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference. Univelt Inc. 2014. p. 2457-2468. (Advances in the Astronautical Sciences).