### 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 language | English (US) |
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Title of host publication | Astrodynamics 2013 - Advances in the Astronautical Sciences |

Subtitle of host publication | Proceedings of the AAS/AIAA Astrodynamics Specialist Conference |

Publisher | Univelt Inc. |

Pages | 2457-2468 |

Number of pages | 12 |

ISBN (Print) | 9780877036050 |

State | Published - Jan 1 2014 |

Event | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 - Hilton Head Island, SC, United States Duration: Aug 11 2013 → Aug 15 2013 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 150 |

ISSN (Print) | 0065-3438 |

### Other

Other | 2013 AAS/AIAA Astrodynamics Specialist Conference, Astrodynamics 2013 |
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Country | United States |

City | Hilton Head Island, SC |

Period | 8/11/13 → 8/15/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*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..

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Approximation of probability density functions propagated through the perturbed two-body problem

AU - Mercurio, Michael

AU - Mandankan, Reza

AU - Singla, Puneet

AU - Majji, Manoranjan

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898971162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898971162&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84898971162

SN - 9780877036050

T3 - Advances in the Astronautical Sciences

SP - 2457

EP - 2468

BT - Astrodynamics 2013 - Advances in the Astronautical Sciences

PB - Univelt Inc.

ER -