Graphical generation of periodic orbits of tschauner-hempel equations

Mai Bando, Akira Ichikawa

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Graphical generation of periodic orbits of Tschauner-Hempel (TH) equations is presented. The general solution of the relative dynamics based on the orbital elements is obtained, and the relative motion invariant manifold, where the solution lies, is determined. The region where all periodic solutions lie is determined by two ellipses, whose size depends on the eccentricity of the leader orbit. Size and phase parameters for periodic orbits are introduced for the TH equations, and a simple way to draw a periodic orbit is proposed for a given pair of size and phase parameters and a given initial true anomaly of the elliptic orbit. Results show that the design of a relative orbit with size and position specifications is as simple as in the Hill-Clohessy-Wiltshire (HCW) case.

Original languageEnglish
Pages (from-to)1002-1007
Number of pages6
JournalJournal of Guidance, Control, and Dynamics
Volume35
Issue number3
DOIs
Publication statusPublished - May 1 2012
Externally publishedYes

Fingerprint

Periodic Orbits
Orbits
orbits
Orbit
Eccentricity
Invariant Manifolds
ellipse
General Solution
eccentricity
Anomaly
Periodic Solution
orbital elements
ellipses
Specification
anomaly
Motion
Graphics
specifications
anomalies
Specifications

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Graphical generation of periodic orbits of tschauner-hempel equations. / Bando, Mai; Ichikawa, Akira.

In: Journal of Guidance, Control, and Dynamics, Vol. 35, No. 3, 01.05.2012, p. 1002-1007.

Research output: Contribution to journalArticle

@article{44fed7229c0749cb97c607e337f0e1c5,
title = "Graphical generation of periodic orbits of tschauner-hempel equations",
abstract = "Graphical generation of periodic orbits of Tschauner-Hempel (TH) equations is presented. The general solution of the relative dynamics based on the orbital elements is obtained, and the relative motion invariant manifold, where the solution lies, is determined. The region where all periodic solutions lie is determined by two ellipses, whose size depends on the eccentricity of the leader orbit. Size and phase parameters for periodic orbits are introduced for the TH equations, and a simple way to draw a periodic orbit is proposed for a given pair of size and phase parameters and a given initial true anomaly of the elliptic orbit. Results show that the design of a relative orbit with size and position specifications is as simple as in the Hill-Clohessy-Wiltshire (HCW) case.",
author = "Mai Bando and Akira Ichikawa",
year = "2012",
month = "5",
day = "1",
doi = "10.2514/1.56326",
language = "English",
volume = "35",
pages = "1002--1007",
journal = "Journal of Guidance, Control, and Dynamics",
issn = "0731-5090",
publisher = "American Institute of Aeronautics and Astronautics Inc. (AIAA)",
number = "3",

}

TY - JOUR

T1 - Graphical generation of periodic orbits of tschauner-hempel equations

AU - Bando, Mai

AU - Ichikawa, Akira

PY - 2012/5/1

Y1 - 2012/5/1

N2 - Graphical generation of periodic orbits of Tschauner-Hempel (TH) equations is presented. The general solution of the relative dynamics based on the orbital elements is obtained, and the relative motion invariant manifold, where the solution lies, is determined. The region where all periodic solutions lie is determined by two ellipses, whose size depends on the eccentricity of the leader orbit. Size and phase parameters for periodic orbits are introduced for the TH equations, and a simple way to draw a periodic orbit is proposed for a given pair of size and phase parameters and a given initial true anomaly of the elliptic orbit. Results show that the design of a relative orbit with size and position specifications is as simple as in the Hill-Clohessy-Wiltshire (HCW) case.

AB - Graphical generation of periodic orbits of Tschauner-Hempel (TH) equations is presented. The general solution of the relative dynamics based on the orbital elements is obtained, and the relative motion invariant manifold, where the solution lies, is determined. The region where all periodic solutions lie is determined by two ellipses, whose size depends on the eccentricity of the leader orbit. Size and phase parameters for periodic orbits are introduced for the TH equations, and a simple way to draw a periodic orbit is proposed for a given pair of size and phase parameters and a given initial true anomaly of the elliptic orbit. Results show that the design of a relative orbit with size and position specifications is as simple as in the Hill-Clohessy-Wiltshire (HCW) case.

UR - http://www.scopus.com/inward/record.url?scp=84861492155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861492155&partnerID=8YFLogxK

U2 - 10.2514/1.56326

DO - 10.2514/1.56326

M3 - Article

VL - 35

SP - 1002

EP - 1007

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 3

ER -