Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits

Thomas J. Waters, Colin R. McInnes

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the previous termsail.next term We consider first the equilibria and linearisation of the system, then examine the non-linear system paying particular attention to its periodic solutions and invariant manifolds. Interestingly, we find there are equilibria admitting homoclinic paths where the stable and unstable invariant manifolds are identical. What is more, we find that periodic orbits about these equilibria also admit homoclinic paths; in fact the entire unstable invariant manifold winds off the periodic orbit, only to wind back onto it in the future. This unexpected result shows that periodic orbits may inherit the homoclinic nature of the point about which they are described.
LanguageEnglish
Pages490-496
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume43
Issue number6
DOIs
Publication statusPublished - Jul 2008

Fingerprint

Three-body Problem
ice ridge
Homoclinic
Invariant Manifolds
Orbits
Orbit
Periodic Orbits
Unstable Manifold
Path
Term
Restricted Three-body Problem
Linearization
Ordinary differential equations
Sun
Equations of motion
Nonlinear systems
Earth (planet)
Equations of Motion
Periodic Solution
Ordinary differential equation

Keywords

  • solar sail
  • homoclinic
  • periodic orbit
  • three-body problem

Cite this

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title = "Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits",
abstract = "In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the previous termsail.next term We consider first the equilibria and linearisation of the system, then examine the non-linear system paying particular attention to its periodic solutions and invariant manifolds. Interestingly, we find there are equilibria admitting homoclinic paths where the stable and unstable invariant manifolds are identical. What is more, we find that periodic orbits about these equilibria also admit homoclinic paths; in fact the entire unstable invariant manifold winds off the periodic orbit, only to wind back onto it in the future. This unexpected result shows that periodic orbits may inherit the homoclinic nature of the point about which they are described.",
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Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits. / Waters, Thomas J.; McInnes, Colin R.

In: International Journal of Non-Linear Mechanics, Vol. 43, No. 6, 07.2008, p. 490-496.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits

AU - Waters, Thomas J.

AU - McInnes, Colin R.

PY - 2008/7

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AB - In this paper we consider the orbital previous termdynamicsnext term of a previous termsolar sailnext term in the Earth-Sun circular restricted three-body problem. The equations of motion of the previous termsailnext term are given by a set of non-linear autonomous ordinary differential equations, which are non-conservative due to the non-central nature of the force on the previous termsail.next term We consider first the equilibria and linearisation of the system, then examine the non-linear system paying particular attention to its periodic solutions and invariant manifolds. Interestingly, we find there are equilibria admitting homoclinic paths where the stable and unstable invariant manifolds are identical. What is more, we find that periodic orbits about these equilibria also admit homoclinic paths; in fact the entire unstable invariant manifold winds off the periodic orbit, only to wind back onto it in the future. This unexpected result shows that periodic orbits may inherit the homoclinic nature of the point about which they are described.

KW - solar sail

KW - homoclinic

KW - periodic orbit

KW - three-body problem

U2 - 10.1016/j.ijnonlinmec.2008.01.001

DO - 10.1016/j.ijnonlinmec.2008.01.001

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SP - 490

EP - 496

JO - International Journal of Non-Linear Mechanics

T2 - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

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ER -