### Abstract

Original language | English |
---|---|

Pages (from-to) | 490-496 |

Number of pages | 6 |

Journal | International Journal of Non-Linear Mechanics |

Volume | 43 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jul 2008 |

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### Keywords

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

### Cite this

*International Journal of Non-Linear Mechanics*,

*43*(6), 490-496. https://doi.org/10.1016/j.ijnonlinmec.2008.01.001

}

*International Journal of Non-Linear Mechanics*, vol. 43, no. 6, pp. 490-496. https://doi.org/10.1016/j.ijnonlinmec.2008.01.001

**Solar sail dynamics in the three-body problem: homoclinic paths of points and orbits.** / Waters, Thomas J.; McInnes, Colin R.

Research output: Contribution to journal › Article

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

Y1 - 2008/7

N2 - 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.

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

M3 - Article

VL - 43

SP - 490

EP - 496

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 6

ER -