From Brake to Syzygy

Richard Moeckel; Richard Montgomery; Andrea Venturelli

doi:10.1007/s00205-012-0502-y

From Brake to Syzygy

Richard Moeckel
, Richard Montgomery
, Andrea Venturelli

School of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincaré map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.

Original language	English (US)
Pages (from-to)	1009-1060
Number of pages	52
Journal	Archive For Rational Mechanics And Analysis
Volume	204
Issue number	3
DOIs	https://doi.org/10.1007/s00205-012-0502-y
State	Published - Jun 2012

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10.1007/s00205-012-0502-y

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title = "From Brake to Syzygy",

abstract = "In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincar{\'e} map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.",

author = "Richard Moeckel and Richard Montgomery and Andrea Venturelli",

year = "2012",

month = jun,

doi = "10.1007/s00205-012-0502-y",

language = "English (US)",

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pages = "1009--1060",

journal = "Archive For Rational Mechanics And Analysis",

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TY - JOUR

T1 - From Brake to Syzygy

AU - Moeckel, Richard

AU - Montgomery, Richard

AU - Venturelli, Andrea

PY - 2012/6

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N2 - In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincaré map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.

AB - In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincaré map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.

UR - https://www.scopus.com/pages/publications/84861006874

UR - https://www.scopus.com/pages/publications/84861006874#tab=citedBy

U2 - 10.1007/s00205-012-0502-y

DO - 10.1007/s00205-012-0502-y

M3 - Article

AN - SCOPUS:84861006874

SN - 0003-9527

VL - 204

SP - 1009

EP - 1060

JO - Archive For Rational Mechanics And Analysis

JF - Archive For Rational Mechanics And Analysis

IS - 3

ER -

From Brake to Syzygy

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