Versal normal form at the Lagrange equilibrium L4

Richard Cushman; Al Kelley; Hüseyin Koçak

doi:10.1016/0022-0396(86)90080-X

Versal normal form at the Lagrange equilibrium L₄

Richard Cushman, Al Kelley, Hüseyin Koçak

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

6 Scopus citations

Abstract

A new normal form, called versal, for the linearized Hamiltonian vector field of the planar restricted three-body problem at the Lagrange equilibrium point L₄ depending smoothly on the mass ratio for all values close to the critical Routh's ratio is described. Then a canonical transformation also depending smoothly on the mass ratio which brings the linear Hamiltonian vector field into this versal normal form is explicitly calculated.

Original language	English (US)
Pages (from-to)	340-374
Number of pages	35
Journal	Journal of Differential Equations
Volume	64
Issue number	3
DOIs	https://doi.org/10.1016/0022-0396(86)90080-X
State	Published - Sep 30 1986
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/0022-0396(86)90080-X

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title = "Versal normal form at the Lagrange equilibrium L4",

abstract = "A new normal form, called versal, for the linearized Hamiltonian vector field of the planar restricted three-body problem at the Lagrange equilibrium point L4 depending smoothly on the mass ratio for all values close to the critical Routh's ratio is described. Then a canonical transformation also depending smoothly on the mass ratio which brings the linear Hamiltonian vector field into this versal normal form is explicitly calculated.",

author = "Richard Cushman and Al Kelley and H{\"u}seyin Ko{\c c}ak",

year = "1986",

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doi = "10.1016/0022-0396(86)90080-X",

language = "English (US)",

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AU - Kelley, Al

AU - Koçak, Hüseyin

PY - 1986/9/30

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N2 - A new normal form, called versal, for the linearized Hamiltonian vector field of the planar restricted three-body problem at the Lagrange equilibrium point L4 depending smoothly on the mass ratio for all values close to the critical Routh's ratio is described. Then a canonical transformation also depending smoothly on the mass ratio which brings the linear Hamiltonian vector field into this versal normal form is explicitly calculated.

AB - A new normal form, called versal, for the linearized Hamiltonian vector field of the planar restricted three-body problem at the Lagrange equilibrium point L4 depending smoothly on the mass ratio for all values close to the critical Routh's ratio is described. Then a canonical transformation also depending smoothly on the mass ratio which brings the linear Hamiltonian vector field into this versal normal form is explicitly calculated.

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DO - 10.1016/0022-0396(86)90080-X

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

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ER -

Versal normal form at the Lagrange equilibrium L₄

Abstract

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