The Poincaré-Hough model applied to the synchronous rotation at low eccentricity

Research output: Book/Report/JournalOther report

Abstract

This paper presents a study of the Poincaré-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like on a low eccentric orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. Starting from a Hamiltonian formulation of the system, we derive the Hamilton equations before integrating them numerically. Then, we use a frequency analysis algorithm to give a quasi-periodic representation, allowing us to split the different contributions and to characterise the equilibrium of the system. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. We also get a shift of the obliquity when the polar flattening of the core is small.
Original languageEnglish
Place of PublicationNamur
PublisherNamur center for complex systems
Publication statusUnpublished - 2011

Fingerprint

eccentricity
flattening
eccentric orbits
Io
libration
natural satellites
vorticity
Earth mantle
formulations
orbitals
cavities
fluids
shift

Keywords

  • Periodic Orbits
  • Hamiltonian Systems
  • Natural satellites
  • Numerical Methods
  • Rotation

Cite this

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title = "The Poincar{\'e}-Hough model applied to the synchronous rotation at low eccentricity",
abstract = "This paper presents a study of the Poincar{\'e}-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like on a low eccentric orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. Starting from a Hamiltonian formulation of the system, we derive the Hamilton equations before integrating them numerically. Then, we use a frequency analysis algorithm to give a quasi-periodic representation, allowing us to split the different contributions and to characterise the equilibrium of the system. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. We also get a shift of the obliquity when the polar flattening of the core is small.",
keywords = "Periodic Orbits, Hamiltonian Systems, Natural satellites, Numerical Methods, Rotation",
author = "Beno{\^i}t Noyelles",
note = "Publication code : FP SB092/2011/19 ; SB04977/2011/19",
year = "2011",
language = "English",
publisher = "Namur center for complex systems",

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The Poincaré-Hough model applied to the synchronous rotation at low eccentricity. / Noyelles, Benoît.

Namur : Namur center for complex systems, 2011.

Research output: Book/Report/JournalOther report

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T1 - The Poincaré-Hough model applied to the synchronous rotation at low eccentricity

AU - Noyelles, Benoît

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PY - 2011

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N2 - This paper presents a study of the Poincaré-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like on a low eccentric orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. Starting from a Hamiltonian formulation of the system, we derive the Hamilton equations before integrating them numerically. Then, we use a frequency analysis algorithm to give a quasi-periodic representation, allowing us to split the different contributions and to characterise the equilibrium of the system. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. We also get a shift of the obliquity when the polar flattening of the core is small.

AB - This paper presents a study of the Poincaré-Hough model of rotation of the synchronous natural satellites, in which these bodies are assumed to be composed of a rigid mantle and a triaxial cavity filled with inviscid fluid of constant uniform density and vorticity. In considering an Io-like on a low eccentric orbit, we describe the different possible behaviors of the system, depending on the size, polar flattening and shape of the core. We use for that the numerical tool. Starting from a Hamiltonian formulation of the system, we derive the Hamilton equations before integrating them numerically. Then, we use a frequency analysis algorithm to give a quasi-periodic representation, allowing us to split the different contributions and to characterise the equilibrium of the system. We show that, even without orbital eccentricity, the system can have complex behaviors, in particular when the core is highly flattened. In such a case, the polar motion is forced by several degrees and longitudinal librations appear. We also get a shift of the obliquity when the polar flattening of the core is small.

KW - Periodic Orbits

KW - Hamiltonian Systems

KW - Natural satellites

KW - Numerical Methods

KW - Rotation

M3 - Other report

BT - The Poincaré-Hough model applied to the synchronous rotation at low eccentricity

PB - Namur center for complex systems

CY - Namur

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