Moto di un satellite artificiale terrestre in un campo gravitazionale con simmetria assiale

Translated title of the contribution: Geodesic motion of an earth’s artificial satellite in an axialsymmetrically gravitational field

Research output: Contribution to journalArticle

Abstract

The trajectory of motion of an Earth’s artificial satellite in an axialsymmetric gravitational field is interpreted as a geodesic flow in a conformally flat Riemannian manifold, here called Maupertuis’ manifold, according to the Maupertuis-Euler-Lagrange variational principle of least action. Two cases of space, namely the case of configuration space and impulse space, are studied. In both cases of space, the relation between the nature of curvature of the Maupertuis’ manifold and the orbital geometry is investigated. We also analyze the tidal matrices and discuss some properties of stability for the Kepler’s motions in the Maupertuis’ manifold by means of the equations of geodesic deviation. Finally, we give embedding spaces of Maupertuis’ manifolds according to the local and isometric embedding theorem.

Original languageItalian
Pages (from-to)257-274
Number of pages18
JournalBollettino di Geodesia e Scienze Affini
Volume57
Issue number3
Publication statusPublished - 1998 Jan 1

Fingerprint

Earth (planet)
Trajectories
Satellites
Geometry
curvature
trajectory
artificial satellite
geometry
matrix

All Science Journal Classification (ASJC) codes

  • Environmental Science(all)
  • Engineering(all)
  • Earth and Planetary Sciences(all)

Cite this

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title = "Moto di un satellite artificiale terrestre in un campo gravitazionale con simmetria assiale",
abstract = "The trajectory of motion of an Earth’s artificial satellite in an axialsymmetric gravitational field is interpreted as a geodesic flow in a conformally flat Riemannian manifold, here called Maupertuis’ manifold, according to the Maupertuis-Euler-Lagrange variational principle of least action. Two cases of space, namely the case of configuration space and impulse space, are studied. In both cases of space, the relation between the nature of curvature of the Maupertuis’ manifold and the orbital geometry is investigated. We also analyze the tidal matrices and discuss some properties of stability for the Kepler’s motions in the Maupertuis’ manifold by means of the equations of geodesic deviation. Finally, we give embedding spaces of Maupertuis’ manifolds according to the local and isometric embedding theorem.",
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Moto di un satellite artificiale terrestre in un campo gravitazionale con simmetria assiale. / You, Rey-Jer.

In: Bollettino di Geodesia e Scienze Affini, Vol. 57, No. 3, 01.01.1998, p. 257-274.

Research output: Contribution to journalArticle

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