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Mathematics of Complexity and Dynamical Systems pp 1301–1313Cite as

Perturbation Theory in Celestial Mechanics

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Article Outline

Glossary

Definition of the Subject

Introduction

Classical Perturbation Theory

Resonant Perturbation Theory

Invariant Tori

Periodic Orbits

Future Directions

Bibliography

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Abbreviations

KAM theory:

Provides the persistence of quasi‐periodic motions under a small perturbation of an integrable system. KAM theory can be applied under quite general assumptions, i. e. a non‐degeneracy of the integrable system and a diophantine condition of the frequency of motion. It yields a constructive algorithm to evaluate the strength of the perturbation ensuring the existence of invariant tori.

Perturbation theory:

Provides an approximate solution of the equations of motion of a nearly‐integrable system.

Spin‐orbit problem:

A model composed of a rigid satellite rotating about an internal axis and orbiting around a central point‐mass planet; a spin‐orbit resonance means that the ratio between the revolutional and rotational periods is rational.

Three‐body problem:

A system composed by three celestial bodies (e. g. Sun‐planet‐satellite) assumed to be point‐masses subject to the mutual gravitational attraction. The restricted three‐body problem assumes that the mass of one of the bodies is so small that it can be neglected.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy

    Alessandra Celletti

Authors
  1. Alessandra Celletti
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Celletti, A. (2012). Perturbation Theory in Celestial Mechanics . In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_80

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