Abstract
The study of the oscillations of a system in the neighborhood of an equilibrium position or a periodic motion usual begins with linearization. The linearized system can be integrated. After this is done, the main properties of the oscillations in the original system can frequently be determined using the theory of normal forms of Poincare-Birkhoff. This theory is an analog of perturbation theory (Ch. 5, §2). Here the linearized system plays the role of the unperturbed system with respect to the original one. In this chapter we describe the basic elements of such an approach.
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© 1997 Springer-Verlag Berlin Heidelberg
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Arnold, V.I., Kozlov, V.V., Neishtadt, A.I. (1997). Theory of Small Oscillations. In: Mathematical Aspects of Classical and Celestial Mechanics. Mathematical Aspects of Classical and Celestial Mechanics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61237-4_7
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DOI: https://doi.org/10.1007/978-3-642-61237-4_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61224-7
Online ISBN: 978-3-642-61237-4
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