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Parabolic fixed points and stability criteria for nonlinear Hill's equation (2000)

Núñez, D. ; Ortega, R.

Springer

Zeitschrift für angewandte Mathematik und Physik 51 (2000), S. 890-911

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ISSN: 0044-2275

Keywords: Key words. Stability, parabolic points, pendulum.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract. We discuss the stability of parabolic fixed points of area-preserving mappings and obtain a new proof of a criterion due to Simó. These results are employed to discuss the stability of the equilibrium of certain periodic differential equations of newtonian type. An example is the pendulum of variable length. In this class of equations the First Lyapunov's Method does not apply but in many cases the stability can be characterized in terms of the variational equation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00001528

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