Displaying similar documents to “The period of oscillations in non-linear systems”

Potentials unbounded below.

Curtright, Thomas (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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The principle of stationary action in the calculus of variations

Emanuel López, Alberto Molgado, José A. Vallejo (2012)

Communications in Mathematics

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We review some techniques from non-linear analysis in order to investigate critical paths for the action functional in the calculus of variations applied to physics. Our main intention in this regard is to expose precise mathematical conditions for critical paths to be minimum solutions in a variety of situations of interest in Physics. Our claim is that, with a few elementary techniques, a systematic analysis (including the domain for which critical points are genuine minima) of non-trivial...

A singular perturbation method for saddle connections and subharmonics of certain nonlinear differential equations with fixed saddle points.

Peter Smith (1990)

Revista Matemática de la Universidad Complutense de Madrid

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Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application...