Subharmonic oscillations of forced pendulum-type equations

Subharmonic Oscillations of Forced Pendulum-Type Equations

where f is periodic with minimal period T and mean value zero. We have in mind as a particular case the pendulum equation, where g(x) = A sin x. First results on the existence of subharmonic orbits in a neighborhood of a given periodic motion were obtained by Birkhoff and Lewis (cf. [3] and [ 143) by perturbation-type techniques. Rabinowitz [ 151 was able to prove the existence of subharmonic s...

Extraordinary oscillations of an ordinary forced pendulum

Several well-known and newly discovered counterintuitive regular and chaotic modes of the sinusoidally driven rigid planar pendulum are discussed and illustrated by computer simulations. The software supporting the investigation offers many interesting predefined examples that demonstrate various peculiarities of this famous physical model. Plausible physical explanations are suggested for some...

Multiplicity of Forced Oscillations for the Spherical Pendulum

where h : S → R is C and tangent to S, η ≥ 0 and φ : R × TS → R is continuous, T -periodic in t, and such that φ(t, q, v) ∈ TqS for any (t, q, v) ∈ R× TS. In the case when φ does not depend on ẋ, the problem of the existence of T -periodic solutions of (1), for any value of λ, has been positively solved in [2] and [3], and extended to the case of even dimensional spheres in [5]. In this paper, ...

Degenerate Equations of Pendulum-type

Subharmonic resonances of the parametrically driven pendulum

A simple qualitative physical explanation is suggested for the phenomenon of subharmonic resonances of a rigid planar pendulum whose axis is forced to oscillate with a high frequency in the vertical direction. An approximate quantitative theory based on the suggested approach is developed. The spectral composition of the subharmonic resonances is investigated quantitatively, and the boundaries ...