Perturbed damped pendulum: finding periodic solutions via averaging method
نویسنده
چکیده
Using the damped pendulum model we introduce the averaging method to study the periodic solutions of dynamical systems with small non–autonomous perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non–linear perturbed damped pendulum. The averaging method provides a useful means to study dynamical systems, accessible to Master and PhD students.
منابع مشابه
On the periodic solutions of a perturbed double pendulum
Abstract. We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations having equations of motion θ̈1 = −2aθ1 + aθ2 + εF1(t, θ1, θ̇1, θ2, θ̇2), θ̈2 = 2aθ1 − 2aθ2 + εF2(t, θ1, θ̇1, θ2, θ̇2), where a and ε are real parameters. The two masses of the unperturbed double pendulum are equal, and its two stems have the same length l....
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