The present paper has the goal of studying the use of “integral indices” to quantify the effects of a perturbing force in the driven harmonic and Duffing oscillators. The main idea is to define a scalar index that can represent the cumulative effects over time that a perturbing force causes in a dynamical system. An index of this type can help to prepare “perturbation maps”, which can identify situations of larger or smaller effects. This idea appeared in the astrodynamics literature with the goal of finding less perturbed orbits for a spacecraft, but it is applied here to the driven harmonic and Duffing oscillators. The reason for those applications is that those problems have analytical solutions, which allows a better comparison of the indices. In particular, the effects of calculating this index using a perturbed and a non-perturbed trajectory are evaluated with the goal of better understanding these effects. The results show that the difference between both indices depends on the frequency and amplitude of the perturbing force.
Astrodynamics Perturbation expansion method Perturbed dynamical analysis Nonlinear systems
Mathematics Subject Classification
70F99 41-02 85-02
This is a preview of subscription content, log in to check access.
de Almeida Prado AFB (2013) Searching for orbits with minimum fuel consumption for station-keeping maneuvers: an application to lunisolar perturbations. Math Probl Eng 2013(Article ID 415015):1–11CrossRefGoogle Scholar
Esmailzadeh E, Mehri B, Nakhaie-jazar G (1996) Periodic solution of a second order. Auton Nonlinear Syst Nonlinear Dyn 10:307–316CrossRefGoogle Scholar