AN EFFICIENT ANCIENT CHINESE ALGORITHM TO INVESTIGATE THE DYNAMICS RESPONSE OF A FRACTAL MICROGRAVITY FORCED OSCILLATOR
Alex Elı́as-Zúñiga, Óscar Martínez-Romero, Daniel Olvera-Trejo, Luis Manuel Palacios-Pineda
Abstract
In this paper, the ancient Chinese algorithm is applied to derive fractal microgravity forced oscillator’s frequency–amplitude response curves using the two-scale fractal transform derivative. Depending on the fractal parameter values, it is shown that the system restoring forces exhibit hardening or softening behavior. Furthermore, the proposed solution approach is simple, efficient, and accurate for obtaining the approximate steady-state solution of a fractal microgravity nonlinear oscillator with a purely nonlinear power-form restoring force.
Topics & Concepts
FractalNonlinear systemRestoring forceMathematicsAmplitudeDynamics (music)Control theory (sociology)SofteningFractal landscapeSimple (philosophy)Statistical physicsMathematical analysisAlgorithmComputer scienceClassical mechanicsPhysicsFractal analysisFractal dimensionArtificial intelligenceAcousticsOpticsControl (management)PhilosophyQuantum mechanicsEpistemologyStatisticsFractional Differential Equations SolutionsAdvanced Mathematical Theories and ApplicationsChaos control and synchronization