Investigation of a dynamical system in a neighborhood of an invariant toroidal manifold in the general case

1994 ◽  
Vol 46 (10) ◽  
pp. 1545-1555
Author(s):  
A. M. Samoilenko ◽  
B. P. Bazhura
Keyword(s):  
Dynamical System ◽  
Toroidal Manifold ◽  
Invariant Toroidal Manifold

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

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