scholarly journals Perturbation analysis of the effective equation for two coupled periodically driven oscillators

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
Andrzej Okniński ◽  
Jan Kyzioł
Keyword(s):  
Dynamical System ◽  
Perturbation Analysis ◽  
Approximate Equation ◽  
Equation Of Motion ◽  
Internal Motion ◽  
Effective Equation ◽  
Periodically Driven

Dynamics of two coupled periodically driven oscillators is analyzed via approximate effective equation of motion. The internal motion is separated off exactly and then approximate equation of motion is derived. Perturbation analysis of the effective equation is used to study the dynamics of the initial dynamical system.

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.

Perturbation Analysis of Diffeomorphisms in Contact Dynamical System

2012 ◽  
Vol 529 ◽  
pp. 264-267
Author(s):  
Da Wei Sun
Keyword(s):  
Dynamical System ◽  
Perturbation Analysis ◽  
Contact System ◽  
Hamiltonian Mechanics ◽  
Perturbation Techniques ◽  
Small Perturbations

This paper studies the perturbations of strictly contact diffeomorphisms in contact dynamical system. By constructing new lifting methods for contact system and using some perturbation techniques in Hamiltonian mechanics, this paper proves that there exists an arbitrary small perturbations such that the corresponding function of the strictly contact isotopy does not equal to a constant at any time.

scholarly journals Dynamical system analysis of quintessence models with exponential potential — Revisited

2019 ◽  
Vol 34 (09) ◽  
pp. 1950069
Author(s):  
A. Savaş Arapoğlu ◽  
A. Emrah Yükselci
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Equation Of State ◽  
System Analysis ◽  
Three Dimensional ◽  
State Parameter ◽  
Late Time ◽  
Exponential Potential ◽  
Effective Equation ◽  
Equation Of State Parameter

Dynamical system analysis of a universe model which contains matter, radiation and quintessence with exponential potential, [Formula: see text], is studied in the light of recent observations and the tensions between different datasets. The three-dimensional phase space is constructed by the energy density parameters and all the critical points of the model with their physical meanings are investigated. This approach provides an easy way of comparing the model directly with the observations. We consider a solution that is compatible with observations and is continuous in the phase space in both directions of time, past and future. Although in many studies of late-time acceleration, the radiation is neglected, here we consider all components together and this makes the calculated effective equation of state parameter more realistic. Additionally, a relation between potential parameter, [Formula: see text], and the value of quintessence equation of state parameter, [Formula: see text], today is found by using numerical analysis. We conclude that [Formula: see text] has to be small in order to explain the current accelerated phase of the universe and this result can be seen directly from the relation we obtain. Finally, we compare the usual dynamical system approach with the approach that we follow in this paper.

scholarly journals A TOPOLOGICAL EXTENSION OF GENERAL RELATIVITY TO EXPLORE THE NATURE OF QUANTUM SPACETIME, DARK ENERGY AND INFLATION

2013 ◽  
Vol 22 (10) ◽  
pp. 1330022
Author(s):  
M. SPAANS
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Discrete Time ◽  
Thought Experiment ◽  
Planck Scale ◽  
Equation Of Motion ◽  
Effective Equation ◽  
Dark Energy Density ◽  
Topological Quantum ◽  
Quantum Spacetime

General Relativity is extended into the quantum domain. A thought experiment is explored to derive a specific topological build-up for Planckian spacetime. The presented arguments are inspired by Feynman's path integral for superposition and Wheeler's quantum foam of Planck mass mini black holes (BHs)/wormholes. Paths are fundamental and prime three-manifolds like T3, S1 × S2 and S3 are used to construct quantum spacetime. A physical principle is formulated that causes observed paths to multiply: It takes one to know one. So topological fluctuations on the Planck scale take the form of multiple copies of any homeomorphically distinct path through quantum spacetime. The discrete time equation of motion for this topological quantum gravity is derived by counting distinct paths globally. The equation of motion is solved to derive some properties of dark energy and inflation. The dark energy density depends linearly on the number of macroscopic BHs in the universe and is time-dependent in a manner consistent with current astrophysical observations, having an effective equation of state w ≈ -1.1 for redshifts smaller than unity. Inflation driven by mini BHs proceeds over n ≈ 55 e-foldings, without strong inhomogeneity. A discrete time effect visible in the cosmic microwave background is suggested.

MOMENTS OF THE SPIN-DEPENDENT PROTON STRUCTURE FUNCTION

1990 ◽  
Vol 05 (14) ◽  
pp. 1125-1130
Author(s):  
D. INDUMATHI ◽  
M. V. N. MURTHY ◽  
V. RAVINDRAN
Keyword(s):  
Structure Function ◽  
Operator Product Expansion ◽  
Equation Of Motion ◽  
Proton Structure Function ◽  
Operator Product ◽  
Effective Equation ◽  
The Third ◽  
Proton Structure ◽  
First Moment ◽  
Third Moment

We discuss the moments of the recently measured spin-dependent structure function, [Formula: see text], of the proton. Using the operator product expansion and an effective equation of motion, we show that the third moment can be related to the first moment.

scholarly journals Characterization of a periodically driven chaotic dynamical system

1997 ◽  
Vol 30 (2) ◽  
pp. 371-383 ◽  
Author(s):  
A Crisanti ◽  
M Falcioni ◽  
G Lacorata ◽  
R Purini ◽  
A Vulpiani
Keyword(s):  
Dynamical System ◽  
Chaotic Dynamical System ◽  
Periodically Driven

Switching Dynamics of a Periodically Forced Discontinuous System With an Inclined Boundary

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon M. Rapp
Keyword(s):  
Dynamical System ◽  
Vector Fields ◽  
Normal Vector ◽  
Periodic Motions ◽  
Separation Boundary ◽  
Discontinuous System ◽  
Normal Vector Field ◽  
Periodically Driven ◽  
Switching Dynamics ◽  
Straight Line

This paper presents the switching dynamics of flow from one domain into another one in the periodically driven, discontinuous dynamical system. The simple inclined straight line boundary in phase space is considered as a control law for the dynamical system to switch. The normal vector-field product for flow switching on the separation boundary is introduced, and the passability condition of flow to the discontinuous boundary is presented. The sliding and grazing conditions to the separation boundary are presented as well. Using mapping structures, periodic motions of such a discontinuous system are predicted, and the local stability and bifurcation analysis are carried out. Numerical illustrations of periodic motions with grazing to the boundary and/or sliding on the boundary are given, and the normal vector fields are illustrated to show the analytical criteria.

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