scholarly journals Numerical aspects of two coupled harmonic oscillators

2020 ◽  
Vol 28 (1) ◽  
pp. 5-15
Author(s):  
Jihad Asad ◽  
Olivia Florea
Keyword(s):  
Linear System ◽  
Analytic Solution ◽  
Initial Conditions ◽  
Harmonic Oscillators ◽  
Lagrange Equations ◽  
Coupled Harmonic Oscillators

AbstractIn this study an interesting symmetric linear system is considered. As a first step we obtain the Lagrangian of the system. Secondly, we derive the classical Euler- Lagrange equations of the system. Finally, numerical and analytic solution for these equations have been presented for some chosen initial conditions.

scholarly journals Heat flow in a harmonic chain due to an impulse disturbance

2020 ◽  
Vol 20 (1) ◽  
pp. 52-57
Author(s):  
A.I. Gudimenko ◽  
Keyword(s):  
Initial Conditions ◽  
Local Heat ◽  
Harmonic Oscillators ◽  
Heat Current ◽  
Maxwell Distribution ◽  
State Correlation ◽  
One Dimensional ◽  
Coupled Harmonic Oscillators ◽  
Harmonic Chain ◽  
Analytical Expressions

The heat motion in a one-dimensional semi-infinite chain of coupled harmonic oscillators is studied for the Maxwell distribution of initial velocities and zero initial displacements of the chain particles. It is believed that such initial conditions are achieved by an impulse heating of the sample. Exact analytical expressions for the state correlation functions, local temperature, and local heat current of the chain are obtained.

scholarly journals Extended and Unscented Kalman Filtering Applied to a Flexible-Joint Robot with Jerk Estimation

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammad Ali Badamchizadeh ◽  
Iraj Hassanzadeh ◽  
Mehdi Abedinpour Fallah
Keyword(s):  
Initial Conditions ◽  
Covariance Matrices ◽  
Flexible Joints ◽  
Velocity Measurements ◽  
Lagrange Equations ◽  
Robust Nonlinear Control ◽  
Flexible Joint ◽  
Flexible Joint Robots ◽  
Simulation Results

Robust nonlinear control of flexible-joint robots requires that the link position, velocity, acceleration, and jerk be available. In this paper, we derive the dynamic model of a nonlinear flexible-joint robot based on the governing Euler-Lagrange equations and propose extended and unscented Kalman filters to estimate the link acceleration and jerk from position and velocity measurements. Both observers are designed for the same model and run with the same covariance matrices under the same initial conditions. A five-bar linkage robot with revolute flexible joints is considered as a case study. Simulation results verify the effectiveness of the proposed filters.

Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders

2013 ◽  
Vol 7 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Housheng Su ◽  
Hongwei Wang ◽  
Michael Z. Q. Chen ◽  
Najl V. Valeyev ◽  
Xiaofan Wang
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Multiple Leaders

scholarly journals Group synchronization of diffusively coupled harmonic oscillators

Kybernetika ◽  
2016 ◽  
pp. 629-647 ◽  
Author(s):  
Liyun Zhao ◽  
Jun Liu ◽  
Lan Xiang ◽  
Jin Zhou
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Group Synchronization
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