scholarly journals On the Behavior of the Generalized Alignment Index (GALI) Method for Regular Motion in Multidimensional Hamiltonian Systems

2020 ◽  
Vol 23 (2) ◽  
pp. 153-164
Author(s):  
H. T. Moges ◽  
Th. Manos ◽  
Ch. Skokos
Keyword(s):  
Numerical Simulations ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Regular Orbit ◽  
Initial Deviation ◽  
Regular Motion ◽  
Fixed Energy ◽  
Stability Island ◽  
Stable Periodic ◽  
The Stability

We investigate the behavior of the Generalized Alignment Index of order k (GALIk ) for regular orbits of multidimensional Hamiltonian systems. The GALIk is an efficient chaos indicator, which asymptotically attains positive values for regular motion when 2≤k ≤N, with N being the dimension (D) of the torus on which the motion occurs. By considering several regular orbits in the neighborhood of two typical simple, stable periodic orbits of the Fermi-Pasta-Ulam-Tsingou (FPUT) β model for various values of the system's degrees of freedom, we show that the asymptotic GALIk values decrease when the order k of the index increases and when the orbit's energy approaches the periodic orbit's destabilization energy where the stability island vanishes, while they increase when the considered regular orbit moves further away from the periodic one for a fixed energy. In addition, by performing extensive numerical simulations we show that the behavior of the index does not depend on the choice of the initial deviation vectors needed for its evaluation.

The New Approach to Analysis of Hamiltonian Systems

2008 ◽  
Author(s):  
N. A. Magnitskii
Keyword(s):  
Nonlinear Systems ◽  
Numerical Simulations ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Kam Theory ◽  
Dissipative System ◽  
Unperturbed System ◽  
Two Dimensional ◽  
New Approach ◽  
Transition To Chaos

It is shown in the present paper, on the basis of numerical simulations, that in some Hamiltonian systems with two degrees of freedom the transition to chaos takes place not through the destruction of two-dimensional tori of the unperturbed system in accordance with the Kolmogorov-Arnold-Moser (KAM) theory but, on the contrary, through the generation of complicated two-dimensional tori around cycles of the approximating expanded nonlinear dissipative system and through an infinite cascades of bifurcations of generation of new cycles and singular trajectories in accordance with the universal Feigenbaum-Sharkovskii-Magnitskii (FSM) theory developed initially for dissipative nonlinear systems.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Fast-Scale Instability and Stabilization by Adaptive Slope Compensation of a PV-Fed Differential Boost Inverter

2021 ◽  
Vol 11 (5) ◽  
pp. 2106
Author(s):  
Abdelali El Aroudi ◽  
Mohamed Debbat ◽  
Mohammed Al-Numay ◽  
Abdelmajid Abouloiafa
Keyword(s):  
Numerical Simulations ◽  
Full Range ◽  
Weather Conditions ◽  
Current Loop ◽  
Point Tracking ◽  
Bifurcation Phenomena ◽  
Slope Compensation ◽  
Power Point ◽  
The Stability ◽  
Detailed Circuit

Numerical simulations reveal that a single-stage differential boost AC module supplied from a PV module under an Maximum Power Point Tracking (MPPT) control at the input DC port and with current synchronization at the AC grid port might exhibit bifurcation phenomena under some weather conditions leading to subharmonic oscillation at the fast-switching scale. This paper will use discrete-time approach to characterize such behavior and to identify the onset of fast-scale instability. Slope compensation is used in the inner current loop to improve the stability of the system. The compensation slope values needed to guarantee stability for the full range of operating duty cycle and leading to an optimal deadbeat response are determined. The validity of the followed procedures is finally validated by a numerical simulations performed on a detailed circuit-level switched model of the AC module.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

scholarly journals Earth-size planet formation in the habitable zone of circumbinary stars

2020 ◽  
Vol 494 (1) ◽  
pp. 1045-1057 ◽  
Author(s):  
G O Barbosa ◽  
O C Winter ◽  
A Amarante ◽  
A Izidoro ◽  
R C Domingos ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Planet Formation ◽  
Terrestrial Planet ◽  
Close Binary ◽  
Habitable Zone ◽  
Density Profiles ◽  
Habitable Planets ◽  
Habitable Zones ◽  
Test Particles ◽  
The Stability

ABSTRACT This work investigates the possibility of close binary (CB) star systems having Earth-size planets within their habitable zones (HZs). First, we selected all known CB systems with confirmed planets (totaling 22 systems) to calculate the boundaries of their respective HZs. However, only eight systems had all the data necessary for the computation of HZ. Then, we numerically explored the stability within HZs for each one of the eight systems using test particles. From the results, we selected five systems that have stable regions inside HZs, namely Kepler-34,35,38,413, and 453. For these five cases of systems with stable regions in HZ, we perform a series of numerical simulations for planet formation considering discs composed of planetary embryos and planetesimals, with two distinct density profiles, in addition to the stars and host planets of each system. We found that in the case of the Kepler-34 and 453 systems, no Earth-size planet is formed within HZs. Although planets with Earth-like masses were formed in Kepler-453, they were outside HZ. In contrast, for the Kepler-35 and 38 systems, the results showed that potentially habitable planets are formed in all simulations. In the case of the Kepler-413system, in just one simulation, a terrestrial planet was formed within HZ.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

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