scholarly journals Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

2011 ◽  
Vol 18 (1-2) ◽  
pp. 365-375 ◽  
Author(s):  
Qingkai Han ◽  
Xueyan Zhao ◽  
Xingxiu Li ◽  
Bangchun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Domain ◽  
Shooting Method ◽  
Viscous Friction ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Amplitude Spectra ◽  
Set Up ◽  
Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

Experimental and Simulation of a Cam and Translated Roller Follower Over a Range of Speeds

2016 ◽  
Author(s):  
Louay S. Yousuf ◽  
Dan B. Marghitu
Keyword(s):  
Experimental Data ◽  
Lyapunov Exponent ◽  
High Resolution ◽  
Lyapunov Exponents ◽  
Planar Motion ◽  
Largest Lyapunov Exponents ◽  
Set Up ◽  
The Impact ◽  
Impact With Friction

In this study a cam and follower mechanism is analyzed. There is a clearance between the follower and the guide. The mechanism is analyzed using SolidWorks simulations taking into account the impact and the friction between the roller follower and the guide. Four different follower guide’s clearances have been used in the simulations like 0.5, 1, 1.5, and 2 mm. An experimental set up is developed to capture the general planar motion of the cam and follower. The measures of the cam and the follower positions are obtained through high-resolution optical encoders (markers). The effect of follower guide’s clearance is investigated for different cam rotational speeds such as 100, 200, 300, 400, 500, 600, 700 and 800 R.P.M. Impact with friction is considered in our study to calculate the Lyapunov exponent. The largest Lyapunov exponents for the simulated and experimental data are analyzed and selected.

scholarly journals First Gaia dynamical model of the Milky Way disc with six phase space coordinates: a test for galaxy dynamics

2020 ◽  
Vol 494 (4) ◽  
pp. 6001-6011 ◽  
Author(s):  
Maria Selina Nitschai ◽  
Michele Cappellari ◽  
Nadine Neumayer
Keyword(s):  
Phase Space ◽  
Milky Way ◽  
Dynamical Model ◽  
Total Density ◽  
Dark Halo ◽  
Stellar Kinematics ◽  
Galaxy Dynamics ◽  
Dispersion Tensor ◽  
External Galaxies ◽  
Solar Position

ABSTRACT We construct the first comprehensive dynamical model for the high-quality subset of stellar kinematics of the Milky Way disc, with full 6D phase-space coordinates, provided by the Gaia Data Release 2. We adopt an axisymmetric approximation and use an updated Jeans Anisotropic Modelling (JAM) method, which allows for a generic shape and radial orientation of the velocity ellipsoid, as indicated by the Gaia data, to fit the mean velocities and all three components of the intrinsic velocity dispersion tensor. The Milky Way is the first galaxy for which all intrinsic phase space coordinates are available, and the kinematics are superior to the best integral-field kinematics of external galaxies. This situation removes the long-standing dynamical degeneracies and makes this the first dynamical model highly overconstrained by the kinematics. For these reasons, our ability to fit the data provides a fundamental test for both galaxy dynamics and the mass distribution in the Milky Way disc. We tightly constrain the volume average total density logarithmic slope, in the radial range 3.6–12 kpc, to be αtot = −2.149 ± 0.055 and find that the dark halo slope must be significantly steeper than αDM = −1 (NFW). The dark halo shape is close to spherical and its density is ρDM(R⊙) = 0.0115 ± 0.0020 M⊙ pc−3 (0.437 ± 0.076 GeV cm−3), in agreement with previous estimates. The circular velocity at the solar position vcirc(R⊙) = 236.5 ± 3.1 km s−1 (including systematics) and its gently declining radial trends are also consistent with recent determinations.

Properties of cross-well chaos in an impacting system

1994 ◽  
Vol 347 (1683) ◽  
pp. 391-410 ◽  
Keyword(s):  
Phase Space ◽  
Poincaré Map ◽  
Poincare Map ◽  
Chaotic Motions ◽  
Higher Harmonics ◽  
Potential Wells ◽  
Duffing's Equation ◽  
Duffing’S Equation ◽  
Phase Space Transport ◽  
Basin Boundaries

In this paper we present results on chaotic motions in a periodically forced impacting system which is analogous to the version of Duffing’s equation with negative linear stiffness. Our focus is on the prediction and manipulation of the cross-well chaos in this system. First, we develop a general method for determining parameter conditions under which homoclinic tangles exist, which is a necessary condition for cross-well chaos to occur. We then show how one may manipulate higher harmonics of the excitation in order to affect the range of excitation amplitudes over which fractal basin boundaries between the two potential wells exist. We also experimentally investigate the threshold for cross-well chaos and compare the results with the theoretical results. Second, we consider the rate at which the system crosses from one potential well to the other during a chaotic motion and relate this to the rate of phase space flux in a Poincare map defined in terms of impact parameters. Results from simulations and experiments are compared with a simple theory based on phase space transport ideas, and a predictive scheme for estimating the rate of crossings under different parameter conditions is presented. The main conclusions of the paper are the following: (1) higher harmonics can be used with some effectiveness to extend the region of deterministic basin boundaries (in terms of the amplitude of excitation) but their effect on steady-state chaos is unreliable; (2) the rate at which the system executes cross-well excursions is related in a direct manner to the rate of phase space flux of the system as measured by the area of a turnstile lobe in the Poincare map. These results indicate some of the ways in which the chaotic properties of this system, and possibly others such as Duffing’s equation, are influenced by various system and input parameters. The main tools of analysis are a special version of Melnikov’s method, adapted for this piecewise-linear system, and ideas of phase space transport.

Phase‐space footprints of truncated periodicity: Time domain wave‐oriented data processing

1994 ◽  
Vol 95 (5) ◽  
pp. 2903-2903
Author(s):  
L. Carin ◽  
L. B. Felsen ◽  
T.‐T. Hsu ◽  
D. Kralj
Keyword(s):  
Phase Space ◽  
Data Processing ◽  
Time Domain

DYNAMICAL ASPECTS OF INTERACTION NETWORKS

2005 ◽  
Vol 15 (11) ◽  
pp. 3467-3480 ◽  
Author(s):  
G. NICOLIS ◽  
A. GARCÍA CANTÚ ◽  
C. NICOLIS
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Lyapunov Exponents ◽  
Network Theory ◽  
Finite Size ◽  
Interaction Networks ◽  
Deterministic Systems ◽  
Connectivity Patterns ◽  
Probabilistic Process

A connection between dynamical systems and network theory is outlined based on a mapping of the dynamics into a discrete probabilistic process, whereby the phase space is partitioned into finite size cells. It is found that the connectivity patterns of networks generated by deterministic systems can be related to the indicators of the dynamics such as local Lyapunov exponents. The procedure is extended to networks generated by stochastic processes.

scholarly journals Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

2003 ◽  
Vol 10 (1) ◽  
pp. 37-50 ◽  
Author(s):  
L.F.P. Franca ◽  
M.A. Savi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Time Series ◽  
Lyapunov Exponents ◽  
Random Noise ◽  
Noise Sensitivity ◽  
Correct Identification ◽  
Chaotic Motions ◽  
Nonlinear Pendulum

This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

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