Numerical study of periodic orbit properties in a dynamical system with three degrees of freedom

1982 ◽  
Vol 28 (3) ◽  
pp. 319-343 ◽  
Author(s):  
P. Magnenat
Keyword(s):  
Dynamical System ◽  
Periodic Orbit ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Three Degrees Of Freedom

Evaluation of 3-D Computational Model of Oscillating Water Column Converter with Constructal Design with Three Degrees of Freedom and Limited Chimney Height

2021 ◽  
Vol 407 ◽  
pp. 128-137
Author(s):  
Vinícius Bloss ◽  
Camila Fernandes Cardozo ◽  
Flávia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha
Keyword(s):  
Water Column ◽  
Wave Energy ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Mechanical Energy ◽  
Ocean Waves ◽  
Response Surfaces ◽  
Oscillating Water Column ◽  
Promising Source ◽  
Three Degrees Of Freedom

Theoretically, ocean waves contain enough mechanical energy to supply the entire world’s demand and, as of late, are seen as a promising source of renewable energy. To this end, several different technologies of Wave Energy Converters (WEC) have been developed such as Oscillating Water Column (OWC) devices. OWCs are characterized by a chamber in which water oscillates inside and out in a movement similar to that of a piston. This movement directs air to a chimney where a turbine is attached to convert mechanical energy. The analysis conducted was based on the Constructive Design Method, in which a numerical study was carried out to obtain the geometric configuration that maximized the conversion of wave energy into mechanical energy. Three degrees of freedom were used: the ratio of height to length of the hydropneumatic chamber (H1/L), the ratio of the height of the chimney to its diameter (H2/d) and the ratio of the width of the hydropneumatic chamber to the width of the wave tank (W/Z). A Design of Experiments (DoE) technique coupled with Central Composite Design (CCD) allowed the simulation of different combinations of degrees of freedom. This allowed the construction of Response Surfaces and correlations for the efficiency of the system depending on the degrees of freedom (width and height of the chamber), as well as the optimization of the system based on the Response Surfaces.

scholarly journals Carter's constant and superintegrability

2018 ◽  
Vol 27 (07) ◽  
pp. 1850066
Author(s):  
Payel Mukhopadhyay ◽  
K. Rajesh Nayak
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Superintegrable System ◽  
Simple Observation ◽  
Superintegrable Systems ◽  
Axisymmetric Spacetime ◽  
Three Degrees Of Freedom

Carter's constant is a nontrivial conserved quantity of motion of a particle moving in stationary axisymmetric spacetime. In the version of the theorem originally given by Carter, due to the presence of two Killing vectors, the system effectively has two degrees of freedom. We propose an extension to the first version of Carter's theorem to a system having three degrees of freedom to find two functionally independent Carter-like integrals of motion. We further generalize the theorem to a dynamical system with [Formula: see text] degrees of freedom. We further study the implications of Carter's constant to superintegrability and present a different approach to probe a superintegrable system. Our formalism gives another viewpoint to a superintegrable system using the simple observation of separable Hamiltonian according to Carter's criteria. We then give some examples by constructing some two-dimensional superintegrable systems based on this idea and also show that all three-dimensional simple classical superintegrable potentials are also Carter separable.

The Vibrations of the Engine with Neo-Hookean Suspension

2013 ◽  
Vol 430 ◽  
pp. 53-59 ◽  
Author(s):  
Nicolae Doru Stanescu ◽  
Dinel Popa
Keyword(s):  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Harmonic Force ◽  
Small Oscillations ◽  
Excited System ◽  
Beat Phenomenon ◽  
Three Degrees Of Freedom

Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

scholarly journals On the Number of Isolating Integrals in Systems with Three Degrees of Freedom

1971 ◽  
Vol 10 ◽  
pp. 110-117
Author(s):  
Claude Froeschle
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Model Problem ◽  
Energy Integral ◽  
Dimensional Mapping ◽  
Three Degrees Of Freedom

AbstractDynamical systems with three degrees of freedom can be reduced to the study of a four-dimensional mapping. We consider here, as a model problem, the mapping given by the following equations: We have found that as soon as b ≠ 0, i.e. even for a very weak coupling, a dynamical system with three degrees of freedom has in general either two or zero isolating integrals (besides the usual energy integral).

scholarly journals Modeling and Stability Analysis for the Vibrating Motion of Three Degrees-of-Freedom Dynamical System Near Resonance

2021 ◽  
Vol 11 (24) ◽  
pp. 11943
Author(s):  
Wael S. Amer ◽  
Tarek S. Amer ◽  
Seham S. Hassan
Keyword(s):  
Dynamical System ◽  
Degrees Of Freedom ◽  
Multiple Scales ◽  
Positive Influence ◽  
Theoretical Physics ◽  
Physical Parameters ◽  
The Third ◽  
Near Resonance ◽  
The Stability ◽  
Three Degrees Of Freedom

The focus of this article is on the investigation of a dynamical system consisting of a linear damped transverse tuned-absorber connected with a non-linear damped-spring-pendulum, in which its hanged point moves in an elliptic path. The regulating system of motion is derived using Lagrange’s equations, which is then solved analytically up to the third approximation employing the approach of multiple scales (AMS). The emerging cases of resonance are categorized according to the solvability requirements wherein the modulation equations (ME) have been found. The stability areas and the instability ones are examined utilizing the Routh–Hurwitz criteria (RHC) and analyzed in line with the solutions at the steady state. The obtained results, resonance responses, and stability regions are addressed and graphically depicted to explore the positive influence of the various inputs of the physical parameters on the rheological behavior of the inspected system. The significance of the present work stems from its numerous applications in theoretical physics and engineering.

scholarly journals The Generalization of the Periodic Orbit Dividing Surface in Hamiltonian Systems with Three or More Degrees of Freedom – I

2021 ◽  
Vol 31 (10) ◽  
pp. 2130028
Author(s):  
Matthaios Katsanikas ◽  
Stephen Wiggins
Keyword(s):  
Periodic Orbit ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Dividing Surface ◽  
Dimensional Object ◽  
Dynamical Information ◽  
Surface Construction ◽  
Three Degrees Of Freedom ◽  
Normally Hyperbolic Invariant Manifolds

We present a method that generalizes the periodic orbit dividing surface construction for Hamiltonian systems with three or more degrees of freedom. We construct a torus using as a basis a periodic orbit and we extend this to a ([Formula: see text])-dimensional object in the ([Formula: see text])-dimensional energy surface. We present our methods using benchmark examples for two and three degrees of freedom Hamiltonian systems to illustrate the corresponding algorithm for this construction. Towards this end, we use the normal form quadratic Hamiltonian system with two and three degrees of freedom. We found that the periodic orbit dividing surface can provide us the same dynamical information as the dividing surface constructed using normally hyperbolic invariant manifolds. This is significant because, in general, computations of normally hyperbolic invariant manifolds are very difficult in Hamiltonian systems with three or more degrees of freedom. However, our method avoids this computation and the only information that we need is the location of one periodic orbit.

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