scholarly journals A New Formulation of a Hénon–Heiles Potential with Additional Singular Gravitational Terms

2020 ◽  
Vol 30 (13) ◽  
pp. 2050197
Author(s):  
Euaggelos E. Zotos ◽  
Wei Chen ◽  
Juan F. Navarro ◽  
Tareq Saeed
Keyword(s):  
Gravitational Potential ◽  
Test Particle ◽  
Orbital Energy ◽  
Orbital Dynamics ◽  
Transition Parameter ◽  
Different Types ◽  
Starting Conditions ◽  
New Formulation ◽  
Parameter Influence

We examine the orbital dynamics in a new Hénon–Heiles system with an additional gravitational potential, by classifying sets of starting conditions of trajectories. Specifically, we obtain the results on how the total orbital energy along with the transition parameter influence the overall dynamics of the massless test particle, as well as the respective time of escape/collision. By using modern diagrams with color codes we manage to present the different types of basins of the system. We show that the character of the orbits is highly dependent on the energy and the transition parameter.

Orbit Taxonomy in an Electromagnetic Binary System of Two Magnetic Dipoles

2020 ◽  
Vol 30 (05) ◽  
pp. 2030011
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Binary System ◽  
Magnetic Moments ◽  
Large Data ◽  
Large Data Sets ◽  
Orbital Dynamics ◽  
Data Sets ◽  
Jacobi Constant ◽  
Magnetic Dipoles ◽  
Different Types ◽  
Starting Conditions

We elucidate the orbital dynamics of a binary system of two magnetic dipoles, by utilizing the grid classification method. Our target is to unveil how the total energy (expressed through the Jacobi constant), as well as the ratio of the magnetic moments affect the character of the trajectories of the test particle. By integrating numerically large data sets of starting conditions of trajectories in different types of 2D maps, we manage to reveal the basins corresponding to bounded, close encounter and escape motion, along with the respective time scales of the phenomena.

scholarly journals Orbital dynamics in the post-Newtonian planar circular restricted Sun–Jupiter system

2018 ◽  
Vol 27 (04) ◽  
pp. 1850036 ◽  
Author(s):  
Euaggelos E. Zotos ◽  
F. L. Dubeibe
Keyword(s):  
Test Particle ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Orbital Dynamics ◽  
Final States ◽  
Jacobi Constant ◽  
Hill Region ◽  
Large Sets ◽  
Different Types ◽  
Three Body

The theory of the post-Newtonian (PN) planar circular restricted three-body problem is used for numerically investigating the orbital dynamics of a test particle (e.g. a comet, asteroid, meteor or spacecraft) in the planar Sun–Jupiter system with a scattering region around Jupiter. For determining the orbital properties of the test particle, we classify large sets of initial conditions of orbits for several values of the Jacobi constant in all possible Hill region configurations. The initial conditions are classified into three main categories: (i) bounded, (ii) escaping and (iii) collisional. Using the smaller alignment index (SALI) chaos indicator, we further classify bounded orbits into regular, sticky or chaotic. In order to get a spherical view of the dynamics of the system, the grids of the initial conditions of the orbits are defined on different types of two-dimensional planes. We locate the different types of basins and we also relate them with the corresponding spatial distributions of the escape and collision time. Our thorough analysis exposes the high complexity of the orbital dynamics and exhibits an appreciable difference between the final states of the orbits in the classical and PN approaches. Furthermore, our numerical results reveal a strong dependence of the properties of the considered basins with the Jacobi constant, along with a remarkable presence of fractal basin boundaries. Our outcomes are compared with the earlier ones regarding other planetary systems.

The Study on the Influence of Pipe-Soil Interaction on VIV for Different Free Span Types

2017 ◽  
Author(s):  
Chongyao Zhou ◽  
Gang Xu ◽  
Zhiming Huang ◽  
Dagang Zhang ◽  
Naiquan Ye ◽  
...  
Keyword(s):  
Time Domain ◽  
Cross Flow ◽  
Sensitivity Study ◽  
Structural Damping ◽  
Flexible Pipe ◽  
Wake Oscillator Model ◽  
Wake Oscillator ◽  
Different Types ◽  
Main Factors ◽  
Parameter Influence

Subsea pipeline laid on the seabed will experience free span when the lay path is long and seabed is rugged. Hydrodynamic loads caused by the currents around the pipeline can induce oscillations in both cross-flow and in-line directions. This phenomenon is called vortex-induced vibration (VIV) which is the most common case that could induce serious fatigue problems. The pipe-soil interaction is one of the main factors that influence the vibration. In this paper, a study focusing on the effect of pipe-soil interaction on VIV for different types of free span is presented. The Milan wake oscillator is applied to calculate the dynamic response induced by VIV in Orcaflex, and the results are compared with experimental data to identify its validity. A sensitivity study is also performed to study the parameter influence of the Milan wake oscillator model. Four types of free span (including the multiple free spans) are modeled in Orcaflex and time domain VIV analysis is carried out to study the influence of pipe-soil interaction. Comparison among different types of free span is discussed. The influence of structural damping is studied for flexible pipe only because its influence on steel pipe is negligible. The influence of structural damping on flexible pipe is studied by means of a predefined moment-curvature curve. In addition, several cases are studied to investigate the influence of tension on VIV by Milan wake oscillator.

scholarly journals Trajectory around a spherically symmetric non-rotating black hole

2011 ◽  
Vol 89 (6) ◽  
pp. 689-695 ◽  
Author(s):  
Sumanta Chakraborty ◽  
Subenoy Chakraborty
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Gravitational Potential ◽  
Test Particle ◽  
Effective Potential ◽  
Particle Motion ◽  
Spherically Symmetric ◽  
Rotating Black Hole

The trajectory of a test particle or a photon around a general spherical black hole is studied, and bending of the light trajectory is investigated. A pseudo-Newtonian gravitational potential describing the gravitational field of the black hole is determined and is compared with the related effective potential for test particle motion. As an example, results are presented for a Reissner–Nordström black hole.

scholarly journals The Effects of ΛCDM Dark Matter Substructure on the Orbital Evolution of Star Clusters

2021 ◽  
Author(s):  
Nicholas Pavanel ◽  
Jeremy Webb
Keyword(s):  
Dark Matter ◽  
Mass Spectrum ◽  
Test Particle ◽  
Star Clusters ◽  
Orbital Evolution ◽  
Orbital Energy ◽  
Particle Simulations ◽  
Single Mass ◽  
Local Mean ◽  
Particle Velocities

Abstract We present a comprehensive study on how perturbations due to a distribution of ΛCDM dark matter subhalos can lead to star clusters deviating from their orbits. Through a large suite of massless test particle simulations, we find that (1) subhalos with masses less than 108M⊙ negligibly affect test particle orbits, (2) perturbations lead to orbital deviations only in environments with substructure fractions $f_{sub} \ge 1\%$, (3) perturbations from denser subhalos produce larger orbital deviations, and (4) subhalo perturbations that are strong relative to the background tidal field lead to larger orbital deviations. To predict how the variation in test particle orbital energy σe(t) increases with time, we test the applicability of theory derived from single-mass subhalo populations to populations where subhalos have a mass spectrum. We find σe(t) can be predicted for test particle evolution within a mass spectrum of subhalos by assuming subhalos all have masses equal to the mean subhalo mass and by using the local mean subhalo separation to estimate the change in test particle velocities due to subhalo interactions. Furthermore, the orbital distance variation at an orbital distance r can be calculated via $\sigma _r=2.98 \times 10^{-5} \pm 8 \times 10^{-8} (\rm kpc^{-1} km^{-2} s^{2}) \times r \times \sigma _e$ with a dispersion about the line of best fit equalling 0.08 kpc. Finally, we conclude that clusters that orbit within 100 kpc of Milky Way-like galaxies experience a change no greater than $2\%$ in their dissolution times.

scholarly journals Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body

2015 ◽  
Vol 24 (08) ◽  
pp. 1550067 ◽  
Author(s):  
L. Iorio
Keyword(s):  
Test Particle ◽  
Central Body ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Mixed Effects ◽  
Orbital Dynamics ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Zonal Harmonic ◽  
Orbital Configuration

The orbital dynamics of a test particle moving in the nonspherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the Keplerian orbital elements of the test particle arising from the crossing among the first even zonal harmonic J2 of the central body and the post-Newtonian static and stationary components of its gravitational field. We also work out the Newtonian shifts per orbit of order [Formula: see text], and the direct post-Newtonian gravitoelectric effects of order J2c-2 arising from the equations of motion. In the case of both the indirect and direct gravitoelectric J2c-2 shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from Earth's artificial satellites to stars orbiting supermassive black holes. As far as their measurability is concerned, highly elliptical orbital configuration are desirable.

Direct and Inverse Kinematics for Coordinated Motion Tasks of a Two-Manipulator System

1996 ◽  
Vol 118 (4) ◽  
pp. 691-697 ◽  
Author(s):  
P. Chiacchio ◽  
S. Chiaverini ◽  
B. Siciliano
Keyword(s):  
Case Studies ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Coordinated Motion ◽  
Different Types ◽  
End Effectors ◽  
New Formulation ◽  
Direct Kinematics

A new formulation for direct kinematics of a system of two manipulators is presented This allows a straightforward description of general coordinated motion tasks in terms of meaningful absolute and relative variables An effective inverse kinematics algorithm is devised which exploits the above formulation where the task Jacobians are expressed in terms of the Jacobians of the single manipulators The scheme is extended to handle the presence of redundant degrees of freedom in the system Different types of grasp between the end effectors and a commonly held object are treated with minimum reformulation effort. Case studies are developed throughout the paper for a system of two PUMA 560 manipulators which illustrate the capabilities of the scheme.

A New Method for Modeling of Fully Flexible Aircrafts

2011 ◽  
Vol 383-390 ◽  
pp. 2350-2355
Author(s):  
Dong Guo ◽  
Min Xu ◽  
Shi Lu Chen ◽  
Yu Qian
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Structural Model ◽  
Equations Of Motion ◽  
Flight Mechanics ◽  
Lagrangian Mechanics ◽  
Seamless Integration ◽  
Different Types ◽  
New Formulation ◽  
Nonlinear Rigid

The purpose of this study is to produce a modeling capability for integrated flight dynamics of flexible aircraft that can better predict some of the complex behaviors in flight due to multi-physics coupling. Based on the studying of the exiting modeling approaches, the author put forward a new modeling method, and developed a new formulation integrating nonlinear rigid-body flight mechanics and linear aeroelastic dynamics for fully elastic aircrafts using Lagrangian mechanics. The new equations of motion overcome the disadvantages of the exiting methods, and include automatically all six rigid-body degrees of freedom and elastic information, the seamless integration is achieved by using the same reference frame and the same variables to describe the aircraft motions and the forces acting on it, including the aerodynamic forces. The formulation is modular in nature, in the sense that the structural model, the aerodynamic theory, and the controls method can be replaced by any other ones to better suit different types of aircraft.

A New Formulation for Establishing the Lateral Interaction Between Buried Steel Pipeline and Sandy Soil Subjected to Strike-Slip Faulting

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Mohammad Ashrafy ◽  
Mehrzad TahamouliRoudsari ◽  
Mahmood Hosseini
Keyword(s):  
Sandy Soil ◽  
Strike Slip ◽  
Lateral Interaction ◽  
Finite Element Models ◽  
Buried Pipelines ◽  
Steel Pipes ◽  
Different Types ◽  
Extreme Hazards ◽  
Full Scale Tests ◽  
New Formulation

Abstract Buried pipelines are faced with and vulnerable to extreme hazards such as earthquakes, different types of faulting, and landslides. Generally, a buried pipeline is modeled as a beam on a series of springs, which represent the surrounding soil. To determine the specifications of these springs, the equations proposed by ASCE Guideline are usually used. Its accuracy was doubted by some recent studies. In this study, two full-scale tests simulating the effect of strike-slip faulting were initially carried out on 4 and 8-in. diameter steel pipes buried in compacted sandy soil. The displacement of the pipe was recorded directly at any moment, along its length. Then through optimization-based simulations, the specifications of the equivalent springs of the soil were calculated so that the deformation of the pipe along its length would be consistent with the experimental results. Then, based upon verified finite element models, a database of different parameters of buried pipes subjected to strike-slip faulting including the diameters and different burial depths was created. The results showed that the ASCE equations need modification at the condition of strike-slip faulting and so, based on the created database, a new form of the equations of lateral interaction between dense sandy soil and steel pipe in the presence of strike-slip fault was proposed.

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