Gravitational waves from dynamical shape transition of protoneutron stars

2021 ◽  
pp. 2150104
Author(s):  
H. Rodrigues ◽  
J. A. Rosero-Gil ◽  
A. M. Endler ◽  
S. B. Duarte ◽  
M. Chiapparini
Keyword(s):  
Angular Momentum ◽  
Gravitational Waves ◽  
Equilibrium Configuration ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Dynamical Evolution ◽  
Angular Frequency ◽  
Triaxial Ellipsoid ◽  
Shape Transition ◽  
Protoneutron Stars

We describe the dynamical behavior of newborn neutron stars modelled as homogeneous rotating spheroids. The dynamical evolution is triggered by the escape of trapped neutrinos, providing the initial equilibrium configuration. It is shown that for a given set of values of the initial angular momentum, a shape transition to a triaxial ellipsoid configuration occurs. Gravitational waves are then generated by the breaking of the axial symmetry, and some aspects of their observation are discussed. We found a narrow window for both, the initial values of the angular frequency and the eccentricity, able to enable a dynamical shape transition, with their upper bound determined by the Kepler frequency. The energy and angular momentum carried away by the gravitational wave are treated consistently with the solution of the equations of motion of the system.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

2021 ◽  
pp. 107754632199358
Author(s):  
Ali Fasihi ◽  
Majid Shahgholi ◽  
Saeed Ghahremani
Keyword(s):  
Energy Harvester ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

scholarly journals Dynamical Evolution of Rotating Globular Clusters

1996 ◽  
Vol 174 ◽  
pp. 375-376
Author(s):  
P.-Y. Longaretti ◽  
C. Lagoute
Keyword(s):  
Angular Momentum ◽  
Stellar Evolution ◽  
Globular Cluster ◽  
Globular Clusters ◽  
Dynamical Evolution

We have computed simplified globular cluster evolutionary tracks which take into account the effects of internal relaxation, of the cluster rotation, of the galactic tidal field, and, in a cruder way, of stellar evolution and of gravitational shocking. The objectives are first to quantify the influence of rotation in the dynamical evolution of globular clusters; and second, to investigate the evolution of globular cluster angular momentum and flattening (Lagoute and Longaretti 1995a, Longaretti and Lagoute 1995b,c).

scholarly journals Secular Mass Loss from Cataclysmic Variables

1977 ◽  
Vol 42 ◽  
pp. 365-370
Author(s):  
Józef Smak
Keyword(s):  
Mass Transfer ◽  
Angular Momentum ◽  
Chemical Composition ◽  
Mass Loss ◽  
Cataclysmic Variables ◽  
Dynamical Evolution ◽  
Good Insight ◽  
Physical Mechanisms ◽  
Cataclysmic Binaries ◽  
Insight Into

The mass loss from cataclysmic binaries seems an important and worth studying phenomenon for a number of reasons. It is probably enough to mention only two of them:(a) Whenever we can directly observe the ejected material, determine its amount and the rate of mass loss, as well as its chemical composition (this being the case of the expanding envelopes of novae), we are getting a good insight into the basic physical mechanisms responsible for the observed phenomena.(b) The mass loss (together with the mass transfer) and the loss of the orbital angular momentum are related directly to the dynamical evolution of a binary system and - indirectly - to the evolution of its components.

scholarly journals Gravitational waves with orbital angular momentum

2020 ◽  
Vol 80 (4) ◽  
Author(s):  
Pratyusava Baral ◽  
Anarya Ray ◽  
Ratna Koley ◽  
Parthasarathi Majumdar
Keyword(s):  
Angular Momentum ◽  
Gravitational Waves ◽  
Orbital Angular Momentum

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

scholarly journals Angular momentum transport in accretion disks: a hydrodynamical perspective

2019 ◽  
Vol 82 ◽  
pp. 391-413 ◽  
Author(s):  
S. Fromang ◽  
G. Lesur
Keyword(s):  
Angular Momentum ◽  
Accretion Disk ◽  
Accretion Disks ◽  
Dynamical Evolution ◽  
Theoretical Work ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Recent Developments ◽  
The Many ◽  
The Universe

The radial transport of angular momentum in accretion disk is a fundamental process in the universe. It governs the dynamical evolution of accretion disks and has implications for various issues ranging from the formation of planets to the growth of supermassive black holes. While the importance of magnetic fields for this problem has long been demonstrated, the existence of a source of transport solely hydrodynamical in nature has proven more difficult to establish and to quantify. In recent years, a combination of results coming from experiments, theoretical work and numerical simulations has dramatically improved our understanding of hydrodynamically mediated angular momentum transport in accretion disk. Here, based on these recent developments, we review the hydrodynamical processes that might contribute to transporting angular momentum radially in accretion disks and highlight the many questions that are still to be answered.

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

Subharmonic Resonance Cascades in a Class of Coupled Resonators

2011 ◽  
Author(s):  
B. Scott Strachan ◽  
Steven Shaw
Keyword(s):  
High Frequency ◽  
Perturbation Methods ◽  
Equations Of Motion ◽  
Dynamical Behavior ◽  
Coupled Resonators ◽  
Frequency Dividers ◽  
Partial Activation ◽  
A Chain ◽  
Frequency Ratios ◽  
Subharmonic Resonances

We consider a chain of N nonlinear resonators with natural frequency ratios of approximately 2:1 along the chain and weak nonlinear coupling of a form that allows energy to flow between resonators. Specifically, the coupling is such that the response of one resonator parametrically excites the next resonator in the chain, and also creates a resonant backaction on the previous resonator in the chain. This class of systems, which is being proposed for micro-electro-mechanical frequency dividers, is shown to have rich dynamical behavior. Of particular interest is the case when the high frequency end of the chain is resonantly excited, and coupling results in the potential for a cascade of sub-harmonic bifurcations down the chain. When the entire chain is activated, that is, when all N resonators have non-zero amplitudes, if the input frequency on the first resonator is Ω, then the terminal resonator responds with frequency Ω/2N. The details of the activation depend on the strength and frequency of the input, the level of resonator dissipation, and the mistuning in the chain. In this paper we present analytical results, based on perturbation methods, which provide useful predictions about these responses in terms of system and input parameters. Parameter conditions for activation of the entire chain are derived, along with results about other phenomena, such as bistability and partial activation of the chain. We demonstrate the utility of the predictive results by direct comparison with simulations of the equations of motion, and we also present samples of mechanical and electromechanical systems that realize the desired properties. These results will be useful for the design and operation of mechanical frequency dividers based on subharmonic resonances.

AN ACTION PRINCIPLE FOR MAGNETOHYDRODYNAMICS

1963 ◽  
Vol 41 (12) ◽  
pp. 2241-2251 ◽  
Author(s):  
M. G. Calkin
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Magnetic Induction ◽  
Vector Potential ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Action Principle ◽  
Invariance Properties ◽  
Conservation Of Momentum

The equations of motion of an inviscid, infinitely conducting fluid in an electromagnetic field are transformed into a form suitable for an action principle. An action principle from which these equations may be derived is found. The conservation laws follow from invariance properties of the action. The space–time invariances lead to the conservation of momentum, energy, angular momentum, and center of mass, while the gauge invariances lead to conservation of mass, a generalization of the Helmholtz vortex theorem of hydrodyanmics, and the conservation of the volume integrals of A∙B and v∙B, where A is the vector potential, B is the magnetic induction, and v is the fluid velocity.

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