On Permanent Rotations of a System of Two Coupled Gyrostats in a Central Newtonian Force Field

2015 ◽  
Author(s):  
Dmitriy Chebanov ◽  
Jose A. Salas
Keyword(s):  
Force Field ◽  
Vertical Axis ◽  
Many Body ◽  
Newtonian Force ◽  
Body Dynamics ◽  
A Chain ◽  
The Many ◽  
The One ◽  
Permanent Rotations ◽  
Newtonian Force Field

This paper studies the problem of the motion of a chain of two gyrostats coupled by an ideal spherical joint. The chain moves about a fixed point in a central Newtonian force field. Under the assumption that the gyrostatic moment of each gyrostat is constant relative to its carrier, the paper establishes and analyzes the conditions for existence of the chain’s permanent rotations about a vertical axis. For a case when each gyrostat has the mass distribution analogous to the one of a Lagrange gyroscope, the paper derives and analyzes the necessary conditions for stability of the permanent rotations. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.

On the Stability of Permanent Rotations of a Chain of Two Lagrange Gyrostats in a Central Gravitational Field

2016 ◽  
Author(s):  
Dmitriy Chebanov ◽  
Jose A. Salas
Keyword(s):  
Gravitational Field ◽  
Sufficient Conditions ◽  
Vertical Axis ◽  
Many Body ◽  
A Chain ◽  
The Stability ◽  
The Many ◽  
The One ◽  
Permanent Rotations ◽  
Central Gravitational Field

In this paper we study the problem of the motion of a two-gyrostat chain about a fixed point in a central gravitational field. We assume that the mass distribution of each gyrostat is analogous to the one of a Lagrange top, the gyrostatic moment of each gyrostat is constant relative to its carrier, and the center of a spherical joint connecting the gyrostats belongs to their dynamic symmetry axes. We establish and analyze sufficient conditions for stability of the chain’s permanent rotations about a vertical axis. Our findings extend corresponding results in the dynamics of a single gyrostat to a case of the two-gyrostat chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.

Precessional Motions of a Chain of Coupled Gyrostats in a Central Newtonian Force Field

2014 ◽  
Author(s):  
Dmitriy Chebanov
Keyword(s):  
Fixed Point ◽  
Force Field ◽  
Multibody Dynamics ◽  
Classical Model ◽  
Newtonian Force ◽  
A Chain ◽  
Modern Analytical ◽  
Newtonian Force Field

This paper studies the problem of the motion of a classical model of modern analytical multibody dynamics — a chain of gyrostats coupled by ideal spherical joints. The chain moves about a fixed point in a central Newtonian force field. The paper develops the equations of chain’s motion and then establishes and analyzes the conditions for existence of some classes of precessional motions of the chain, under the assumption that the barycenter of each gyrostat is located on the line connecting the points where it is attached to other gyrostats. The findings of the paper extend corresponding results in the dynamics of a single gyrostat to a case of the multibody chain as well as generalize some of the known properties of precessional motions in the dynamics of many bodies.

scholarly journals The Stability of Certain Motion of a Charged Gyrostat in Newtonian Force Field

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
A. A. Elmandouh ◽  
Fatimah H. Alsaad
Keyword(s):  
Force Field ◽  
Equations Of Motion ◽  
Sufficient Conditions ◽  
Newtonian Force ◽  
Hamilton System ◽  
Principal Axes ◽  
Axis Parallel ◽  
The Stability ◽  
Permanent Rotations ◽  
Newtonian Force Field

This work aims to study the stability of certain motions of a rigid body rotating about its fixed point and carrying a rotor that rotates with constant angular velocity about an axis parallel to one of the principal axes. This motion is presumed to take place due to the combined influence of the magnetic field and the Newtonian force field. The equations of motion are deduced, and moreover, they are expressed as a Lie–Poisson Hamilton system. The permanent rotations are calculated and interpreted mechanically. The sufficient conditions for instability are presented employing the linear approximation method. The energy-Casimir method is applied to gain sufficient conditions for stability. The regions of linear stability and Lyapunov stability are illustrated graphically for certain values of the parameters.

scholarly journals Entangling Lattice-Trapped Bosons with a Free Impurity: Impact on Stationary and Dynamical Properties

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 290
Author(s):  
Maxim Pyzh ◽  
Kevin Keiler ◽  
Simeon I. Mistakidis ◽  
Peter Schmelcher
Keyword(s):  
Structural Changes ◽  
Many Body ◽  
Wide Range ◽  
Entropy Measures ◽  
Particle Level ◽  
The Many ◽  
The One ◽  
Tunneling Dynamics ◽  
The Individual ◽  
Trapped Bosons

We address the interplay of few lattice trapped bosons interacting with an impurity atom in a box potential. For the ground state, a classification is performed based on the fidelity allowing to quantify the susceptibility of the composite system to structural changes due to the intercomponent coupling. We analyze the overall response at the many-body level and contrast it to the single-particle level. By inspecting different entropy measures we capture the degree of entanglement and intraspecies correlations for a wide range of intra- and intercomponent interactions and lattice depths. We also spatially resolve the imprint of the entanglement on the one- and two-body density distributions showcasing that it accelerates the phase separation process or acts against spatial localization for repulsive and attractive intercomponent interactions, respectively. The many-body effects on the tunneling dynamics of the individual components, resulting from their counterflow, are also discussed. The tunneling period of the impurity is very sensitive to the value of the impurity-medium coupling due to its effective dressing by the few-body medium. Our work provides implications for engineering localized structures in correlated impurity settings using species selective optical potentials.

Many-body Green functions in nuclear physics

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740025 ◽  
Author(s):  
J. Speth ◽  
N. Lyutorovich
Keyword(s):  
Nuclear Physics ◽  
Green Functions ◽  
Many Body ◽  
General Applicability ◽  
Pair Correlations ◽  
Self Consistent ◽  
The Many ◽  
The One ◽  
General Relations ◽  
Three Body

Many-body Green functions are a very efficient formulation of the many-body problem. We review the application of this method to nuclear physics problems. The formulas which can be derived are of general applicability, e.g., in self-consistent as well as in nonself-consistent calculations. With the help of the Landau renormalization, one obtains relations without any approximations. This allows to apply conservation laws which lead to important general relations. We investigate the one-body and two-body Green functions as well as the three-body Green function and discuss their connection to nuclear observables. The generalization to systems with pair correlations are also presented. Numerical examples are compared with experimental data.

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