Topology of Jacobi levels with no zero velocity curves in the restricted three-body problem

1987 ◽  
Vol 38 (1) ◽  
pp. 10-20
Author(s):  
Ernesto A. Lacomba ◽  
Carles Sim�
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Zero Velocity Curves ◽  
Three Body

scholarly journals Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

2019 ◽  
Vol 488 (2) ◽  
pp. 1894-1907
Author(s):  
Saleem Yousuf ◽  
Ram Kishor
Keyword(s):  
Linear Stability ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Zero Velocity Curves ◽  
Three Body

ABSTRACT The important aspects of a dynamical system are its stability and the factors that affect its stability. In this paper, we present an analysis of the effects of the albedo and the disc on the zero velocity curves, the existence of equilibrium points and their linear stability in a generalized restricted three-body problem (RTBP). The proposed problem consists of the motion of an infinitesimal mass under the gravitational field of a radiating-oblate primary, an oblate secondary and a disc that is rotating about the common centre of mass of the system. Significant effects of the albedo and the disc are observed on the zero velocity curves, on the positions of equilibrium points and on the stability region. A linear stability analysis of collinear equilibrium points L1, 2, 3 is performed with respect to the mass parameter μ and albedo parameter QA of the secondary, separately. It is found that L1, 2, 3 are unstable in both cases. However, the non-collinear equilibrium points L4, 5 are stable in a finite range of mass ratio μ. After analysing the individual as well as combined effects of the radiation pressure force of the primary, the albedo force of the secondary, the oblateness of both the primary and secondary and the disc, it is found that these perturbations play a significant role in the design of the trajectories in the vicinity of equilibrium points and in the analysis of their stability property. In the future, the results obtained will improve existing results and will help in the analysis of different space missions. These results are limited to the regular symmetric disc and radiation pressure, which can be extended later.

scholarly journals Boundaries for the Equipotential Curves in the Elliptic Restricted Three-Body Problem

1983 ◽  
Vol 74 ◽  
pp. 317-323
Author(s):  
Magda Delva
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Time Intervals ◽  
The Third ◽  
Circular Problem ◽  
Long Time ◽  
Zero Velocity Curves ◽  
Three Body

AbstractIn the elliptic restricted three body problem an invariant relation between the velocity square of the third body and its potential is studied for long time intervals as well as for different values of the eccentricity. This relation, corresponding to the Jacobian integral in the circular problem, contains an integral expression which can be estimated if one assumes that the potential of the third body remains finite. Then upper and lower boundaries for the equipotential curves can be derived. For large eccentricities or long time intervals the upper boundary increases, while the lower decreases, which can be interpreted as shrinking respectively growing zero velocity curves around the primaries.

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

scholarly journals Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
A. Narayan ◽  
Amit Shrivastava
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Zero Velocity ◽  
Simulation Techniques ◽  
The Stability ◽  
Three Body

The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.

BIFURCATIONS IN THE TOPOLOGY OF ZERO-VELOCITY SURFACES IN THE PHOTO-GRAVITATIONAL COPENHAGEN PROBLEM

2009 ◽  
Vol 19 (03) ◽  
pp. 1097-1111 ◽  
Author(s):  
T. J. KALVOURIDIS
Keyword(s):  
Body Problem ◽  
Small Body ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Radiation Sources ◽  
Trapping Regions ◽  
Zero Velocity Surfaces ◽  
Three Body

We study the evolution of the regions where three-dimensional motions of a small body are allowed in the Copenhagen case of the restricted three-body problem where one or both primaries, are radiation sources. We discuss the bifurcations in the topology of the zero-velocity surfaces, as well as in the trapping regions of the particle motion for various cases.

scholarly journals Dynamics in the circular restricted three body problem with perturbations

2017 ◽  
Vol 5 (1) ◽  
pp. 19 ◽  
Author(s):  
Abdullah Abduljabar Ansari ◽  
Mehtab Alam
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equations Of Motion ◽  
Solar Radiation Pressure ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity Curves ◽  
Three Body

This paper presents the dynamics in the restricted problem with perturbations i.e. the circular restricted three body problem by considering one of the primaries as oblate and other one having the solar radiation pressure and all the masses are variable (primaries and infinitesimal body). For finding the autonomized equations of motion, we have used the Meshcherskii transformation. We have drawn the libration points, the time series, the zero velocity curves and Poincare surface of sections for the different values of the oblateness and solar radiation pressure. Finally, we have examined the stability and found that all the libration points are unstable.

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