The "third" Integral in the Restricted Three-Body Problem.

1965 ◽  
Vol 142 ◽  
pp. 802 ◽  
Author(s):  
G. Contopoulos
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
The Third ◽  
Three Body

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.

A third order canonical approximation of the general solution of the restricted problem of three bodies in the neighbourhood of L4

1966 ◽  
Vol 25 ◽  
pp. 170-175
Author(s):  
A. Deprit
Keyword(s):  
General Solution ◽  
Restricted Problem ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Order ◽  
The Third ◽  
Transformation Of Variables ◽  
Definition Of ◽  
Three Body

A canonical transformation of variables is introduced in the plane restricted three-body problem which gives the Hamiltonian in the form of a power series with normalized second order terms. Then a generating function is constructed, step by step, that permits the definition of new action and angle variables, such that the Hamiltonian is independent of the angle variables. This procedure has been done explicitly up to the third order terms.

scholarly journals Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 110
Author(s):  
Fabao Gao ◽  
Yongqing Wang
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
The Third ◽  
Velocity Surface ◽  
Solution Point ◽  
Zero Velocity Surface ◽  
Three Body

Against the background of a restricted three-body problem consisting of a supergiant eclipsing binary system, the two primaries are composed of a pair of bright oblate stars whose mass changes with time. The zero-velocity surface and curve of the problem are numerically studied to describe the third body’s motion area, and the corresponding five libration points are obtained. Moreover, the effect of small perturbations, Coriolis and centrifugal forces, radiative pressure, and the oblateness and mass parameters of the two primaries on the third body’s dynamic behavior is discussed through the bifurcation diagram. Furthermore, the second- and third-order approximate analytical periodic solutions around the collinear solution point L3 in two-dimensional plane and three-dimensional spaces are presented by using the Lindstedt-Poincaré perturbation method.

scholarly journals Nonlinear Stability of Oblate Infinitesimal in Elliptic Restricted Three-Body Problem Influenced by the Oblate and Radiating Primaries

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
A. Narayan ◽  
A. Chakraborty ◽  
A. Dewangan
Keyword(s):  
Nonlinear Stability ◽  
Binary Systems ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Order ◽  
Order Resonance ◽  
The Third ◽  
The Stability ◽  
Three Body

This work deals with the nonlinear stability of the elliptical restricted three-body problem with oblate and radiating primaries and the oblate infinitesimal. The stability has been analyzed for the resonance cases around ω1=2ω2 and ω1=3ω2 and also the nonresonance cases. It was observed that the motion of the infinitesimal in this system shows instable behavior when considered in the third order resonance. However, for the fourth order resonance the stability is shown for some mass parameters. The motion in the case of nonresonance was found to be unstable. The problem has been numerically applied to study the movement of the infinitesimal around two binary systems, Luyten-726 and Sirius.

scholarly journals Energy of Sitnikov's restricted three body problem if the primaries are source of radiation and triaxial rigid bodies

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 53-58
Author(s):  
R. R. Thapa
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Equation Of Motion ◽  
Joint Effect ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
The Third ◽  
Three Body

In this paper the joint effect of source of radiation and triaxial rigid body has been studied. The energy of Sitnikov's restricted three body problem when primaries are sources of radiation and energy of Sitnikov's restricted problem of three bodies when primaries are triaxial rigid bodies have been studied to calculate the joint effect. Equation of motion of the third body of infitesimal mass, if primaries are sources of radiation and triaxial rigid bodies,  are calculated.    DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11707BIBECHANA 12 (2015) 53-58

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