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 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

Displacement of the Lagrange Equilibrium Points in the Restricted Three Body Problem With Rigid Body Satellite

1978 ◽  
Vol 41 ◽  
pp. 305-314
Author(s):  
W.J. Robinson
Keyword(s):  
Rigid Body ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractIn the restricted problem of three point masses, the positions of the equilibrium points are well known and are tabulated. When the satellite is a rigid body, these values no longer correspond to the equilibrium points. This paper seeks to determine the magnitudes of the discrepancies.

scholarly journals Quasi-Lntegrals of the Plane Restricted Three-Body Problem

1993 ◽  
Vol 132 ◽  
pp. 309-319
Author(s):  
E.M. Nezhinskij
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Test Body ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Integral ◽  
Three Body ◽  
Two Bodies

AbstractThe paper is concerned with studying the domain of possible motion and a field of the test body velocities in the plane restricted problem of three bodies. The study is based on existence of a quasi-integral of areas (similar to an integral of areas in the problem of two bodies) as well as on the Jacobi integral. The method of constructing the quasi-integrals is a standard one (see, for example, [1],[2].

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.

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

Special cases of the restricted problem of three bodies

1966 ◽  
Vol 25 ◽  
pp. 187-193 ◽  
Author(s):  
J. Schubart
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Disturbing Function ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Long Period ◽  
Period Effects ◽  
Special Cases ◽  
Three Body

The long-period effects in nearly commensurable cases of the restricted three-body problem were studied according to the ideas of Poincaré. The secular and critical terms of the disturbing function were isolated by a numerical averaging process, by use of an IBM 7094 computer.

scholarly journals The Libration Points and Hill Surfaces in the Restricted Problem of Three Variable-Mass Bodies

1993 ◽  
Vol 132 ◽  
pp. 277-288 ◽  
Author(s):  
A.A. Bekov
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Stellar Systems ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Time Dependencies ◽  
Three Body

The paper deals with the study of the arising and disappearence of collinear (Eulerian) L1, L2, L3, triangular (Lagrangian) L4, L5, coplanar L6, L7, ring L0 and infinitely distant L±∞ solutions in a restricted problem of three variable-mass bodies for different time dependencies of main bodies masses and for some additional conditions imposed on the systems parameters. In this case it is assumed that the motion of variable-mass main bodies is determined by the Gylden-Mestschersky problem. The Bill surfaces in the restricted three-body problem where main bodies masses variate isotropically according to the Mestschersky law are studied. Certain possibilities of applying the results of investigations to nonstationary double stellar systems are discussed.

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