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

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 Comparison of Energy of the Sitnikov's Restricted three Body Problem if the Primaries are Sources of Radiation, Oblate Spheroids and Triaxial Rigid Bodies

2015 ◽  
Vol 20 (1) ◽  
pp. 59-63
Author(s):  
Raju Ram Thapa
Keyword(s):  
Body Problem ◽  
Science And Technology ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Oblate Spheroids ◽  
Three Body

The paper establishes the energy of Stinikov's restricted three body problem when the primaries are source of radiations, oblate spheroids and triaxial rigid bodies. The effect of source of radiations, oblate spheroids and triaxial rigid bodies with their corresponding equation of motions has been studied. The equation of motions of third body is used to calculate the required energy of the infinitesimal body.Journal of Institute of Science and Technology, 2015, 20(1): 59-63

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 Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid

BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 149-156
Author(s):  
RR Thapa
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Independent Variable ◽  
The Stability ◽  
Three Body ◽  
Special Case

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156

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.

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