Equations of motion of elliptic restricted problem of three bodies with variable mass

Das, Rik; Shrivastava, Ajay Kumar; Ishwar, B.

doi:10.1007/bf01245759

Cited by 17 publications

(15 citation statements)

References 6 publications

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“…They use the same (wrong) Lagrange's equations of SI (Equations (1)-(4) of Singh and Ishwar, 1984). Das et al (1989) study the elliptical restricted three-body problem under the assumption that the principal masses are constant, while the small body loses mass isotropically. They also do not include the forces Q~, Qy, Qz in their Lagrange's equations (Equations (1)-(3) of Das et al, 1989).…”

Section: Ol Olmentioning

confidence: 99%

“…For example, Shrivastava and Ishwar (1983), Singh and Ishwar (1984), and Das et al (1989), who analyzed the restricted three-body problem when the mass of the infinitesimal body varies, and Saslaw (1985), who discussed the virial theorem for a collection of bodies of variable mass, incorrectly applied Newton's second law (or the equivalent Lagrange's equations) to deal with the variable masses and obtained erroneous results.…”

mentioning

confidence: 99%

“…So, in this case, the correct equation will be re(t) (4) This fact had been recognized long ago by Mescerskii (1897; according to Hadjidemetriou, 1963). However, there are still some authors: Shrivastava and Ishwar (1983), Singh and Ishwar (1984), Das et al (1989) and Saslaw (1985), that will use Equation (1) in the case of isotropical mass loss. Shrivastava and Ishwar (1983) (to be shortened herefrom SI) consider a modified version of the circular restricted three-body problem.…”

mentioning

confidence: 99%

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On the use and abuse of Newton's second law for variable mass problems

Plastino¹,

Muzzio²

1992

Celestial Mech Dyn Astr

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Section: Ol Olmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the use and abuse of Newton's second law for variable mass problems

Plastino¹,

Muzzio²

1992

Celestial Mech Dyn Astr

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“…Following Jeans [1], Verhulst [4] discussed the two body problem with slowly decreasing mass, by a non-linear, non-autonomous system of differential equations. Shrivastava and Ishwar [5] derived the equations of motion in the circular restricted problem of three bodies with variable mass with the assumption that the mass of the infinitesimal body varies with respect to time.…”

Section: Introductionmentioning

confidence: 99%

“…Das et al [5] developed the equations of motion in elliptic restricted problem of three bodies with variable mass. Lukyanov [7] discussed the stability of equilibrium points in the restricted problem of three bodies with variable mass.…”

Section: Introductionmentioning

confidence: 99%

Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

Hassan¹,

Kumari²,

Hassan³

2017

IJAA

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The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters; the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points; whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.

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The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

et al. 2018

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This paper shows the effect of small perturbations in the Coriolis and centrifugal forces in the restricted four‐body problem (R4BP) with variable mass. The existence, location, and stability of the libration points are investigated numerically and graphically under these perturbations. In the present problem, a fourth body with infinitesimal mass is moving under the Newtonian gravitational attraction of three primaries which are moving in a circular orbit around their common center of mass fixed at the origin of the coordinate system. Moreover, according to the solution of Lagrange, the primaries are fixed at the vertices of an equilateral triangle. The fourth body does not affect the motion of three primaries. Furthermore, the fourth body's mass varies according to Jeans' law. The equations of motion of the test particle, i.e., fourth body moving under the gravitational influence of the primaries, are derived. Throughout the paper, we consider the case where the primary body placed along the x‐axis is dominant while the other two small primaries are equal. Further, it is shown that there exist either 8 or 10 libration points out of which 2 or 4 are collinear with the dominating primary and the rest are non‐collinear for fixed values of the parameters. The linear stability of all the libration points under consideration is investigated, and these libration points are found to be unstable. The allowed regions of motion are determined by using the zero‐velocity surface, and the positions of the libration points on the orbital plane are presented. Moreover, by using the Newton–Raphson iterative scheme, we unveiled the effects of the Coriolis and centrifugal forces on the topology of the basins of convergence associated with the libration points.

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Equations of motion of elliptic restricted problem of three bodies with variable mass

Cited by 17 publications

References 6 publications

On the use and abuse of Newton's second law for variable mass problems

On the use and abuse of Newton's second law for variable mass problems

Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

The effect of small perturbations in the Coriolis and centrifugal forces on the existence of libration points in the restricted four‐body problem with variable mass

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