Homographic Three-Body Motions With Positive and Negative Masses

Celli, Martin

doi:10.1142/9789812702142_0010

Cited by 3 publications

(3 citation statements)

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“…Remark 7. The mechanics of systems with negative masses (either gravitational, or inertial) is the subject of active study not only in celestial mechanics (see, e. g., [22][23][24][25]), but also in theoretical physics (see, e. g., [26]). Objects with cavities are, in our opinion, good examples of systems that often exhibit somewhat unexpected dynamical effects (see, e. g., [27]).…”

Section: General Remarksmentioning

confidence: 99%

Libration Points Inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball

Burov¹,

Nikonov²

2021

Nelin. Dinam.

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The problem of the existence and stability of relative equilibria (libration points) of a uniformly rotating gravitating body, which is a homogeneous ball with a spherical cavity, is considered. It is assumed that the rotation is carried out around an axis perpendicular to the axis of symmetry of the body and passing through its center of mass. The libration points located inside the cavity are investigated. Families of both isolated and nonisolated relative equilibria are found. Their stability and bifurcations are investigated. Realms of possible motion are constructed.

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Section: General Remarksmentioning

confidence: 99%

Libration Points Inside a Spherical Cavity of a Uniformly Rotating Gravitating Ball

Burov¹,

Nikonov²

2021

Nelin. Dinam.

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“…Let us notice that this property is only the static variant of a more general fact: for M = 0, the vector λ is the first integral which replaces the center of inertia. As it is invariant under translations, the N -body problem becomes 'more integrable' [6,7].…”

Section: Proposition 4 a Planar Non-collinear Four-body Configuratiomentioning

confidence: 99%

“…It can be shown that it is homothetic with fixed center if, and only if, the configuration is central with multiplier ξ = 0 [6]. This motivates the study of central configurations.…”

Section: Introductionmentioning

confidence: 99%

The central configurations of four masses x, −x, y, −y

Celli

2007

Journal of Differential Equations

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The configuration of a homothetic motion in the N -body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, −x, y, −y with x = y (a parallelogram and two trapezoids) and two planar non-collinear central configurations for masses x, −x, x, −x (two diamonds). Except the case studied here, the only known case where the four-body central configurations with non-vanishing masses can be listed is the case with equal masses (A. Albouy, 1995(A. Albouy, -1996, which requires the use of a symbolic computation program. Thanks to a lemma used in the proof of our result, we also show that a co-circular four-body central configuration has nonvanishing total mass or vanishing multiplier.

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