Symmetry and Perturbation Theory 2005
DOI: 10.1142/9789812702142_0010
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Homographic Three-Body Motions With Positive and Negative Masses

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Cited by 3 publications
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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%
“…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%
“…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%