Precession and Chaos in the Classical Two-Body Problem in a Spherical Universe

Lindner, John F.; Roseberry, Martha; Shai, Daniel; Harmon, Nicholas J.; Olaksen, Katherine D.

doi:10.1142/s0218127408020380

Cited by 4 publications

(1 citation statement)

References 5 publications

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“…In the theoretical framework of scalar-tensor gravitation, Zhou et al [4] found that there is a collinear solution to the three-body problem in the presence of a scalar field, and studied the effect of the scalar field on this solution and the positions of Lagrange points through numerical examples. For the three-body problem in the spherical universe, their perturbation theory analysis showed that the rate of precession of two small and nearly circular solutions of identical particles is proportional to the square root of their initial distance and inversely proportional to the square of the radius of the universe [5]. In addition, the three-body problem is also widely used in the evolution of binary systems [6] and the dynamic analysis of binary asteroids [7,8], as well as other fields in the universe such as dark matter, galaxies, GW170817 (GW is short for gravitational wave), and Mukhanov-Sasaki Hamiltonian dynamics, and so forth (see References [9][10][11][12][13] for more information).…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Gao

Wang

2020

Universe

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Against the background of a restricted three-body problem consisting of a supergiant eclipsing binary system, the two primaries are composed of a pair of bright oblate stars whose mass changes with time. The zero-velocity surface and curve of the problem are numerically studied to describe the third body’s motion area, and the corresponding five libration points are obtained. Moreover, the effect of small perturbations, Coriolis and centrifugal forces, radiative pressure, and the oblateness and mass parameters of the two primaries on the third body’s dynamic behavior is discussed through the bifurcation diagram. Furthermore, the second- and third-order approximate analytical periodic solutions around the collinear solution point L3 in two-dimensional plane and three-dimensional spaces are presented by using the Lindstedt-Poincaré perturbation method.

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Section: Introductionmentioning

confidence: 99%

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Gao

Wang

2020

Universe

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Order and chaos in the rotation and revolution of a line segment and a point mass

et al. 2010

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We study the classical dynamics of two bodies, a massive line segment or slash (/) and a massive point or dot (.), interacting gravitationally. For this slash-dot (/.) body problem, we derive algebraic expressions for the force and torque on the slash, which greatly facilitate analysis. The diverse dynamics include a stable synchronous orbit, generic chaotic orbits, sequences of unstable periodic orbits, spin-stabilized orbits, and spin-orbit coupling that can unbind the slash and dot. The extension of the slash provides an extra degree of freedom that enables the interplay between rotation and revolution. In this way, the slash-dot body problem exhibits some of the richness of the three body problem with only two bodies and serves as a valuable prototype for more realistic systems. Applications include the dynamics of asteroid-moonlet pairs and asteroid rotation and escape rates.

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Order and chaos in the rotation and revolution of two massive line segments

et al. 2014

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As a generalization of Newton's two body problem, we explore the dynamics of two massive line segments interacting gravitationally. The extension of each line segment or slash (/) provides extra degrees of freedom that enable the interplay between rotation and revolution in an especially simple example. This slash-slash (//) body problem can thereby elucidate the dynamics of nonspherical space structures, from asteroids to space stations. Fortunately, as we show, Newton's laws imply exact algebraic expressions for the force and torque between the slashes, and this greatly facilitates analysis. The diverse dynamics include a stable synchronous orbit, families of unstable periodic orbits, generic chaotic orbits, and spin-orbit coupling that can unbind the slashes. In particular, retrograde orbits where the slashes spin opposite to their orbits are stable, with regular dynamics and smooth parameter spaces, while prograde orbits are unstable, with chaotic dynamics and fractal parameter spaces.

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Precession and Chaos in the Classical Two-Body Problem in a Spherical Universe

Cited by 4 publications

References 5 publications

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Approximate Analytical Periodic Solutions to the Restricted Three-Body Problem with Perturbation, Oblateness, Radiation and Varying Mass

Order and chaos in the rotation and revolution of a line segment and a point mass

Order and chaos in the rotation and revolution of two massive line segments

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