Laplace–Runge–Lenz symmetry in general rotationally symmetric systems

Ben-Ya'acov, Uri

doi:10.1063/1.3520521

Cited by 13 publications

(22 citation statements)

References 48 publications

(95 reference statements)

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“…The purpose of the present paper is thus to discuss in detail the internal symmetry in composite Lorentz-Poincaré symmetric systems, in a manifestly covariant manner in Minkowski space-time, tracing the appearance of LRL vectors in these systems, all in association with the issue of determining the CM coordinate and its properties. The paper extends and completes recent publications on the subject 22,25 .…”

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confidence: 79%

Center-of-mass and internal symmetries in classical relativistic systems

Ben-Ya'acov¹

2011

Journal of Mathematical Physics

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The internal symmetry of composite relativistic systems is discussed. It is demonstrated that Lorentz-Poincaré symmetry implies the existence of internal moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL) vectors. The LRL symmetry is thus found to be the internal symmetry universally associated with the global Lorentz transformations, in much the same way as internal spatial rotations are associated with global spatial rotations. Two applications are included, for an interacting 2-body system and for an interaction-free many-body system of particles. The issue of localizability of the relativistic CM coordinate is also discussed.

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confidence: 79%

Center-of-mass and internal symmetries in classical relativistic systems

Ben-Ya'acov¹

2011

Journal of Mathematical Physics

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“…Reviews on the LRL vector can be found in [50][51][52]. The notation and approach used here follow closely those of Ref.…”

Section: B Lrl Vector Dynamics With and Without The External Potentimentioning

confidence: 99%

“…Here we consider both a version of the PPN formalism and the Laplace-Runge-Lenz (LRL) vector technique [e.g., [50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

2016

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General Relativity extensions based on Renormalization Group effects are motivated by a known physical principle and constitute a class of extended gravity theories that have some unexplored unique aspects. In this work we develop in detail the Newtonian and post Newtonian limits of a realisation called Renormalization Group extended General Relativity (RGGR). Special attention is taken to the external potential effect, which constitutes a type of screening mechanism typical of RGGR. In the Solar System, RGGR depends on a single dimensionless parameterν , and this parameter is such that forν = 0 one fully recovers GR in the Solar System. Previously this parameter was constrained to be |ν | 10 −21 , without considering the external potential effect. Here we show that under a certain approximation RGGR can be cast in a form compatible with the Parametrised Post-Newtonian (PPN) formalism, and we use both the PPN formalism and the Laplace-Runge-Lenz technique to put new bounds onν , either considering or not the external potential effect. With the external potential effect the new bound reads |ν | 10 −16 . We discuss the possible consequences of this bound to the dark matter abundance in galaxies.

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“…In fact, in the equatorial case the said problem constitutes a particular case of motion in a central force field, and is therefore superintegrable in the sense of Liouville (Ben-Ya'acov 2010;Calkin 1996). The relative motion in the equatorial plane of an axially-symmetric planet therefore inherits this super-integrability.…”

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confidence: 95%

Solutions and periodicity of satellite relative motion under even zonal harmonics perturbations

Martinusi

Gurfil

2011

Celest Mech Dyn Astr

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Finding relative satellite orbits that guarantee long-term bounded relative motion is important for cluster flight, wherein a group of satellites remain within bounded distances while applying very few formationkeeping maneuvers. However, most existing astrodynamical approaches utilize mean orbital elements for detecting bounded relative orbits, and therefore cannot guarantee long-term boundedness under realistic gravitational models. The main purpose of the present paper is to develop analytical methods for designing long-term bounded relative orbits under high-order gravitational perturbations. The key underlying observation is that in the presence of arbitrarily high-order even zonal harmonics perturbations, the dynamics are superintegrable for equatorial orbits. When only J 2 is considered, the current paper offers a closed-form solution for the relative motion in the equatorial plane using elliptic integrals. Moreover, necessary and sufficient periodicity conditions for the relative motion are determined. The proposed methodology for the J 2 -perturbed relative motion is then extended to non-equatorial orbits and to the case of any high-order even zonal harmonics (J 2n , n ≥ 1). Numerical simulations show how the suggested methodology can be implemented for designing bounded relative quasiperiodic orbits in the presence of the complete zonal part of the gravitational potential.

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Laplace–Runge–Lenz symmetry in general rotationally symmetric systems

Abstract: The universality of the Laplace-Runge-Lenz symmetry in all rotationally symmetric systems is discussed. The independence of the symmetry on the type of interaction is proven using only the most generic properties of the Poisson brackets. General-

Cited by 13 publications

References 48 publications

Center-of-mass and internal symmetries in classical relativistic systems

Center-of-mass and internal symmetries in classical relativistic systems

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

Solutions and periodicity of satellite relative motion under even zonal harmonics perturbations

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