Relativistic orbits of classical charged bodies in a spherically symmetric electrostatic field

Frommert, H.

doi:10.1007/bf02085769

Cited by 5 publications

(2 citation statements)

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“…The relativistic central force orbits were previously studied in Refs. [2,3,4,5]. A brief description of the central force problem in a relativistic setting in a Coulomb potential was presented in the book on classical theory of fields by Landau and Lifshitz [6].…”

Section: Introductionmentioning

confidence: 99%

“…We first set up the relativistic orbit equation for a particle in the central potential presumed to be dependent on the radial coordinate only. The relativistic central force orbits were previously studied in [2][3][4][5]. A brief description of the central force problem in a relativistic setting in a Coulomb potential was presented in the book on classical theory of fields by Landau and Lifshitz [6].…”

Section: Introductionmentioning

confidence: 99%

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Possible potentials responsible for stable circular relativistic orbits

Kumar¹,

Bhattacharya²

2011

Eur. J. Phys.

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Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center. *

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Possible potentials responsible for stable circular relativistic orbits

Kumar¹,

Bhattacharya²

2011

Eur. J. Phys.

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Scattering Problem for a Classical Particle with Spin in a Coulomb Field

Musin

2004

Theoretical and Mathematical Physics

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Relativistic dynamics of the deuteron: An estimate of the nuclear force parameters

Sigalotti

Mejías²

2007

American Journal of Physics

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A relativistic dynamical model of the deuteron nucleus is presented. The neutron and proton are assumed to interact via a short-range Yukawa interaction of strength g2. A close parallel between the Bohr model of the hydrogen atom and the deuteron nucleus is established by quantizing the angular momentum for the Yukawa interaction in the same way that is done for the Coulomb interaction. The measured value of the deuteron binding energy for circular orbits is used to calculate the coupling constant g2, the tangential velocity of the component nucleons, and their separation. The results compare favorably with those obtained employing more sophisticated methods. By using the experimentally known root-mean-square radius of the electric charge of the deuteron, the model is also used to estimate the mean radius of the proton. The model highlights many important features of the nuclear force from basic principles.

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Relativistic orbits of classical charged bodies in a spherically symmetric electrostatic field

Cited by 5 publications

References 1 publication

Possible potentials responsible for stable circular relativistic orbits

Possible potentials responsible for stable circular relativistic orbits

Scattering Problem for a Classical Particle with Spin in a Coulomb Field

Relativistic dynamics of the deuteron: An estimate of the nuclear force parameters

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