Geometrical formulation of relativistic mechanics

Chanda, Sumanto; Guha, Partha

doi:10.1142/s0219887818500627

Cited by 12 publications

(6 citation statements)

References 30 publications

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“…(where r ij with i, j ∈ {1, 2, 3} denote the components of the rotation matrix) and note that the product still fulfills Eq. (15). With this in mind, we can claim that our derivation is valid for the momentary rest IRF of a particle moving in an arbitrary direction relative to T .…”

Section: Interpretation and Generalizationmentioning

confidence: 84%

“…[14], which likewise does not discuss the relativistic Lagrangian formalism. Chanda and Guha [15] discuss relativistic particle Lagrangians in detail, however that discussion does not consider the transformation properties of the Lagrangian and the Euler-Lagrange equations. These properties are crucial for motivating our development of the relativistic Lagrangian formalism.…”

Section: B Reviewmentioning

confidence: 99%

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Demystifying the Lagrangians of special relativity

Wagner,

Guthrie

2021

Preprint

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Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back in its physics context, and to make the subject approachable. The Lagrangian formulation of special relativity follows logically by combining the Lagrangian approach to mechanics and the postulates of special relativity. In this paper, we derive and explicate some of the most important results of how the Lagrangian formalism and Lagrangians themselves behave in the context of special relativity. We derive two foundations of special relativity: the invariance of any spacetime interval, and the Lorentz transformation. We then develop the Lagrangian formulation of relativistic particle dynamics, including the transformation law of the electromagnetic potentials, the Lagrangian of a relativistic free particle, and Einstein's mass-energy equivalence law (E = mc 2 ). We include a discussion of relativistic field Lagrangians and their transformation properties, showing that the Lagrangians and the equations of motion for the electric and magnetic fields are indeed invariant under Lorentz transformations.

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Section: Interpretation and Generalizationmentioning

confidence: 84%

Section: B Reviewmentioning

confidence: 99%

Demystifying the Lagrangians of special relativity

Wagner,

Guthrie

2021

Preprint

View full text Add to dashboard Cite

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“…In this section we shall proceed by considering a non-relativistic Lagrangian involving magnetic fields. Starting from the relativistic Lagrangian (1), defining g 00 (x) and parametrizing with respect to time g 00 (x) = 1 + 2U(x) mc 2 ,ṫ = 1, and taking non-relativistic approximation by expanding binomially up to first order as shown in [10], we will have the non-relativistic Lagrangian involving magnetic fields:…”

Section: Jacobi Metric For a Lagrangian With Magnetic Fieldsmentioning

confidence: 99%

“…and taking non-relativistic approximation by expanding binomially up to first order as shown in [10], we will have the non-relativistic Lagrangian involving magnetic fields:…”

Section: Constraint For Momenta Of a Geodesicmentioning

confidence: 99%

Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect

Chanda

Gibbons

Guha

et al. 2019

Journal of Mathematical Physics

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In this paper we return to the subject of Jacobi metrics for timelike and null geodsics in stationary spactimes, correcting some previous misconceptions. We show that not only null geodesics, but also timelike geodesics are governed by a Jacobi-Maupertuis type variational principle and a Randers-Finsler metric for which we give explicit formulae. The cases of the Taub-NUT and Kerr spacetimes are discussed in detail. Finally we show how our Jacobi-Maupertuis Randers-Finsler metric may be expressed in terms of the effective medium describing the behaviour of Maxwell's equations in the curved spacetime. In particular, we see in very concrete terms how the magnetolectric susceptibility enters the Jacobi-Maupertuis-Randers-Finsler function.

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“…1 n( r) − 1 , according to [26], we can write the optical-mechanical relativistic Lagrangian from (3.1), using (3.2), as follows:…”

Section: Optical-mechanical Formulationmentioning

confidence: 99%

Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2

Chanda,

Guha

2017

Preprint

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We have studied optical metrics via null geodesics and optical-mechanical formulation of classical mechanics, and described the geometry and optics of mechanical systems with drag dependent quadratically on velocity. Then we studied null geodesics as a central force system, deduced the related Binet's equation applied the analysis to other solutions of Einstein's equations in spherically symmetric spaces, paying special attention to the Tomimatsu-Sato metric. Finally, we examined the dualities between different systems arising from conformal transformations that preserve the Jacobi metric.

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Geometrical formulation of relativistic mechanics

Cited by 12 publications

References 30 publications

Demystifying the Lagrangians of special relativity

Demystifying the Lagrangians of special relativity

Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect

Dynamical systems of null geodesics and solutions of Tomimatsu-Sato 2

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