Angular Parametrization in Relativistic Kinematics: A Methodological Note

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Autor principal: Mindiashvili, Mikheili
Formato: Recurso digital
Publicado: Zenodo 2026
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author Mindiashvili, Mikheili
author_facet Mindiashvili, Mikheili
contents <p><em>Geometric representations play a central role in developing physical intuition, particularly when they make the structure of invariant relations explicit. Many key expressions in relativistic kinematics can be recast in a common Pythagorean form, which sometimes reveals geometric structure that is not immediately apparent in the standard algebraic formulation. Yet this structure is rarely emphasized in standard presentations.</em></p> <p><em>In this work, we first recast the standard relativistic relations in Pythagorean form and then introduce a systematic angular parametrization. The resulting structure is compact, visually transparent, and fully equivalent to the conventional formulation.</em></p> <p><em>A parametrization of this form highlights the bounded nature of relativistic variables and makes the geometric meaning of limiting regimes directly and intuitively visible. As a secondary benefit, it offers a convenient route to algebraically stable expressions in ultra-relativistic computations.</em></p> <p><em>From a pedagogical perspective, the approach connects concepts often introduced separately, supporting both conceptual understanding and analytical reasoning. The proposed framework therefore offers a novel representational approach that may serve both as a teaching tool and as a complementary perspective in relativistic physics.</em></p>
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spellingShingle Angular Parametrization in Relativistic Kinematics: A Methodological Note
Mindiashvili, Mikheili
Angular parametrization
Relativistic kinematics
Lorentz factor
Rapidity
Velocity addition
Energy–momentum invariant
Numerical stability
Floating-point arithmetic
<p><em>Geometric representations play a central role in developing physical intuition, particularly when they make the structure of invariant relations explicit. Many key expressions in relativistic kinematics can be recast in a common Pythagorean form, which sometimes reveals geometric structure that is not immediately apparent in the standard algebraic formulation. Yet this structure is rarely emphasized in standard presentations.</em></p> <p><em>In this work, we first recast the standard relativistic relations in Pythagorean form and then introduce a systematic angular parametrization. The resulting structure is compact, visually transparent, and fully equivalent to the conventional formulation.</em></p> <p><em>A parametrization of this form highlights the bounded nature of relativistic variables and makes the geometric meaning of limiting regimes directly and intuitively visible. As a secondary benefit, it offers a convenient route to algebraically stable expressions in ultra-relativistic computations.</em></p> <p><em>From a pedagogical perspective, the approach connects concepts often introduced separately, supporting both conceptual understanding and analytical reasoning. The proposed framework therefore offers a novel representational approach that may serve both as a teaching tool and as a complementary perspective in relativistic physics.</em></p>
title Angular Parametrization in Relativistic Kinematics: A Methodological Note
topic Angular parametrization
Relativistic kinematics
Lorentz factor
Rapidity
Velocity addition
Energy–momentum invariant
Numerical stability
Floating-point arithmetic
url https://doi.org/10.5281/zenodo.19162796