Angular Parametrization in Relativistic Kinematics: A Methodological Note
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901648150888448 |
|---|---|
| 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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19162796 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| 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 |