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Lagrangian and Hamiltonian formalisms: An analysis of classical mechanics on tangent and cotangent bundles

Лагранжев и Гамильтонов формализмы. Анализ классической механики на семействах кривых тангенсов и котангенсов

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Il Nuovo Cimento B (1971-1996)

Summary

The notion of dynamical system in classical mechanics is built starting from the trajectories on the configuration space. Classes of equivalent vector fields on tangent and cotangent bundles are obtained. This leads to a re-examination in detail of the meaning of the Hamiltonian and Lagrangian functions.

Riassunto

Si costruisce la nozione di sistema dinamico partendo dalle traiettorie sullo spazio delle configurazioni. Si ottengono classi di equivalenze di campi vettoriali sul fibrato tangente e cotangente. Ciò porta a riesaminare in dettaglio il significato delle funzioni hamiltoniana e lagrangiana.

Резюме

Исходя из траекторий в коифигурационном пространстве, определяется понятие динамической системы в классической механике. Получаются классы эквивалентных векторных полей на семействе тангенсов и котангенсов. Предложенный подход позволяет заново подробно исследовать физический смысл функций Гамильтона и Лагранжа.

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References

  1. We are here generalizing (by applying it toTM) and globalizing the notion of «fouling transformations» as introduced byY. Gelman andE. J. Saletan:Nuovo Cimento,18 B, 53 (1972) for transformations on phase space.

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  2. SeeG. Marmo: in theProceedings of the IV International Colloquium on Group Theoretical Methods in Physics, Nijmegen, June 1975.

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Authors and Affiliations

  1. Istituto di Fisica Teorica dell'Università, Napoli

    G. Caratù, G. Marmo, A. Simoni, B. Vitale & F. Zaccaria

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Napoli, Italy

    G. Caratù, G. Marmo, A. Simoni, B. Vitale & F. Zaccaria

Authors
  1. G. Caratù
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  2. G. Marmo
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  3. A. Simoni
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  4. B. Vitale
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  5. F. Zaccaria
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Additional information

While this work was being completed, B.V. has been a guest of the CERN theoretical group and of Bern University.

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Caratù, G., Marmo, G., Simoni, A. et al. Lagrangian and Hamiltonian formalisms: An analysis of classical mechanics on tangent and cotangent bundles. Nuov Cim B 31, 152–172 (1976). https://doi.org/10.1007/BF02730325

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  • DOI: https://doi.org/10.1007/BF02730325

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