Some results in Lagrangian mechanics

Emanuele Fiorani

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 591-603
  • ISSN: 0392-4041

Abstract

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We associate to a dynamic equation ξ three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities q ˙ are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.

How to cite

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Fiorani, Emanuele. "Some results in Lagrangian mechanics." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 591-603. <http://eudml.org/doc/195314>.

@article{Fiorani2005,
abstract = {We associate to a dynamic equation $\xi $ three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities $\dot\{q\}$ are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.},
author = {Fiorani, Emanuele},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {591-603},
publisher = {Unione Matematica Italiana},
title = {Some results in Lagrangian mechanics},
url = {http://eudml.org/doc/195314},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Fiorani, Emanuele
TI - Some results in Lagrangian mechanics
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 591
EP - 603
AB - We associate to a dynamic equation $\xi $ three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities $\dot{q}$ are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.
LA - eng
UR - http://eudml.org/doc/195314
ER -

References

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  2. GIACHETTA, G. - MANGIAROTTI, L. - SARDANASHVILY, G., New Lagrangian and Hamiltonian methods in field theories, World Scientific, Singapore, 1997. Zbl0913.58001MR2001723
  3. SAUNDERS, D., The geometry of jet bundles, Cambridge University Press, Cambridge, 1989. Zbl0665.58002MR989588
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  5. CRAMPIN, M. - PRINCE, G. F. - THOMPSON, G., A geometrical version of the Helmholtz conditions in time-dependent Lagrangian mechanics, J. Phys. A: Math. Gen., 17 (1984), 1437-1447. Zbl0545.58020MR748776
  6. CRAMPIN, M. - MARTÍNEZ, E. - SARLET, W., Linear connections for systems of second order ordinary differential equations, Ann. Inst. Henri Poincaré, 65 (1996), 223-249. Zbl0912.58002MR1411267
  7. GIACHETTA, G., Jet methods in nonholonomic mechanics, J. Math. Phys., 33 (1992), 1652-1665. Zbl0758.70010MR1158984
  8. HAVAS, P., Four-dimensional formulations of Newtonian mechanics and their relation to the special and general theory of relativity, Rev. Modern Phys., 36 (1964), 938-965. Zbl0123.44101MR180329
  9. MASSA, E. - PAGANI, E., Jet bundle geometry, dynamical connections and the inverse problem of Lagrangian mechanics, Ann. Inst. Henri Poincaré, 61 (1994), 17-62. Zbl0813.70004MR1303184

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