Variational metrics on 𝐑 × T M and the geometry of nonconservative mechanics

Olga Krupková

Mathematica Slovaca (1994)

  • Volume: 44, Issue: 3, page 315-335
  • ISSN: 0139-9918

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Krupková, Olga. "Variational metrics on ${\bf R}\times TM$ and the geometry of nonconservative mechanics." Mathematica Slovaca 44.3 (1994): 315-335. <http://eudml.org/doc/31555>.

@article{Krupková1994,
author = {Krupková, Olga},
journal = {Mathematica Slovaca},
keywords = {variational connections; generalized connections; non-conservative time- dependent mechanical systems; semispray connections; variational metrics},
language = {eng},
number = {3},
pages = {315-335},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Variational metrics on $\{\bf R\}\times TM$ and the geometry of nonconservative mechanics},
url = {http://eudml.org/doc/31555},
volume = {44},
year = {1994},
}

TY - JOUR
AU - Krupková, Olga
TI - Variational metrics on ${\bf R}\times TM$ and the geometry of nonconservative mechanics
JO - Mathematica Slovaca
PY - 1994
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 44
IS - 3
SP - 315
EP - 335
LA - eng
KW - variational connections; generalized connections; non-conservative time- dependent mechanical systems; semispray connections; variational metrics
UR - http://eudml.org/doc/31555
ER -

References

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  4. KRUPKA D., Geometry of Lagrangean structures 2, 3, In: Proc. 14th Winter School on Abstract Analysis, Jan. 1986, Srní (Czech Rep.), Rend. Circ. Mat. Palermo (2) Suppl. 14 (1987), 178-224; Arch. Math. (Brno) 22 (1986), 211-228. (1986) MR0868536
  5. KRUPKA D., SATTAROV A. E., The inverse problem of the calculus of variations for Finsler structures, Math. Slovaca 35 (1985), 217-222. (1985) Zbl0585.53019MR0808354
  6. KRUPKOVÁ O., Lepagean 2-forms in higher order Hamiltonian mechanics. II. Inverse problem, Arch. Math. (Brno) 23 (1987), 155-170. (1987) Zbl0651.58010MR0930318
  7. KRUPKOVÁ O., A note on the Helmholtz conditions, In: Differential Geometry and Its Applications. Proc. Conf., August 1986, Brno, Czechoslovakia, J.E. Purkyně University. Brno, 1986, pp. 181-188. (1986) MR0923379
  8. KRUPKOVÁ O., Variational metrics on RxTM, Preprint, Silesian University at Opava, Opava (Czech Republic) (1991), 1-15. (1991) 
  9. de LEÓN M., RODRIGUES P. R., Generalized Classical Mechanics and Field Theory, , North-Holland, Amsterdam, 1985. (1985) Zbl0581.58015MR0808964
  10. MANGIAROTTI L., MODUGNO M., Fibered spaces, jet spaces and connections for field theories, In: Proc. of the Meeting "Geometry and Physics", Oct. 1982, Florence, Pitagora, Bologna, 1982, pp. 135-165. (1982) MR0760841
  11. MODUGNO M., Torsion and Ricci tensor for non-linear connections, Differential Geom. Appl. 1 (1991), 177-192. (1991) MR1244443
  12. SAUNDERS D. J., Jet fields, connections and second-order differential equations, J. Phys. A 20 (1987), 3261-3270. (1987) Zbl0627.70013MR0914055
  13. SHIMADA H., Cartan-like connections of special generalized Finsler spaces, In: Differential Geometry and Its Applications. Proc. Conf., Sept. 1989, Brno, Czechoslovakia, World Sci., Singapore, 1990, pp. 270-275. (1989) MR1062029
  14. VONDRA A., Connections in the Geometry of Non-Autonomous Regular Higher-Order Dynamics, Thesis, Masaryk University, Brno (Czech Republic), 1991. (1991) 
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