| Title:
|
Geometrical aspects of the covariant dynamics of higher order (English) |
| Author:
|
Opris, D. |
| Author:
|
Albu, I. D. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
395-412 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present some geometrical aspects of a higher-order jet bundle which is considered a suitable framework for the study of higher-order dynamics in continuous media. We generalize some results obtained by A. Vondra, [7]. These results lead to a description of the geometrical dynamics of higher order generated by regular equations. (English) |
| MSC:
|
53B15 |
| MSC:
|
53C05 |
| MSC:
|
58A20 |
| MSC:
|
58F05 |
| MSC:
|
70H03 |
| MSC:
|
70H35 |
| MSC:
|
73B99 |
| idZBL:
|
Zbl 0955.53013 |
| idMR:
|
MR1637910 |
| . |
| Date available:
|
2009-09-24T10:14:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127427 |
| . |
| Reference:
|
[1] I. M. Anderson: Aspects of the inverse problem to the calculus of variations.Arch. Math. (Brno) 24 (1988), 181–202. Zbl 0674.58017, MR 0983236 |
| Reference:
|
[2] M. Ferraris, M. Francaviglia: On the Global Structure of Lagrangian and Hamiltonian Formalisms in Higher Order Calculus of Variations, Proceedings of the Meeting “Geometry and Physics”.Florence, October 12–15 (1982), 43–70. MR 0760836 |
| Reference:
|
[3] H. Goldschmidt, S. Stemberg: The Hamilton-Cartan Formalism in the Calculus of Variations.Ann. Inst. Fourier, Grenoble 23 (1973), 203–267. MR 0341531, 10.5802/aif.451 |
| Reference:
|
[4] M. J. Gotay: A multisymplectic Framework for Classical Field Theory aud the Calculus of Variations.I. Covariant Hamiltonian Formalism, Mechanics, Analysis and Geometry 200 Years after Lagrange, Amsterdam, 1990. MR 1098517 |
| Reference:
|
[5] A. Vondra: Semisprays, connections and regular equations in higher order mechanics.Proc. Conf. Diff. Geom. and Its. Appl., World Scientific, Singapore (1990), 276–287. Zbl 0809.58015, MR 1062030 |
| Reference:
|
[6] A. Vondra: Some connections related to the geometry of regular higher-order dynamics.Sbornik VA Brno, Řada “B” 2 (1992), 7–18. |
| Reference:
|
[7] A. Vondra: Natural Dynamical Connections.Czechoslovak Math. J., Praha 41(116) (1991), 724–730. Zbl 0764.53019, MR 1134961 |
| . |
