| Title:
|
Variational metrics on ${\bf R}\times TM$ and the geometry of nonconservative mechanics (English) |
| Author:
|
Krupková, Olga |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
315-335 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53B40 |
| MSC:
|
53C05 |
| MSC:
|
53Z05 |
| MSC:
|
58B20 |
| MSC:
|
70H03 |
| idZBL:
|
Zbl 0818.53026 |
| idMR:
|
MR1307321 |
| . |
| Date available:
|
2009-09-25T10:57:13Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128660 |
| . |
| Reference:
|
[1] GRIFONE J.: Structure presque-tangente et connexions.I, Ann. Inst. Fourier (Grenoble) 22 (1972), 287-334. Zbl 0301.53020, MR 0336636 |
| Reference:
|
[2] KAWAGUCHI H.: The d-connections in Lagrange geometry.In: Differential Geometry and Its Applications. Proc. Conf., Sept. 1989, Brno, Czechoslovakia, World Sci., Singapore. 1990, pp. 230-235. MR 1062025 |
| Reference:
|
[3] KRUPKA D.: Lepagean forms in higher order variational theory.In: Proc. IUTAM-ISIMM Symp. on Modern Developments in Analytical Mechanics, June 1982, Turin; Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., Suppl. al Vol. 117 (1983), 197-238. MR 0773488 |
| Reference:
|
[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. MR 0868536 |
| Reference:
|
[5] KRUPKA D., SATTAROV A. E.: The inverse problem of the calculus of variations for Finsler structures.Math. Slovaca 35 (1985), 217-222. Zbl 0585.53019, MR 0808354 |
| Reference:
|
[6] KRUPKOVÁ O.: Lepagean 2-forms in higher order Hamiltonian mechanics. II. Inverse problem.Arch. Math. (Brno) 23 (1987), 155-170. Zbl 0651.58010, MR 0930318 |
| Reference:
|
[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. MR 0923379 |
| Reference:
|
[8] KRUPKOVÁ O.: Variational metrics on RxTM.Preprint, Silesian University at Opava, Opava (Czech Republic) (1991), 1-15. |
| Reference:
|
[9] de LEÓN M., RODRIGUES P. R.: Generalized Classical Mechanics and Field Theory., North-Holland, Amsterdam, 1985. Zbl 0581.58015, MR 0808964 |
| Reference:
|
[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. MR 0760841 |
| Reference:
|
[11] MODUGNO M.: Torsion and Ricci tensor for non-linear connections.Differential Geom. Appl. 1 (1991), 177-192. MR 1244443 |
| Reference:
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[12] SAUNDERS D. J.: Jet fields, connections and second-order differential equations.J. Phys. A 20 (1987), 3261-3270. Zbl 0627.70013, MR 0914055 |
| Reference:
|
[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. MR 1062029 |
| Reference:
|
[14] VONDRA A.: Connections in the Geometry of Non-Autonomous Regular Higher-Order Dynamics.Thesis, Masaryk University, Brno (Czech Republic), 1991. |
| Reference:
|
[15] VONDRA A.: Semisprays, connections and regular equations in higher order mechanics.In: Differential Geometry and Its Applications. Proc. Conf., Brno, Czechoslovakia, 1989, World Scientific, Singapore, 1990, pp. 276-287. MR 1062030 |
| . |
