Geodesic
Variational metrics on ${\bf R}\times TM$ and the geometry of nonconservative mechanics
Mathematica slovaca, Tome 44 (1994) no. 3, pp. 315-335
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Classification : 53B40, 53C05, 53Z05, 58B20, 70H03 
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Krupková, Olga. Variational metrics on ${\bf R}\times TM$ and the geometry of nonconservative mechanics. Mathematica slovaca, Tome 44 (1994) no. 3, pp. 315-335. http://geodesic.mathdoc.fr/item/MASLO_1994_44_3_a3/

[1] GRIFONE J.: Structure presque-tangente et connexions. I, Ann. Inst. Fourier (Grenoble) 22 (1972), 287-334. | MR | Zbl

[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

[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

[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

[5] KRUPKA D., SATTAROV A. E.: The inverse problem of the calculus of variations for Finsler structures. Math. Slovaca 35 (1985), 217-222. | MR | Zbl

[6] KRUPKOVÁ O.: Lepagean 2-forms in higher order Hamiltonian mechanics. II. Inverse problem. Arch. Math. (Brno) 23 (1987), 155-170. | MR | Zbl

[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

[8] KRUPKOVÁ O.: Variational metrics on RxTM. Preprint, Silesian University at Opava, Opava (Czech Republic) (1991), 1-15.

[9] de LEÓN M., RODRIGUES P. R.: Generalized Classical Mechanics and Field Theory. North-Holland, Amsterdam, 1985. | MR | Zbl

[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

[11] MODUGNO M.: Torsion and Ricci tensor for non-linear connections. Differential Geom. Appl. 1 (1991), 177-192. | MR

[12] SAUNDERS D. J.: Jet fields, connections and second-order differential equations. J. Phys. A 20 (1987), 3261-3270. | MR | Zbl

[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

[14] VONDRA A.: Connections in the Geometry of Non-Autonomous Regular Higher-Order Dynamics. Thesis, Masaryk University, Brno (Czech Republic), 1991.

[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