Geodesic
The generalized Lagrangian mechanical systems
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 74-80 
Radu Miron. The generalized Lagrangian mechanical systems. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 74-80. http://geodesic.mathdoc.fr/item/BASM_2012_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A generalized Lagrangian mechanics is a triple $\Sigma_{GL}=(M,\mathcal E,F_e)$ formed by a real $n$-dimensional manifold $M$, the generalized kinetic energy $\mathcal E$ and the external forces $F_e$. The Lagrange equations (or fundamental equations) can be defined for a generalized Lagrangian mechanical system $\Sigma_{GL}$. We get a straightforward extension of the notions of Riemannian, or Finslerian, or Lagrangian mechanical systems studied in the recent book [7]. The applications of this systems in Mechanics, Physical Fields or Relativistic Optics are pointed out. Much more information can be found in the books or papers from References [1–10].

[1] Anastasiei M., Selected Papers, Al. I. Cuza University, Iaşi, 2012 | MR

[2] Bucataru I., Miron R., Finsler-Lagrange Geometry. Applications to Dynamical Systems, Romanian Academy, Bucureşti, 2007 | MR | Zbl

[3] Miron R., “A Lagrangian Theory of Relativity, I”, Ann. Şt. Univ. “Al. I. Cuza” (Iaşi), 32:2 (1986), 37–62 | MR | Zbl

[4] Miron R., “A Lagrangian Theory of Relativity, II”, Ann. Şt. Univ. “Al. I. Cuza” (Iaşi), 32:3 (1985), 7–16 | MR | Zbl

[5] Miron R., “Dynamical Systems of Lagrangian and Hamiltonian Mechanical Co Systems”, Advanced Studies in Pure Mathematics, 48 (2007), 309–340 | MR | Zbl

[6] Miron R., “Compendium on the Geometry of Lagrange Spacers”, Handbook of Differential Geometry, v. I, eds. Dillen E. J. T., Verstrahele L. C A., 2006, 437–512 | DOI | MR | Zbl

[7] Miron R., Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics, Romanian Academy Fair Partners, 2011 | MR | Zbl

[8] Miron R., Anastasiei M., The Geometry of Lagrange Spaces. Theory and Applications, FTPH, 50, Kluwer Acad. Publ., 1994 | MR

[9] Miron R., Hrimiuc D., Shimada H., Sabau S. V., The Geometry of Hamilton and Lagrange Spaces, FTPH, 118, Kluwer Acad. Publ., 2001 | MR | Zbl

[10] Pavlov D. G., Kokarev S. S., “Conformal Gauges of the Berwald-Moor Geometries and their Induced Nonlinear Symmetries”, Hypercomplex Number in Geometry and Physics, 5:2(10) (2004), 5–18 (in Russian)