Geodesic
From Euler-Lagrange equations to canonical nonlinear connections
Archivum mathematicum, Tome 42 (2006) no. 3, pp. 255-263 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of this paper is to construct a canonical nonlinear connection $\Gamma =(M_{(\alpha )\beta }^{(i)}, N_{(\alpha )j}^{(i)})$ on the 1-jet space $J^{1}(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function \[ L=h^{\alpha \beta }(t)g_{ij}(t,x)x_{\alpha }^{i}x_{\beta }^{j}+U_{(i)}^{(\alpha )}(t,x)x_{\alpha }^{i}+F(t,x)\,. \]
The aim of this paper is to construct a canonical nonlinear connection $\Gamma =(M_{(\alpha )\beta }^{(i)}, N_{(\alpha )j}^{(i)})$ on the 1-jet space $J^{1}(T,M)$ from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function \[ L=h^{\alpha \beta }(t)g_{ij}(t,x)x_{\alpha }^{i}x_{\beta }^{j}+U_{(i)}^{(\alpha )}(t,x)x_{\alpha }^{i}+F(t,x)\,. \]
Classification : 53C80, 70G45, 70S05
Keywords: 1-jet fibre bundles; nonlinear connections; quadratic Lagrangian functions 
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Neagu, Mircea. From Euler-Lagrange equations to canonical nonlinear connections. Archivum mathematicum, Tome 42 (2006) no. 3, pp. 255-263. http://geodesic.mathdoc.fr/item/ARM_2006_42_3_a7/

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