Geodesic
The Regularization of the Second Order Lagrangians in Example
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 157-165.

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This paper is devoted to geometric formulation of the regular (resp. strongly regular) Hamiltonian system. The notion of the regularization of the second order Lagrangians is presented. The regularization procedure is applied to concrete example.
Classification : 35R01, 49S05, 53Z05
Keywords: Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lagrangian; Lepagean equivalents; Poincaré–Cartan form; regular and strongly regular systems 
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Smetanová, Dana. The Regularization of the Second Order Lagrangians in Example. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 157-165. http://geodesic.mathdoc.fr/item/AUPO_2016__55_2_a12/