"In this paper, we discuss possible extensions of the concept of the Cartan form of classical mechanics to higher-order mechanics on manifolds, higher-order field theory on jet bundles and to parametric variational problems on slit tangent bundles and on bundles of nondegenerate velocities. We present a generalization of the Cartan form, known as a Lepage form, and basic properties of the Lepage forms. Both earlier and recent examples of differential forms generalizing the Cartan form are reviewed" . "24"^^ . "1"^^ . "14310" . "THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS" . "249661" . "0219-8878" . . . "RIV/00216224:14310/10:00073366" . . . "[A448A0C9D96C]" . . "000279516400007" . "Krupka, Demeter" . . "THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS"@en . "Saunders, David" . . . "Krupkov\u00E1, Olga" . "SG - Singapursk\u00E1 republika" . "4" . . . "THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS" . "P(GA201/09/0981)" . . "THE CARTAN FORM AND ITS GENERALIZATIONS IN THE CALCULUS OF VARIATIONS"@en . . . . "RIV/00216224:14310/10:00073366!RIV15-GA0-14310___" . "7" . "International Journal of Geometric Methods in Modern Physics" . . . "In this paper, we discuss possible extensions of the concept of the Cartan form of classical mechanics to higher-order mechanics on manifolds, higher-order field theory on jet bundles and to parametric variational problems on slit tangent bundles and on bundles of nondegenerate velocities. We present a generalization of the Cartan form, known as a Lepage form, and basic properties of the Lepage forms. Both earlier and recent examples of differential forms generalizing the Cartan form are reviewed"@en . "10.1142/S0219887810004488" . "3"^^ . "Fibered manifold; calculus of variations; first variation formula; Cartan form; Lepage form"@en . .