"1" . . "RIV/61988987:17310/12:A13016A7!RIV13-GA0-17310___" . . . "We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are regular (in a natural sense that we define) form a projective equivalence class of homogeneous systems. We show further that the geodesics, or base integral curves, of projectively equivalent homogeneous differential equation fields are the same apart from orientation-preserving reparametrization; that is, homogeneous differential equation fields determine systems of paths." . "Ordinary differential equations; homogeneity; projective equivalence; parametric Lagrangian; reparametrization"@en . "21"^^ . . . . "RIV/61988987:17310/12:A13016A7" . . "17310" . . "Homogeneity and projective equivalence of differential equation fields" . "We propose definitions of homogeneity and projective equivalence for systems of ordinary differential equations of order greater than two, which allow us to generalize the concept of a spray (for systems of order two). We show that the Euler-Lagrange fields of parametric Lagrangians of order greater than one which are regular (in a natural sense that we define) form a projective equivalence class of homogeneous systems. We show further that the geodesics, or base integral curves, of projectively equivalent homogeneous differential equation fields are the same apart from orientation-preserving reparametrization; that is, homogeneous differential equation fields determine systems of paths."@en . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . . . "4" . "1941-4889" . "2"^^ . "[F9FDB35024B9]" . . . "P(GA201/09/0981)" . "J. Geom. Mech." . "Homogeneity and projective equivalence of differential equation fields"@en . "1"^^ . "Saunders, David john" . . "Homogeneity and projective equivalence of differential equation fields"@en . "Homogeneity and projective equivalence of differential equation fields" . . . . "Crampin, Mike" . "139557" .