Complete separability of time-dependent second-order ordinary differential equations

DOI10.1007/BF01064171zbMath0842.34009MaRDI QIDQ1909380

A. Vandecasteele, Frans Cantrijn, Willy Sarlet, Eduardo Martínez

Publication date: 28 July 1996

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

separabilitycoordinate transformationtensor fieldsdiagonalizability

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Geometric methods in ordinary differential equations (34A26) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Normal forms for dynamical systems (37G05) Connections (general theory) (53C05)

Related Items (6)

Compatibility aspects of the method of phase synchronization for decoupling linear second-order differential equations ⋮ Tangent bundle geometry induced by second order partial differential equations ⋮ A case study of separability of second-order differential equations ⋮ Linearization of nonlinear connections on vector and affine bundles, and some applications ⋮ Helmholtz conditions and symmetries for the time dependent case of the inverse problem of the calculus of variations ⋮ Unnamed Item

Cites Work

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• Derivations of differential forms along the tangent bundle projection
• Nonautonomous submersive second-order differential equations and Lie symmetries
• Derivations of differential forms along the tangent bundle projection. II
• Derivations of forms along a map: The framework for time-dependent second-order equations
• A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
• A separability theorem for dynamical systems admitting alternative Lagrangian descriptions
• Submersive second order ordinary differential equations
• Application of the theory of separability of second-order differential equations
• Geometric characterization of separable second-order differential equations

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