The Helmholtz conditions in terms of constants of motion in classical mechanics

DOI10.1063/1.528243zbMath0676.70023OpenAlexW2092773878MaRDI QIDQ3832110

Francisco Pardo

Publication date: 1989

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528243

zbMATH Keywords

variational principlesecond-order differential equationsnecessary and sufficient conditionsHelmholtz conditionsinverse problem in classical mechanics

Mathematics Subject Classification ID

Dynamics of a system of particles, including celestial mechanics (70F99) Other variational principles in mechanics (70H30) Variational principles of physics (49S05)

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Cites Work

• Equations of motion, commutation relations and ambiguities in the Lagrangian formalism
• The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
• Equivalent Lagrangians: Multidimensional case
• First-order equivalent Lagrangians and conservation laws
• Symmetries and conserved quantities in geodesic motion
• On the inverse problem of the calculus of variations
• On the inverse problem of the calculus of variations