On the inversion of the Lagrange-Dirichlet stability theorem mechanical and generalized systems

DOI10.1007/BF00962611zbMath0509.70010OpenAlexW1976452138MaRDI QIDQ1838335

Miguel Sofer

Publication date: 1983

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00962611

zbMATH Keywords

geodesicsstable equilibriumFinsler spaceconservativeunstable equilibriumminimum of potential energyLagrange-Dirichlet stability theoremno differentiability of energy

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Statics (70C20)

Related Items (4)

The stability of the equilibrium of holonomic conservative systems ⋮ On inversion of the Lagrange–Dirichlet theorem and instability of conservative systems ⋮ A simple variational approach to a converse of the Lagrange-Dirichlet theorem ⋮ Instability of an equilibrium in a potential field

Cites Work

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• An inversion of the Lagrange-Dirichlet stability theorem
• On instability of equilibrium when the force function is not a maximum
• Die Umkehrung der Stabilitätssätze von Lagrange-Dirichlet und Routh. (The inversion of the stability theorems of Lagrange-Dirichlet and Routh.)

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