Helmholtz conditions, covariance, and invariance identities

DOI10.1007/BF00670805zbMath0571.70017MaRDI QIDQ1061517

Giacomo Caviglia

Publication date: 1985

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse problemgravitationmetric tensortorsion free connectioncovariance requirementsHelmholtz's self-adjointness conditionsinvariance identity

Mathematics Subject Classification ID

General relativity (83C99) Lagrange's equations (70H03)

Related Items

Composite variational principles, added variables, and constants of motion ⋮ On the inverse problem of the discrete calculus of variations ⋮ The inverse problem in the calculus of variations and the geometry of the tangent bundle ⋮ Variational principles for nonpotential operators ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inverse problem in classical mechanics: Dissipative systems
• Tensorial Euler-Lagrange expressions and conservation laws
• Quadratic integrals for linear nonconservative systems and their connection with the inverse problem of Lagrangian dynamics
• Equations of motion, commutation relations and ambiguities in the Lagrangian formalism
• Conditions on a connection to be a metric connection
• The Variational Principle and natural transformations II. Time dependent theory
• The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
• Conditions for the local existence of metric in a generic affine manifold
• On the differential geometry of the Euler-Lagrange equations, and the inverse problem of Lagrangian dynamics
• The Variational Principle and natural transformations I. Autonomous dynamical systems
• Lagrangians for spherically symmetric potentials
• Symmetries, first integrals, and the inverse problem of Lagrangian mechanics. II