Noether's theorem and its inverse of Birkhoffian system in event space based on Herglotz variational problem

DOI10.1007/s10773-017-3621-2zbMath1431.70013OpenAlexW2773821552MaRDI QIDQ726016

Yi Zhang, Xue Tian

Publication date: 2 August 2018

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

Full work available at URL: https://doi.org/10.1007/s10773-017-3621-2

zbMATH Keywords

Noether's theoremBirkhoffian systemNoether's inverse theoremevent spaceHerglotz variational principle

Mathematics Subject Classification ID

Other variational principles in mechanics (70H30) Symmetries and conservation laws in mechanics of particles and systems (70S10) Optimality conditions for free problems in two or more independent variables (49K10) Special quantum systems, such as solvable systems (81Q80) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51)

Related Items (8)

Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem ⋮ Adiabatic invariants of Herglotz type for perturbed nonconservative Lagrangian systems ⋮ A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type ⋮ Noether's theorem for fractional Herglotz variational principle in phase space ⋮ Design of evolutionary optimized finite difference based numerical computing for dust density model of nonlinear Van-der Pol Mathieu's oscillatory systems ⋮ Noether symmetry and conserved quantity for Hamiltonian system of Herglotz type on time scales ⋮ Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems ⋮ Variational and optimal control approaches for the second-order Herglotz problem on spheres

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem
• Noether's theorem for higher-order variational problems of Herglotz type
• Killing and Noether symmetries of plane symmetric spacetime
• Fractional variational principle of Herglotz
• The Noether's theory of Birkhoffian systems
• First Noether-type theorem for the generalized variational principle of Herglotz
• Noether's theorem for nonholonomic systems of non-Chetaev's type with unilateral constraints in event space
• Poincaré bifurcation in second-order autonomous perturbed Birkhoff system
• The conservation law of nonholonomic system of second-order non-Chetaev's type in event space
• Noether theorem in higher-order Lagrangian mechanics
• Lie symmetries and conserved quantities of Birkhoffian system
• Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems
• Fractional Noether theorem based on extended exponentially fractional integral
• Conformal Invariance and Noether Symmetry, Lie Symmetry of Birkhoffian Systems in Event Space
• Noether theorem for Birkhoffian systems on time scales
• Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration
• Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem

This page was built for publication: Noether's theorem and its inverse of Birkhoffian system in event space based on Herglotz variational problem