A new Lie symmetrical method of finding a conserved quantity for a dynamical system in phase space

DOI10.1007/s00707-012-0729-6zbMath1307.70015OpenAlexW2056831134MaRDI QIDQ2392838

Zhuang-Jun Li, Lin Li, Shao-Kai Luo

Publication date: 5 August 2013

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-012-0729-6

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Dynamical systems in classical and celestial mechanics (37N05) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (18)

Accurate conserved quantity and approximate conserved quantity deduced from Noether symmetry for a weakly Chetaev nonholonomic system ⋮ Conformal invariance and Mei conserved quantity for generalized Hamilton systems with additional terms ⋮ Stability for manifolds of equilibrium state of generalized Hamiltonian system with additional terms ⋮ Fractional generalized Hamiltonian mechanics ⋮ Lie algebraic structure and generalized Poisson conservation law for fractional generalized Hamiltonian systems ⋮ On the families of fractional dynamical models ⋮ Conserved quantities of conservative continuous systems by Mei symmetries ⋮ Fractional generalized Hamiltonian equations and its integral invariants ⋮ Special Lie symmetry and Hojman conserved quantity of Appell equations for a Chetaev nonholonomic system ⋮ Fractional generalized Hamiltonian mechanics and Poisson conservation law in terms of combined Riesz derivatives ⋮ A new method of dynamical stability, i.e. fractional generalized Hamiltonian method, and its applications ⋮ A new method of fractional dynamics, i.e., fractional generalized Hamilton method with additional terms, and its applications to physics ⋮ A general method of fractional dynamics, i.e., fractional Jacobi last multiplier method, and its applications ⋮ Stability for manifolds of the equilibrium state of fractional Birkhoffian systems ⋮ Stability for manifolds of equilibrium states of fractional generalized Hamiltonian systems ⋮ Fractional Nambu dynamics ⋮ Conformal invariance and conserved quantity of Mei symmetry for Appell equations in a nonholonomic system of Chetaev's type ⋮ Fractional Birkhoffian mechanics

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