scientific article; zbMATH DE number 3220202

zbMath0135.42601MaRDI QIDQ5508816

Vladimir I. Arnold

Publication date: 1961

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

stabilityequilibrium positionHamiltonian systemgeneral elliptic case

Mathematics Subject Classification ID

Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14)

Related Items (24)

A review of the ``Third integral ⋮ On the stability of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy ⋮ Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame ⋮ The preservation of the stability of a mechanical system when a non- retaining constraint is weakened ⋮ The behaviour of a nonlinear Hamiltonian system with one degree of freedom at the boundary of a parametric resonance domain ⋮ The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition ⋮ Bifurcation of closed orbits from equilibria of Newtonian systems with Coriolis forces ⋮ Symplectic coordinates on \(S^2\times S^2\) for perturbed Keplerian problems: application to the dynamics of a generalised Størmer problem ⋮ Translation of the V. I. Arnold paper ``From superpositions to KAM theory ⋮ Stability of a one-degree-of-freedom canonical system in the case of zero quadratic and cubic part of a Hamiltonian ⋮ Nonlinear stability of the equilibria in a double-bar rotating system ⋮ Lyapunov instability in KAM stable Hamiltonians with two degrees of freedom ⋮ Families of invariant tori in KAM theory: interplay of integer characteristics ⋮ The stability in a strict non-linear sense of a trivial relative equilibrium position in the classical and generalized versions of Sitnikov's problem ⋮ Stability of steady rotations of a heavy gyrostat about its principal axis ⋮ Boundedness in asymmetric oscillations under the non-resonant case ⋮ Unnamed Item ⋮ Extended Lissajous variables for oscillators in resonance. ⋮ On the stability of permanent rotation of a heavy solid body about a fixed point ⋮ Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem ⋮ Stability analysis of apsidal alignment in double-averaged restricted elliptic three-body problem ⋮ Super-exponential stability for generic real-analytic elliptic equilibrium points ⋮ On the applicability of the third integral of motion ⋮ The stability of the Lagrange triangular point and a theorem of Arnold

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