The separatrix of an unstable position of equilibrium of a Hess-Appelrot gyroscope

DOI10.1016/0021-8928(92)90009-WzbMath0809.70004MaRDI QIDQ1314203

S. A. Dovbysh

Publication date: 7 March 1994

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

zbMATH Keywords

splittingfirst-order perturbation theorylong-period solutionspaired separatricesperturbed Lagrange gyroscope

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Motion of the gyroscope (70E05)

Related Items (3)

The Hess-Appelrot system. III: Splitting of separatrices and chaos ⋮ Asymptotic invariant surfaces for non-autonomous pendulum-type systems ⋮ Melnikov functions in the rigid body dynamics

Cites Work

• Some new dynamical effects in the perturbed Euler-Poinsot problem, due to splitting of separatrices
• Intersection of asymptotic surfaces of the perturbed Euler-Poinsot problem
• Splitting of separatrices for unstable uniform rotations and nonintegrability of perturbed Lagrange problem
• SPLITTING OF THE SEPARATRICES AND THE NONEXISTENCE OF FIRST INTEGRALS IN SYSTEMS OF DIFFERENTIAL EQUATIONS OF HAMILTONIAN TYPE WITH TWO DEGREES OF FREEDOM
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