Rigorous proof of chaotic behaviour in a dumbbell satellite model

DOI10.1006/jmaa.2000.7143zbMath0965.37023OpenAlexW2048158024MaRDI QIDQ1593780

Urs Kirchgraber, Daniel Stoffer, Ulrich Manz

Publication date: 31 July 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.7143

zbMATH Keywords

chaotic behaviourshadowingnon-autonomous differential equation\(T\)-periodic differential equationdumbbell satellite model

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Nonautonomous smooth dynamical systems (37C60)

Related Items

On the dynamics of planar oscillations for a dumbbell satellite in \(J_{2}\) problem ⋮ Chaos and the shadowing property ⋮ Chaotic satellite synchronization using neural and nonlinear controllers ⋮ Some properties of the dumbbell satellite attitude dynamics ⋮ Shadowing is generic -- a continuous map case ⋮ Genericity of inverse shadowing property ⋮ Transversal homoclinic points of the Hénon map ⋮ Dynamics of a dumbbell satellite under the zonal harmonic effect of an oblate body ⋮ Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration ⋮ A note on chaos and the shadowing property ⋮ Hamiltonian symmetry reduction via localizations: theory and application to a barbell system

Cites Work

• Der Tayloralgorithmus
• Rigorous chaos verification in discrete dynamical systems
• Rigorous computational shadowing of orbits of ordinary differential equations
• Isolating neighborhoods and chaos
• Chaotic Behaviour in Simple Dynamical Systems
• Computer assisted proof of chaos in the Rössler equations and in the Hénon map
• Rigorous verification of chaotic behaviour of maps using validated shadowing
• Verification of chaotic behaviour in the planar restricted three body problem
• Unnamed Item

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