Dynamics of the tippe top via Routhian reduction

DOI10.1134/S1560354707060032zbMath1229.37049arXiv0704.1221WikidataQ63598588 ScholiaQ63598588MaRDI QIDQ655290

Bavo Langerock, Maria-Christina Ciocci

Publication date: 3 January 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1221

zbMATH Keywords

relative equilibriabifurcationsymmetriestippe topLagrangian equations(linear) stabilityeccentric sphereRouthian reduction

Mathematics Subject Classification ID

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Motion of a rigid body in contact with a solid surface (70E18) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Lagrange's equations (70H03)

Related Items (12)

Towards a prototype of a spherical tippe top ⋮ The influence of the first integrals and the rolling resistance model on tippe top inversion ⋮ Dynamics of an unbalanced disk with a single nonholonomic constraint ⋮ Non‐holonomic rolling of a ball on the surface of a rotating cylinder ⋮ Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane ⋮ Implementation of orbital attitude control laws on a nonholonomic platform ⋮ What does it mean to explain the rising of the tippe top? ⋮ Dynamics of the tippe top on a vibrating base ⋮ The mathematical model for the tippe top inversion ⋮ Comments on the paper by M. C. Ciocci, B. Malengier, B. Langerock, and B. Grimonprez ``Towards a prototype of a spherical tippe top ⋮ Bounded relative motions for formation flying in displaced orbits by low-thrust propulsion ⋮ ROUTH REDUCTION FOR SINGULAR LAGRANGIANS

Cites Work

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• Routh's sphere
• Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics
• A new analysis of the tippe top: Asymptotic states and Lyapunov stability
• Mathematical analysis of the tippe top
• Phase space of rolling solutions of the tippe top
• Reduction theory and the Lagrange–Routh equations
• Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximation
• The Dynamics of a Tippe Top
• Tippe Top Inversion as a Dissipation-Induced Instability
• Motion of the Tippe Top: Gyroscopic Balance Condition and Stability

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