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References (30)
-
A. Borisov, I. Mamaev (2003)
The Rolling Body Motion Of a Rigid Body on a Plane and a Sphere. Hierarchy of DynamicsarXiv: Exactly Solvable and Integrable Systems
-
T. Glad, S. Rauch, Markus Sköldstam (2005)
Mathematical Analysis of the Tippe TopRegular & Chaotic Dynamics, 10
-
Zulassungsar- beit zum 1. Staatsexamen, Universität Augsburg -
(2004)
Private Communications. The Hycaro Tipe Top was presented for the first time during the meeting Geometric Mechanics and its Applications (MASIE), 12–16/07/2004 -
J. Marsden, T. Ratiu, J. Scheurle (2000)
Reduction theory and the Lagrange-Routh equationsJournal of Mathematical Physics, 41
-
L. Pars (1981)
A Treatise on Analytical Dynamics -
(1973)
Classical machanics -
H. Moffatt, Y. Shimomura, M. Branicki (2004)
Dynamics of an axisymmetric body spinning on a horizontal surface. I. Stability and the gyroscopic approximationProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460
-
Stefan Ebenfeld, F. Scheck (1995)
A New Analysis of the Tippe Top: Asymptotic States and Liapunov StabilityAnnals of Physics, 243
-
Nawaf Bou-Rabee, J. Marsden, L. Romero (2004)
Tippe Top Inversion as a Dissipation-Induced InstabilitySIAM J. Appl. Dyn. Syst., 3
-
A.V. Borisov, I.S. Mamaev (2002)
Rolling of a Rigid Body on Plane and Sphere. Hierarchy of DynamicsRegular and Chaotic Dyn., 7
-
T. Kane, D. Levinson (1978)
A Realistic Solution of the Symmetric Top ProblemJournal of Applied Mechanics, 45
-
Takahiro Ueda, Kenjiro Sasaki, Shinsuke Watanabe (2005)
Motion of the Tippe Top: Gyroscopic Balance Condition and StabilitySIAM J. Appl. Dyn. Syst., 4
-
A. Ishlinsky (1973)
On the dynamics of a system of rigid bodies -
J. Jellett (2008)
A Treatise on the Theory of Friction -
C. Gray, B. Nickel (2000)
Constants of the motion for nonslipping tippe tops and other tops with round pegsAmerican Journal of Physics, 68
-
Assume that a Lagrangian L is given, defined on the tangent space of a manifold M on which a local coordinate system -
A. Or (1994)
The Dynamics of a Tippe TopSIAM J. Appl. Math., 54
-
R. Cohen (1977)
The tippe top revisitedAmerican Journal of Physics, 45
-
S. Glad, D. Petersson, S. Rauch-Wojciechowski (2007)
Phase Space of Rolling Solutions of the Tippe TopSymmetry Integrability and Geometry-methods and Applications, 3
-
(2007)
Contribution to the Vadim Kuznetsov Memorial Issue -
Dynamics of the spherical tippe top with small friction -
(2006)
Spinning eggs -a paradox resolved -
T. Tokieda (2004)
Geometric Mechanics and its Applications (MASIE) -
E.J. Routh (1905)
Dynamics of a System of Rigid Bodies -
R. Cushman (1998)
The Routh’s SphereReports on Mathematical Physics, 42
-
R. Cushman (1998)
Routh's sphereRegular & Chaotic Dynamics
-
A Routhian reduction for dissipative systems -
M. Gopal, Vimal Singh (1976)
Control Systems EngineeringIEEE Transactions on Systems, Man, and Cybernetics, 6
-
V. Barger, M. Olsson, J. Casey (2002)
Classical Mechanics: A Modern Perspective
- Publisher
- Springer Journals
- Copyright
- Copyright © 2007 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354707060032
- Publisher site
- See Article on Publisher Site
Abstract
We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced system is a two dimensional system of second order differential equations, that allows an elegant and compact way to retrieve the classification of tippe tops in six groups as proposed in [1] according to the existence and stability type of the steady states.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Dec 18, 2007