Dissipation-induced heteroclinic orbits in tippe tops.
Journal Article
·
· Proposed for publication in SIAM Review.
OSTI ID:949032
- Caltech, Pasadena, CA
This paper demonstrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell-Bloch equations. A standard linear analysis reveals that the modified Maxwell-Bloch equations describe the spectral instability of the noninverted state and Lyapunov stability of the inverted state. Standard nonlinear analysis based on the energy momentum method gives necessary and sufficient conditions for the existence of a dissipation-induced connecting orbit between these relative equilibria.
- Research Organization:
- Sandia National Laboratories
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 949032
- Report Number(s):
- SAND2008-2784J
- Journal Information:
- Proposed for publication in SIAM Review., Journal Name: Proposed for publication in SIAM Review.
- Country of Publication:
- United States
- Language:
- English
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