Dissipation-Induced Heteroclinic Orbits in Tippe Tops

@article{BouRabee2008DissipationInducedHO,
  title={Dissipation-Induced Heteroclinic Orbits in Tippe Tops},
  author={Nawaf Bou-Rabee and Jerrold E. Marsden and Louis A. Romero},
  journal={SIAM Review},
  year={2008},
  volume={50},
  pages={325-344}
}
This paper demontrates 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 Liapunov stability of the inverted state. Standard nonlinear analysis… CONTINUE READING