@article{4127,
  keywords = {asteroids, celestial mechanics, planets, satellites},
  author = {Ann-Marie Madigan and Alexander Zderic and Michael McCourt and Jacob Fleisig},
  title = {On the Dynamics of the Inclination Instability},
  abstract = {<p>Axisymmetric disks of eccentric\&nbsp;<em>Kepler</em>\&nbsp;orbits are vulnerable to an instability that causes orbits to exponentially grow in inclination, decrease in eccentricity, and cluster in their angle of pericenter. Geometrically, the disk expands to a cone shape that is asymmetric about the mid-plane. In this paper, we describe how secular gravitational torques between individual orbits drive this "inclination instability". We derive growth timescales for a simple two-orbit model using a Gauss\&nbsp;N-ring code, and generalize our result to larger\&nbsp;N\&nbsp;systems with\&nbsp;N-body simulations. We find that two-body relaxation slows the growth of the instability at low\&nbsp;N\&nbsp;and that angular phase coverage of orbits in the disk is important at higher\&nbsp;N. As N\textrightarrow$\infty$\&nbsp;, the e-folding timescale converges to that expected from secular theory.</p>},
  year = {2018},
  journal = {The Astronomical Journal},
  volume = {156},
  month = {2018-09},
  url = {http://iopscience.iop.org/article/10.3847/1538-3881/aad95c/pdf},
  doi = {10.3847/1538-3881/aad95c},
}