For more information about this meeting, contact Becky Halpenny.
|Title:||"Effect of tidal dissipation on the motion of celestial bodies"|
|Seminar:||Ph.D. Thesis Defense|
|Speaker:||Chong Ai, Adviser: Mark Levi, Penn State|
|Tidal eﬀects in celestial bodies manifest themselves in many ways. Tides cause
periodic changes in sea and ground levels, they aﬀect the length of day, and even volcanic activity. Tides cause eﬀects on the scale larger than that of an individual body, aﬀecting entire orbits of planets and moons.
In this thesis we focus on the eﬀect of tides on the dynamics of orbits, leaving
aside internal eﬀects of tides on planets. This thesis addresses a gap in the literature. On the one hand, mathematical theory of celestial mechanics is a classical subject going back to Newton, and it reached a high level of development at the hands of people like Legendre, Lagrange, Laplace, Jacobi, Poincar´e, Moser, Arnold and others. Without exception (to our knowledge) this theory treats planets as point masses subject to Newtonian gravitational attraction, and without account for tidal eﬀects. On the other hand, astronomers take more realistic models of the planets, but get few if any rigorous results. In this thesis we study problems which fall in the gap between these two approaches: they do include dissipation on the one hand, making them more realistic than the classical system which completely
ignores them, but we make this dissipation simple enough to be tractable mathematically.
To build dissipation into the equations of motion, we use the Routh method
of introducing dissipation into Lagrangian equations of motion. According to this method, to write the equations of motion one only needs, in addition to the Lagrangian of the system, also the so–called Routh dissipation function: the power dissipated as a function of generalized coordinates and generalized velocities of the system. We choose a simple class of dissipation functions, leaving more general questions for future work.|
Room Reservation Information
|Date:||08 / 20 / 2012|
|Time:||03:00pm - 05:00pm|