Discussion Overview
The discussion centers on the exploration of the Kepler problem in the context of rigid bodies with spin, specifically examining how the inclusion of spin affects trajectories, periods, and the overall validity of the problem's solutions. Participants are considering both theoretical and mathematical approaches to this complex issue.
Discussion Character
- Exploratory
- Technical explanation
- Mathematical reasoning
Main Points Raised
- One participant questions the differences in trajectory or period when comparing point bodies to rigid bodies with spin, seeking methods to incorporate spin into the Kepler problem.
- Another participant suggests using a barbell model (two mass points connected by a rod) in a gravitational field as a simple example to illustrate the complexities involved.
- There is a suggestion to compute the motion of the barbell rotating around a central mass and compare it to the general solution without spin.
- One participant proposes writing down the Lagrange equations and solving them numerically, indicating that the system may exhibit chaotic behavior and diverge from the classical Kepler problem.
- There is mention of the possibility of introducing a small parameter to simplify the problem, though this remains speculative.
Areas of Agreement / Disagreement
Participants express varying views on the feasibility of solving the Kepler problem with spin, with some acknowledging the complexity and difficulty of finding solutions, while others propose specific approaches without reaching a consensus on the best method.
Contextual Notes
The discussion highlights the limitations of existing literature, noting that only partial results are available in articles rather than textbooks. There is also an acknowledgment of the potential chaotic nature of the system when spin is included.