Brainstorm Ideas for Project - Get Suggestions on Differential Equations

[faradayscat]

I will be writing a paper by modelling a system and its differential equations. I have just started brainstorming ideas but I would also like to hear other peoples' ideas as well!

I have these ideas so far, can anybody suggest relevant articles or papers on these topics (avoid wikipedia if possible):

-Orbital mechanics/dynamics
-Kepler's laws of planetary motion
-General and/or special relativity
-Pendulum motion
-Wave motion

I look forward to reading your ideas and suggestions!

 

[Dr. Courtney]

It helps to have a better idea of the specific goals, boundaries, and tools.

The double pendulum can be interesting, as can a number of other dynamical systems in 2 dimensions, but you need to be able to numerically integrate the diff eqs quickly with lots of different initial conditions.

Wikipedia can be a good place to find ideas and the related more reliable sources.

 

[zinq]

If you are newish to differential equations, the planar differential equation of the position and velocity of the damped (simple) pendulum is extremely enlightening.

 

[jackmell]

The non-linear pendulum. Know it? In the linear case, you can only (initially) perturb the pendulum a small amount before the solution looses accuracy. However, in the non-linear case, you can smack the pendulum so hard so that it goes round and round and the solution will still accurately describe it's motion. Pretty sure. You can investigate this assertion and determine if it is true.

 

[faradayscat]

Thank you all for your answers, I'm going with the double pendulum.

 

[Chestermiller]

Numerically solving advection-dominated transport problems (with weak diffusion present) to obtain accurate solutions without requiring minute time steps for stability or for avoiding wiggles in the concentration profiles.