I made some progress if you are interested. Instead of plugging the differential equations of l(t) and h(t) I built the extended Lagrangian with the constraints and the multipliers. Now the energy is conserved and the angle theta does not increase randomly.
Here is link to the new mathematica...
I am uploading plots from Mathematica for a result of simulation. The plots are for [theta, phi, l , T, U, L] respectively. You can see how theta keeps growing and how the energy is also increasing.
line 12 is active. That's where U is being calculated. I've just checked and it does not matter if I use line 12 or 13 for U. The l(t) in line 13 is an error.
In lines 14,15 I am practically plugging the differential equations of l(t) and h(t) into T because it contains the derivatives. Is that...
I have a small Mathematica script that solves the equations numerically. Another thing that I'm not sure about is how to use the differential equations of l(t) and h(t). Do they come in the Lagrangian as constraints?
But you can see what I did clearly in the script...
yes I guess U = mgz would be easier. But isn't it just a convention issue? I've actually already tried that with similar results. I know only the difference in energy is actually what matters. it is that just at some point i wanted to have it in a form I could imagine. And maximum potential...
Oh I'm sorry I thought the template was just there for guidance.
Well the first part of U is the normal pendulum like potential energy. I might have chosen a weird zero point though. I thought I want the minimum of potential energy when the ball is hanging down. The maximum would be then when...
I'm trying to write down the equations of motion for a tetherball moving in 3D around a pole while the string is getting shorter.I've started with lagrange equations:
x(t)=l(t) \sin (\theta) \cos (\phi)\\
y(t)=l(t) \sin (\theta) \sin (\phi)\\
z(t)=h(t)+l(t) \cos(\theta)\\ \\
T =...