Hi, there all you guys. I’m so happy to be part of the community.
For a couple of days, I’ve been working on both simple and double pendulum motion. By Lagrange’s equation, I just managed to find the motion equations of both problems. Graphing the motion equation of the simple pendulum wasn’t a great deal, but I’m stuck trying to graph the motion equation in the second one. Perhaps I’m not using the DSolve command correctly to solve the system of the differential equation I have to deal with.
I just managed to “solve” the problem, but now I’m pretending to interact with the program so the user can add values as the mass or the length of the string; (All those values were taken as the unit in this example) as well as the initial conditions to solve the differential equations to get particular solutions.
I’ll be looking for any advice or suggestion. Thanks so much.
You should also consider using Wolfram SystemModeler (WSM). WSM makes it much easier to get the results and animation. You can even run WSM from within Mathematica.
For example, open either the example “Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulum” or “Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulumInitTip”
The animation looks like this (and it can be customized and run at various speeds):
You can run it in WSM or simulate it in Mathematica:
model = SystemModel["Modelica.Mechanics.MultiBody.Examples.Elementary.DoublePendulum"]
sim = SystemModelSimulate[model]
Lastly, you can even get the equations of motion in Mathematica with some simplification and elimination of extraneous variables.
For a problem like this, WSM is far faster than Mathematica (unless you are trying to learn the equation approach). WSM also eliminates the common problem with Lagrangian approaches in which an error results in non-conservative or incorrect equations.
