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Mathematica beginners question.
This is my first reddit post and I am not a native speaker.
I am a complete beginner with Mathematica, watched a 30min introduction video on YT on the topic functions, plotting, differential equations and solving equation systems. but still not able to solve a relatively simple differential equation system. Link!
So the problem is a simple physics problem, to which I already have a visualized solution (copied from a wired.com blog). Here it can be watched: link! (requires Chrome or Firefox). Its the "vertical pen flipping over" problem.
I have the following variables: alpha(t): alpha is a function of time and represents the angle of the pen at any given time to the vertical. alpha(t) has the constraints: 0
omega(t) is the angular velocity if the pen
beta(t) is the angular acceleration
I also have the following equation: beta(t)=3gsin(alpha(t))/(2*L) //g and L are constants
I want to solve this differential equation for alpha(t), beta(t), omega(t) with t being the independent variable.
My problem is that i put these equations into Mathematica but it wont work, i suppose I have syntax problems. Dont know when to use omega(t_):= instead of omega(t)== or omega(t)= and the like
Could somebody please give the correct format for putting the above equations into Mathematica in order to get the solutions and to plot the graphs..
thanks in advance! J.
Time derivatives in Mathematica, with pictures!
You know how, especially in physics, sometimes we have to derive a function with respect to time, yet that function has many variables that change with time.
Example from a physics problem [Double pendulum with Lagrangian]
As you can see from the example, 4 variables change with time: Theta1, Theta2, ThetaDot1, ThetaDot2. The first term is easy, since ThetaDot2 just becomes ThetaDotDot2 (as for acceleration), yet the 2nd term gets a bit messy.
The product rule is used to separate the blue parts, and then the chain rule for the red part.
Notice how on the chain rule, the difference of both thetas became the difference of thetadot1-thetadot2.
By hand is fairly easy, but I would like to know if there is a way to do this with Mathematica.