Coding a Numerical Solution to the Simple Pendulum Problem using Python

Using Python to code a numerical method to solve the nonlinear equation of motion for the simple pendulum.

[adrpsch]

Great stuff! Thanks for the video. As a suggestion, Python in the title could be useful while searching.

[prof.onkarsalavi]

At 45 deg or even more than that..wave must be flattened at the picks...so that nonlinear case would be clearly visible... check alternative numerical method

[David-bgrj]

why when I write def equation(t, y0), instead of def equation(y0, t) I have this error message :
theta, x = y0

TypeError: cannot unpack non-iterable float object

And for example for this code the inverse works...
def dSdx(x, S):
y1, y2 = S
return [y1 + y2**2 + 3*x,
3*y1 + y2**3 - np.cos(x)]
y1_0 = 0
y2_0 = 0
S_0 = (y1_0, y2_0)
x = np.linspace(0, 1, 100)
sol = odeint(dSdx, S_0, x, tfirst=True)

Thanks for the answer

[mckenflores]

Hello, Sir. I tried implementing the same routine using the odeint function. I noticed that the resulting values for theta using the nonlinear solution do not vary, even when I try to use different time steps (0.001s, 0.01s, and 0.05s). Shouldn't there be noticeable differences in the resulting values of theta with varying time steps? Thank you.

[natorgas]

Hello, very clear explanation, but what exactly happens with all the time steps? Like where are they used? Because in the function itself there in no variable "t" so then what does the program do with those values?

[n.nailiirsya]

may i know how to using this method but to plot angular velocity vs time and angular velocity vs angle? and may I know theta1 and theta2 are represent for what (angular acceleration or angle). thank you.

[KonradGebura]

If anyone is having errors if you do not know pip install scipy in terminal

[carlosaugustoramosjaramill]

How would it be using curve_fit () function instead of odeint() ? and what differences would it have?

[isaacmutie]

This is awesome, How do I do the phase space plot?

[pranaypurohit]

please do more videos please please these are awesome

[PrashantKumar-cqlj]

What is the initial vector space 'y0'?
You haven't defined it anywhere.

[furkanakal]

What causes the difference between linear and nonlinear solutions?

[JeXuZ]

what's the numeric method that odeint() uses for solving the equations?, can we change it? (I use Euler on Matlab)

[pulkitmahera]

Watch the following video for the graph plotting using python language:-