Loop inside of a loop in Python-CodePudding

The below is code for the modelling of a cannoball's movement with drag, where solve_euler is a predefined function, that produces an array of arrays (like a table) of values. Of these values the xs and the ys are exported for this bit of code and are called xs_euler and ys_euler. These values are the x and y coordinates of the cannonball until time t1 (some defined number used in the solve_euler function, in this case t1 = 300). What I am trying to now do, is plot a graph of the new x and y values (by multiplying by velocity and time), showing how the paths differ depending on the launch angle. The following is what I have at the moment:

import math as m
import matplotlib.pylab as plot
import numpy

n_steps = 1000
theta = numpy.arange(m.pi/36, m.pi/2, m.pi/36)

v = 200
g = 9.81


initial_conditions = [0, 0, 88.38834764831843, 88.38834764831843]    
values_euler = solve_euler(initial_conditions, 300, n_steps)

xs_euler, ys_euler = values_euler[:,0], values_euler[:,1]

plt.plot(xs_euler, ys_euler, color='blue', linestyle='--')
plt.xlim(0,1500)
plt.ylim(0,800);


t = numpy.linspace(0, 500, num=1000) # Set time as 'continous' parameter.


for i in theta: # Calculate trajectory for every angle
    for k in t:
        x = ((v*k)*xs_euler*numpy.cos(i)) # get positions at every point in time
        y = ((v*k)*ys_euler*numpy.sin(i))-((0.5*g)*(k**2))

    
    plot.plot(x1, y1) # Plot for every angle

plot.show() # And show on one graphic

Here it should be pretty obvious that I don't know how to use xs_euler and the ys_euler, in the loop, whilst also being able to do a loop on the time and on the launch angle (theta). Can someone show me where I am going wrong and how to fix it?

CodePudding user response：

I'm assuming you want your graphs to be y(t) vs x(t) for all time points, in that case you will need to store all values of x and y over time while iterating for each theta:

My suggestion would be to create a list of the x and y values for a given theta, iterating over time. This can be written with list comprehension to overwrite for each value of i, if you don't need to store it. If you do, I would just write it to columns of a dataframe.

And another thing that I am slightly confused by is your plot is called "plt" in some instances and "plot" in others. I would recommend keeping it consistent with how you import it (which is as "plot" in import matplotlib.pylab as plot)

for i in theta: # Calculate trajectory for every angle
    x = [((v*k)*xs_euler*numpy.cos(i)) for k in t] # get positions at every point in time
    y = [((v*k)*ys_euler*numpy.sin(i))-((0.5*g)*(k**2)) for k in t]

    plot.plot(x, y) # Plot for every angle
plot.show()

CodePudding user response：

Your problem isn't with coding, it's with the math.

Unless I'm not understanding what solve_euler is, you shouldn't need to modify xs_euler or ys_euler, those are already the x and y coordinates of the ball at different points in time. BUT the solve_euler function only returns data for ONE initial condition - meaning if you want data for a different initial angle, you need to call it again (You can't use data from one initial condition to calculate trajectories of a different initial condition. This system doesn't work that way - almost no systems do).

So you have to iterate through angles and call solve_euler each time, and plot the data that it returns.

Some pseudocode:

create matplotlib figure, set all axes and whatnot

for angle-you-want-to-iterate-through:
    vx0 = x-component of initial velocity (will have a cos(angle))
    vy0 = y-component of initial velocity (will have a sin(angle))
    initial conditions are [x0, y0, vx0, vy0]
    data = result of solve_euler with the new initial conditions
    plot data[:0] vs data[:1], label with angle

add a legend to plot