I have a physics problem and have never used odeint or any numerical solving for ODE on python and am a little confused. I tried looking at other examples but could not understand and am hoping for a little help. My ODE is:
Where α is a given angle and g is a constant.
r=sqrt(x^2+y^2)
The program will ask for x_0, dx/dt_0 and dy/dt_0.
I'm mostly unsure how to solve ODE's in python. I have seen that I should split my ODE into dr'/dt because odeint will only do a first order ODE's. Could someone help explain how to do this?
I tried using another example to do as much as possible but am stuck:
import numpy as np
import matplotlib.pylab as plt
from scipy.integrate import odeint
pi=np.pi
sin=np.sin
cos=np.cos
sqrt=np.sqrt
alpha=pi/4
g=9.80665
y0=0.0
theta0=0.0
x=[]
y=[]
sina = sin(alpha)**2
second_term = g*sin(alpha)*cos(alpha)
x0 = float(raw_input('What is the initial x in meters?'))
x_vel0 = float(raw_input('What is the initial velocity in the x direction in m/s?'))
y_vel0 = float(raw_input('what is the initial velocity in the y direction in m/s?'))
t_f = float(raw_input('What is the maximum time in seconds?'))
r0 = x0
r = sqrt(float(x)**2 + float(y)**2)
def deriv_z(z,r):
r, rdot=z
return [rdot,r*sina-second_term]
zdot0=x_vel0**2+y_vel0**2
z0 = [r0,zdot0]
times = np.linespace(0, t_f, 1000)
z = odeint(deriv_z,z0,times)
