import streamlit as st
import matplotlib.pyplot as plt
import math

st.title("Simulação de esfera em queda livre")

m = st.slider("mass", 2.0, 3.0, 2.6)
L = st.slider("length", 0.5, 2.0, 1.0)

def run_simulation():

 R = 0.03
rho = 1.28
g = 9.81
cd = 0.1
A = math.pi * R**2
b = 1/2 * rho * cd * A
theta0 = 0.05
w0 = 0.0
t0 = 0.0
h = 0.1
t = [t0]
theta = [theta0]
w = [w0]
k1x = 0
k1v = 0
k2x = 0
k2v = 0
while t[-1] < 100.0:
 k1x = w[-1]
 k1v = -math.copysign(1, w[-1]) * (((bL)/m) * w[-1]**2) - (g / L) * theta[-1]
 k2x = w[-1] + k1v * h
 k2v = -math.copysign(1, w[-1] + k1v * h) * (((bL)/m )* (w[-1] + k1v * h)**2) - (g / L) * (theta[-1] + k1x * h)
theta.append(theta[-1] + ((k1x + k2x) / 2.0)*h)
w.append(w[-1] + ((k1v + k2v) / 2.0)*h)
t.append(t[-1] + h)
plt.plot(t, theta, 'r')
plt.plot(t, w, 'b')
plt.legend(['Theta', 'w'])
plt.xlabel('time (s)')
plt.ylabel('Theta (rad), w (rad/s)')
st.pyplot()

if st.button("Run simulation"):

 run_simulation()