# -*- coding: utf-8 -*-
"""
Created on Tue Jan 20 15:55:08 2015

Listing 11.1 : pendule par l'algorithme d'Euler
@author: grivet
"""

from pylab import *

def smy(t,y,z):
    return z 

def smz(t,y,z):
    return -sin(y)

def euler(h,ti,yi,zi):
    yf = yi + h*smy(ti,yi,zi); zf = zi + h*smz(ti,yi,zi)
    tf = ti + h
    return yf,zf,tf

np = 1200
t = zeros((np,1)) 
y = zeros_like(t); z = zeros_like(t)
y0 = float(input('position initiale (rd): '))
z0 = float(input('vitesse initiale (rd/s): '))
pas = float(input('longueur du pas (rd): '))
t[0] = 0; y[0] = y0; z[0] = z0
for i in range (1,np):
    y[i],z[i],t[i] = euler(pas,t[i-1],y[i-1],z[i-1]);

plot(t,y)
title("mouvement d'un pendule simple")
xlabel('temps')
ylabel('angle')