import matplotlib.pyplot as plt
import numpy as np

g=9.81
alpha=np.pi/4
v0=10.
tf=2.
N=100
tau=tf/N
Nbis=10
lamb=0.
deltalamb=0.1

t=[tau*i for i in range(N)]

for j in range(Nbis):
    vx=[v0*np.cos(alpha)]
    vy=[v0*np.sin(alpha)]
    for i in range(N-1):
        vx.append(vx[i]-lamb*vx[i]*tau)
        vy.append(vy[i]-lamb*vy[i]*tau-g*tau)
    x=[0]
    y=[0]
    for i in range(N-1):
        x.append(x[i]+vx[i]*tau)
        y.append(y[i]+vy[i]*tau)
    lamb=lamb+deltalamb
    plt.plot(x,y)
    plt.axis([0,10,0,5])
    plt.xlabel("x(m)")
    plt.ylabel("y(m)")
    plt.title("Trajectoire en présence de frottements linéaires")
    plt.show()