#!/usr/bin/python # -*- coding: utf8 -*- import matplotlib.pyplot as plt import matplotlib as mpl import numpy as np from math import * code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp' try: import mplwp except ImportError, er: print 'ImportError:', er print 'You need to download mplwp.py from', code_website exit(1) name = 'mplwp_ballistic_trajectories_velocities.svg' fig = mplwp.fig_standard(mpl) xlim = 0,2.6; fig.gca().set_xlim(xlim) ylim = 0,2.6*355/515.; fig.gca().set_ylim(ylim) fig.gca().xaxis.set_major_locator(mpl.ticker.MultipleLocator(0.4)) fig.gca().yaxis.set_major_locator(mpl.ticker.MultipleLocator(0.4)) from scipy.integrate import odeint from scipy.optimize import brentq def ballistic(g, k, xy0, v0, alpha0, tt): # use a four-dimensional vector function vec = [x, y, vx, vy] def dif(vec, t): v = sqrt(vec[2]**2 + vec[3]**2) return [vec[2], vec[3], -k*v*vec[2], -g -k*v*vec[3]] # solve the differential equation numerically vec = odeint(dif, [xy0[0], xy0[1], v0*cos(alpha0), v0*sin(alpha0)], tt) return vec[:,0], vec[:,1] # return x(tt) and y(tt) g = 1.0 k = 1.0 alpha0 = pi/4 for v0 in np.linspace(0, 10, 6)[1:]: t1 = brentq(lambda t: ballistic(g,k,[0,0],v0,alpha0,[0,t])[1][1],0.1,5) t = np.linspace(0, t1, 5001) x, y = ballistic(g, k, [0, 0], v0, alpha0, t) while len(y) > 1 and y[-2] <= 0.0: x = x[:-1]; y = y[:-1] plt.plot(x, y, label=ur'$v_0=\,{:.0f}$'.format(v0)) mpl.rc('legend', borderaxespad=1.0) plt.legend(loc='upper left').get_frame().set_alpha(0.9) plt.savefig(name) mplwp.postprocess(name) 
