#!/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_skydive_trajectory.svg' fig = mplwp.fig_standard(mpl) fig.set_size_inches(480. / fig.dpi, 500. / fig.dpi) mplwp.move_axes(fig, 24, 6) xlim = -10,320; fig.gca().set_xlim(xlim) ylim = -340,20; fig.gca().set_ylim(ylim) fig.gca().set_aspect('equal') fig.gca().xaxis.set_major_locator(mpl.ticker.MultipleLocator(100)) fig.gca().yaxis.set_major_locator(mpl.ticker.MultipleLocator(100)) from scipy.integrate import odeint from scipy.optimize import brentq def ballistic(g, mu, 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], -mu*v*vec[2], -g -mu*v*vec[3]] # solve the differenctial 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 = 9.81 vmax = 50. mu = g / vmax**2 alpha0 = 0. for iv, v0 in enumerate((0, 17, 33, 50)): t1 = brentq(lambda t: ballistic(g,mu,[0,0],v0,alpha0,[0,t])[1][1]-ylim[0],0,20) t = np.linspace(0, t1, 5001) x, y = ballistic(g, mu, [0, 0], v0, alpha0, t) plt.plot(x, y, label='$v_0 = {:.0f}\,m/s$'.format(v0), zorder=-iv) col = fig.gca().lines[-1].get_color() xmax = ballistic(g, mu, [0, 0], v0, alpha0, [0, 100*vmax/g])[0][-1] plt.axvline(xmax, 0, 0.33, linestyle='--', dashes=[10,10], color=col, zorder=-5, lw=1.5) times = np.arange(t1) xt, yt = ballistic(g, mu, [0, 0], v0, alpha0, times) plt.plot(xt, yt, '.', color=col, label=None, zorder=-iv-0.5) if v0 == 50.: for ti, xi, yi in zip(times, xt, yt): plt.text(xi+8*sin(pi/2*ti/10), yi+8*cos(pi/2*ti/10), '{:.0f}s'.format(ti), ha='left', va='center', fontsize=10) plt.xlabel('x [m]') plt.ylabel('y [m]') fig.gca().xaxis.labelpad = 0 fig.gca().yaxis.set_label_coords(-0.08, 0.95) mpl.rc('legend', borderaxespad=0.4) plt.legend(loc='upper right') plt.savefig(name) mplwp.postprocess(name)