189 lines
4.2 KiB
Python
189 lines
4.2 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Created on Sat Jul 05 09:54:39 2014
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@author: rlabbe
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"""
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from __future__ import division, print_function
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import matplotlib.pyplot as plt
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from scipy.integrate import ode
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import math
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import numpy as np
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from numpy import random, radians, cos, sin
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class BallTrajectory2D(object):
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def __init__(self, x0, y0, velocity, theta_deg=0., g=9.8, noise=[0.0,0.0]):
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theta = radians(theta_deg)
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self.vx0 = velocity * cos(theta)
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self.vy0 = velocity * sin(theta)
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self.x0 = x0
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self.y0 = y0
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self.x = x
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self.g = g
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self.noise = noise
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def position(self, t):
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""" returns (x,y) tuple of ball position at time t"""
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self.x = self.vx0*t + self.x0
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self.y = -0.5*self.g*t**2 + self.vy0*t + self.y0
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return (self.x +random.randn()*self.noise[0], self.y +random.randn()*self.noise[1])
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class BallEuler(object):
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def __init__(self, y=100., vel=10., omega=0):
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self.x = 0.
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self.y = y
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omega = radians(omega)
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self.vel = vel*np.cos(omega)
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self.y_vel = vel*np.sin(omega)
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def step (self, dt):
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g = -9.8
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self.x += self.vel*dt
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self.y += self.y_vel*dt
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self.y_vel += g*dt
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#print self.x, self.y
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def rk4(y, x, dx, f):
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"""computes 4th order Runge-Kutta for dy/dx.
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y is the initial value for y
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x is the initial value for x
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dx is the difference in x (e.g. the time step)
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f is a callable function (y, x) that you supply to compute dy/dx for
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the specified values.
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"""
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k1 = dx * f(y, x)
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k2 = dx * f(y + 0.5*k1, x + 0.5*dx)
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k3 = dx * f(y + 0.5*k2, x + 0.5*dx)
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k4 = dx * f(y + k3, x + dx)
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return y + (k1 + 2*k2 + 2*k3 + k4) / 6.
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def fx(x,t):
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return fx.vel
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def fy(y,t):
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return fy.vel - 9.8*t
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class BallRungeKutta(object):
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def __init__(self, x=0, y=100., vel=10., omega = 0.0):
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self.x = x
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self.y = y
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self.t = 0
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omega = math.radians(omega)
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fx.vel = math.cos(omega) * vel
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fy.vel = math.sin(omega) * vel
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def step (self, dt):
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self.x = rk4 (self.x, self.t, dt, fx)
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self.y = rk4 (self.y, self.t, dt, fy)
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self.t += dt
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print(fx.vel)
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return (self.x, self.y)
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def ball_scipy(y0, vel, omega, dt):
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vel_y = math.sin(math.radians(omega)) * vel
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def f(t,y):
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return vel_y-9.8*t
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solver = ode(f).set_integrator('dopri5')
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solver.set_initial_value(y0)
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ys = [y0]
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while brk.y >= 0:
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t += dt
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brk.step (dt)
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ys.append(solver.integrate(t))
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def RK4(f):
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return lambda t, y, dt: (
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lambda dy1: (
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lambda dy2: (
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lambda dy3: (
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lambda dy4: (dy1 + 2*dy2 + 2*dy3 + dy4)/6
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)( dt * f( t + dt , y + dy3 ) )
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)( dt * f( t + dt/2, y + dy2/2 ) )
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)( dt * f( t + dt/2, y + dy1/2 ) )
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)( dt * f( t , y ) )
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def theory(t): return (t**2 + 4)**2 /16
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from math import sqrt
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dy = RK4(lambda t, y: t*sqrt(y))
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t, y, dt = 0., 1., .1
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while t <= 10:
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if abs(round(t) - t) < 1e-5:
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print("y(%2.1f)\t= %4.6f \t error: %4.6g" % (t, y, abs(y - theory(t))))
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t, y = t + dt, y + dy(t, y, dt)
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t = 0.
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y=1.
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def test(y, t):
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return t*sqrt(y)
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while t <= 10:
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if abs(round(t) - t) < 1e-5:
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print("y(%2.1f)\t= %4.6f \t error: %4.6g" % (t, y, abs(y - theory(t))))
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y = rk4(y, t, dt, test)
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t += dt
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if __name__ == "__main__":
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1/0
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dt = 1./30
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y0 = 15.
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vel = 100.
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omega = 30.
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vel_y = math.sin(math.radians(omega)) * vel
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def f(t,y):
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return vel_y-9.8*t
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be = BallEuler (y=y0, vel=vel,omega=omega)
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#be = BallTrajectory2D (x0=0, y0=y0, velocity=vel, theta_deg = omega)
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ball_rk = BallRungeKutta (y=y0, vel=vel, omega=omega)
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while be.y >= 0:
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be.step (dt)
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ball_rk.step(dt)
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print (ball_rk.y - be.y)
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'''
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p1 = plt.scatter (be.x, be.y, color='red')
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p2 = plt.scatter (ball_rk.x, ball_rk.y, color='blue', marker='v')
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plt.legend([p1,p2], ['euler', 'runge kutta'])
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''' |