134 lines
2.7 KiB
Python
134 lines
2.7 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
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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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class BallEuler(object):
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def __init__(self, y=100., vel=10.):
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self.x = 0.
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self.y = y
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self.vel = vel
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self.y_vel = 0.0
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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 fy(y, t):
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""" returns velocity of ball at time t. """
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return -9.8*t
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def fx(y, t):
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""" returns velocity of ball. Need to set vx.vel prior to first call"""
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return fx.vel
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def fx2(x,t):
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return fx2.vel
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def fy2(y,t):
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return fy2.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.omega = math.radians(omega)
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self.vx = math.cos(self.omega) * vel
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self.vy = math.sin(self.omega) * vel
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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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fx2.vel = self.vx
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fy2.vel = self.vy
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def step (self, dt):
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self.x = rk4 (self.x, self.t, dt, fx2)
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self.y = rk4 (self.y, self.t, dt, fy2)
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self.t += dt
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print self.x, self.y
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if __name__ == "__main__":
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dt = 1./30
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y0 = 15.
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vel = 100.
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omega = 10.
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vel_y = math.sin(math.radians(omega)) * vel
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print vel_y
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def f(t,y):
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#print t,y
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return vel_y-9.8*t
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be = BallEuler (y=y0, vel=vel)
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brk = BallRungeKutta (y=y0, vel=vel, omega=omega)
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solver = ode(f).set_integrator('dopri5')
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solver.set_initial_value(y0)
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t = 0
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y = y0
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while be.y >= 0:
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be.step (dt)
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#plt.scatter (be.x, be.y, color='red')
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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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y = solver.integrate(t)
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plt.scatter (brk.x, brk.y, color='blue', marker='v')
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plt.scatter (brk.x, y[0], color='green', marker='+')
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plt.axis('equal')
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