F = m * a(9.81m/s^2)
x(t) = v(t)
v(t) = a(t) = F/m
small time steps of size h
x(h) = x(0) + hv(0)
v(h) = v(0) + h F/m
from xxxplots import
def forward_euler():
h = 0.1
g = 9.81
num_steps = 50
t = numpy.zeros(num_steps + 1)
x = numpy.zeros(num_steps + 1)
v = numpy.zeros(num_steps + 1)
for step in range(num_steps):
t[step + 1] = h * (step + 1)
x[step + 1] = x[step] + h * v[step]
v[step + 1] = v[step] - h * g
return t, x, v
t, x, v = forward_euler()
@show_plot
def plot_me():
axes_height = matplotlib.pyplot.subplot(211)
matplotlib.pyplot.plot(t, x)
axes_velocity = matplotlib.pyplot.subplot(212)
matplotlib.pyplot.plot(t, v)
axes_height.set_ylabel('Height in m')
axes_velocity.set_ylabel('Velocity in m/s')
axes_velocity.set_xlabel('Time in s')
# Uncomment the line below when running locally.
# matplotlib.pyplot.show()
plot_me()
import numpy import matplotlib.pyplot def forward_euler(): h = 0.1 g = 9.81 num_steps = 50 t = numpy.zeros(num_steps + 1) x = numpy.zeros(num_steps + 1) v = numpy.zeros(num_steps + 1) for step in range(num_steps): t[step + 1] = h * (step + 1) x[step + 1] = x[step] + h * v[step] v[step + 1] = v[step] - h * g return t, x, v t, x, v = froward_euler()
