def plot_move_odeint():
states = [array([x1, y1, vx1, vy1, x2, y2, vx2, vy2])]
states = odeint(move_, states[-1], times)
states = array(states)
earth = [states[:,0], states[:,1]]
jupiter = [states[:,4], states[:,5]]
sun = mpimg.imread('sun.png')
fig, ax = subplots()
ax.imshow(sun, aspect='auto', extent=(-.1, .1, -.1, .1), zorder=1)
e_mark0, = ax.plot(earth[0], earth[1], 'b-', lw=2, alpha=.4)
e_mark1, = ax.plot(earth[0], earth[1], 'bo', ms=5, alpha=.4)
j_mark0, = ax.plot(jupiter[0], jupiter[1], 'r-', lw=2, alpha=.4)
j_mark1, = ax.plot(jupiter[0], jupiter[1], 'ro', ms=7, alpha=.4)
legend( [(e_mark0, e_mark1), (j_mark0, j_mark1)],
['Earth Orbit:\t$m_{\mathcal{E}}='+str(m1)+'$',
'Jupiter Orbit:\t$m_{\mathcal{J}}='+str(m2)+'$'],
numpoints=1)
configure( ax=ax,
title=r'$'+str(tf-t0)+'$ Years; $\Delta t='+str(dt)+'$',
xlabel=r'Displacement (AU)',
ylabel=r'Displacement (AU)',
xbounds=None, ybounds=None)
fig.suptitle('VODE - Orbit of Two Planets About a Fixed Star', size=30)
fig.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.08)
show()
def main():
#~ State Variables
t0 = 0
tf = .3
dt = .001
times = arange(t0, tf + dt, dt)
#/~ State Variables
#~ Bullet-specific Variables
name = '50 ATV BT'
b = bullet(name, mass=50., bc=0.242, model=G1)
#~/ Bullet-Specific Variables
#~ Get Samples
from sample_data import samples
vm = samples[name]['v'][:, 1][0]
sight = samples[name]['st'][:, 0][2]
x = samples[name]['st'][:, 0]
y = samples[name]['st'][:, 1]
#/~ Get Samples
#~ Integrate
theta = find_angle(sight, vm, b, times)
print "THETA:", theta
y0 = [0., 0., vm * cos(theta), vm * sin(theta)]
states = odeint(b.shoot, y0, times)
states = array(states)
#/~ Integrate
#~ Plot
fig, ax = subplots()
r_mark, = ax.plot(x, y, 'ro-', alpha=.8)
b_mark, = ax.plot(states[:, 0] / 3.,
states[:, 1] * 12.,
'b-',
lw=3,
alpha=.8)
legend([r_mark, b_mark],
['Sample Trajectory', 'Simulated (' + str(b) + ')'],
numpoints=1)
configure(ax=ax,
title=r'G1 Model of Remington .233 cartridge' + '\n' +
r'$\theta\approx' + str(round(theta, 6)) + r'$ radians',
xlabel=r'Horizontal Displacement (yards)',
ylabel=r'Height (inches)',
xbounds=None,
ybounds=None)
fig.suptitle('Bullet Trajectory Simulation', size=30)
fig.subplots_adjust(left=0.05, right=0.95, top=0.9, bottom=0.08)
show()
def main():
#~ State Variables
t0 = 0
tf = 0.5
dt = .001
times = np.linspace(t0, tf, 200)
#/~ State Variables
#~ Bullet-specific Variables
name = '50 ATV BT'
b = bullet(name, mass=50, bc=0.242, model=G1)
vtot = 3300 #
theta = 0.05
vxi = vtot * (cos(theta * pi / 180))
vyi = vtot * (sin(theta * pi / 180))
#~/ Bullet-Specific Variables
#~ Integrate
y0 = [0., 0., vxi, vyi]
states = odeint(b.shoot, y0, times)
states = array(states)
#/~ Integrate
#~ Get Samples
from sample_data import samples
x = samples[name]['st'][:, 0]
#print len(x)
y = samples[name]['st'][:, 1]
#print len(y)
#/~ Get Samples
#~ Plot
fig, ax = subplots()
r_mark, = ax.plot(x, y, 'ro', alpha=.8)
b_mark, = ax.plot(states[:, 0], states[:, 1] * 12., 'bo', lw=3, alpha=.8)
legend([r_mark, b_mark],
['Sample Trajectory', 'Simulated (' + str(b) + ')'],
numpoints=1)
configure(ax=ax,
title=r'G1 Model of Remington .233 cartridge',
xlabel=r'Horizontal Displacement (yards)',
ylabel=r'Height (inches)',
xbounds=None,
ybounds=None)
fig.suptitle('Bullet Trajectory Simulation', size=30)
fig.subplots_adjust(left=0.05, right=0.95, top=0.9, bottom=0.08)
show()
def main():
# ~ State Variables
t0 = 0
tf = 0.3
dt = 0.001
times = arange(t0, tf + dt, dt)
# /~ State Variables
# ~ Bullet-specific Variables
name = "50 ATV BT"
b = bullet(name, mass=50.0, bc=0.242, model=G1)
# ~/ Bullet-Specific Variables
# ~ Get Samples
from sample_data import samples
vm = samples[name]["v"][:, 1][0]
sight = samples[name]["st"][:, 0][2]
x = samples[name]["st"][:, 0]
y = samples[name]["st"][:, 1]
# /~ Get Samples
# ~ Integrate
theta = find_angle(sight, vm, b, times)
print "THETA:", theta
y0 = [0.0, 0.0, vm * cos(theta), vm * sin(theta)]
states = odeint(b.shoot, y0, times)
states = array(states)
# /~ Integrate
# ~ Plot
fig, ax = subplots()
r_mark, = ax.plot(x, y, "ro-", alpha=0.8)
b_mark, = ax.plot(states[:, 0] / 3.0, states[:, 1] * 12.0, "b-", lw=3, alpha=0.8)
legend([r_mark, b_mark], ["Sample Trajectory", "Simulated (" + str(b) + ")"], numpoints=1)
configure(
ax=ax,
title=r"G1 Model of Remington .233 cartridge" + "\n" + r"$\theta\approx" + str(round(theta, 6)) + r"$ radians",
xlabel=r"Horizontal Displacement (yards)",
ylabel=r"Height (inches)",
xbounds=None,
ybounds=None,
)
fig.suptitle("Bullet Trajectory Simulation", size=30)
fig.subplots_adjust(left=0.05, right=0.95, top=0.9, bottom=0.08)
show()
def main():
#~ State Variables
t0 = 0; tf = 0.5; dt=.001;
times = np.linspace(t0, tf, 200)
#/~ State Variables
#~ Bullet-specific Variables
name = '50 ATV BT'
b = bullet(name, mass=50, bc=0.242, model=G1)
vtot = 3300 #
theta = 0.05
vxi = vtot*(cos(theta*pi/180))
vyi = vtot*(sin(theta*pi/180))
#~/ Bullet-Specific Variables
#~ Integrate
y0 = [0., 0., vxi, vyi]
states = odeint(b.shoot, y0, times)
states = array(states)
#/~ Integrate
#~ Get Samples
from sample_data import samples
x = samples[name]['st'][:,0]; #print len(x)
y = samples[name]['st'][:,1]; #print len(y)
#/~ Get Samples
#~ Plot
fig, ax = subplots()
r_mark, = ax.plot(x, y, 'ro', alpha=.8)
b_mark, = ax.plot(states[:,0], states[:,1]*12., 'bo', lw=3, alpha=.8)
legend( [r_mark, b_mark],
['Sample Trajectory',
'Simulated ('+str(b)+')'],
numpoints=1)
configure( ax=ax,
title=r'G1 Model of Remington .233 cartridge',
xlabel=r'Horizontal Displacement (yards)',
ylabel=r'Height (inches)',
xbounds=None, ybounds=None)
fig.suptitle('Bullet Trajectory Simulation', size=30)
fig.subplots_adjust(left=0.05, right=0.95, top=0.9, bottom=0.08)
show()
def plot_conservation():
fig, ax = subplots()
tax = ax.twinx()
atols = [.00001, .000001, .0000001]
y0 = array([x1, y1, vx1, vy1, x2, y2, vx2, vy2])
for i,atol in enumerate(atols):
states = odeint(move_, y0, times, atol=atol)
enrgy = []
for state in states:
enrgy.append(energy(state))
am = []
for state in states:
am.append(angular_momentum(state))
alpha = (i+1.) / (len(atols)+1.)
e_mark, = ax.plot(times, enrgy, 'b--', lw=3, alpha=alpha)
am_mark, = tax.plot(times, am, 'r--', lw=3, alpha=alpha)
legend( [e_mark, am_mark],
[r'$E = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 - \frac{GMm_1}{r_1} - \frac{GMm_2}{r_2} - \frac{Gm_2m1}{r_21}$',
r'$L = m_1 \left( x_1 v_{y1} - y_1 v_{x1} \right) + m_2 \left( x_2 v_{y2} - y_2 v_{x2} \right)$'],
numpoints=1, loc='upper right')
configure( ax=ax,
title=r'Absolute Tolerances: '+str(atols),
xlabel=r'Time (years)',
ylabel=r'Energy (Joules)',
colors=('k', 'b'))
configure( ax=tax,
ylabel=r'Angular Momentum $\left(kg\frac{m^2}{s}\right)$',
xbounds=(t0,tf+dt), colors=('k', 'r'), suppress=True)
fig.suptitle('Conservation of Energy and Angular Momentum', size=30)
fig.subplots_adjust(left=0.075, right=0.95, top=0.9, bottom=0.08)
show()
