N-body problem: Difference between revisions

Line 4,065:

t = 0.18 : +2.919e-10 +3.488e-18 +0.000e+00 +1.500e+11 +5.376e+03 +0.000e+00 +1.497e+11 +5.563e+03 +0.000e+00 +3.243e-09 +5.814e-17 +0.000e+00 -1.078e-03 +2.987e+04 +0.000e+00 -2.712e-04 +3.090e+04 +0.000e+00

t = 0.19 : +3.252e-10 +4.102e-18 +0.000e+00 +1.500e+11 +5.674e+03 +0.000e+00 +1.497e+11 +5.872e+03 +0.000e+00 +3.423e-09 +6.477e-17 +0.000e+00 -1.138e-03 +2.987e+04 +0.000e+00 -2.863e-04 +3.090e+04 +0.000e+00</pre>

=={{header|Python}}==

<lang python>import math

class Vector:

def __init__(self, x, y, z):

self.x = x

self.y = y

self.z = z

def __add__(self, other):

return Vector(self.x + other.x, self.y + other.y, self.z + other.z)

def __sub__(self, other):

return Vector(self.x - other.x, self.y - other.y, self.z - other.z)

def __mul__(self, other):

return Vector(self.x * other, self.y * other, self.z * other)

def __div__(self, other):

return Vector(self.x / other, self.y / other, self.z / other)

def __eq__(self, other):

if isinstance(other, Vector):

return self.x == other.x and self.y == other.y and self.z == other.z

return False

def __ne__(self, other):

return not self.__eq__(other)

def __str__(self):

return '({x}, {y}, {z})'.format(x=self.x, y=self.y, z=self.z)

def abs(self):

return math.sqrt(self.x*self.x + self.y*self.y + self.z*self.z)

origin = Vector(0, 0, 0)

class NBody:

def __init__(self, fileName):

with open(fileName, "r") as fh:

lines = fh.readlines()

gbt = lines[0].split()

self.gc = float(gbt[0])

self.bodies = int(gbt[1])

self.timeSteps = int(gbt[2])

self.masses = [0.0 for i in range(self.bodies)]

self.positions = [origin for i in range(self.bodies)]

self.velocities = [origin for i in range(self.bodies)]

self.accelerations = [origin for i in range(self.bodies)]

for i in range(self.bodies):

self.masses[i] = float(lines[i*3 + 1])

self.positions[i] = self.__decompose(lines[i*3 + 2])

self.velocities[i] = self.__decompose(lines[i*3 + 3])

print "Contents of", fileName

for line in lines:

print line.rstrip()

print

print "Body : x y z |",

print " vx vy vz"

def __decompose(self, line):

xyz = line.split()

x = float(xyz[0])

y = float(xyz[1])

z = float(xyz[2])

return Vector(x, y, z)

def __computeAccelerations(self):

for i in xrange(self.bodies):

self.accelerations[i] = origin

for j in xrange(self.bodies):

if i != j:

temp = self.gc * self.masses[j] / math.pow((self.positions[i] - self.positions[j]).abs(), 3)

self.accelerations[i] += (self.positions[j] - self.positions[i]) * temp

return None

def __computePositions(self):

for i in xrange(self.bodies):

self.positions[i] += self.velocities[i] + self.accelerations[i] * 0.5

return None

def __computeVelocities(self):

for i in xrange(self.bodies):

self.velocities[i] += self.accelerations[i]

return None

def __resolveCollisions(self):

for i in xrange(self.bodies):

for j in xrange(self.bodies):

if self.positions[i] == self.positions[j]:

(self.velocities[i], self.velocities[j]) = (self.velocities[j], self.velocities[i])

return None

def simulate(self):

self.__computeAccelerations()

self.__computePositions()

self.__computeVelocities()

self.__resolveCollisions()

return None

def printResults(self):

fmt = "Body %d : % 8.6f % 8.6f % 8.6f | % 8.6f % 8.6f % 8.6f"

for i in xrange(self.bodies):

print fmt % (i+1, self.positions[i].x, self.positions[i].y, self.positions[i].z, self.velocities[i].x, self.velocities[i].y, self.velocities[i].z)

return None

nb = NBody("nbody.txt")

for i in xrange(nb.timeSteps):

print "\nCycle %d" % (i + 1)

nb.simulate()

nb.printResults()</lang>

<pre>Contents of nbody.txt

0.01 3 20

1

0 0 0

0.01 0 0

0.1

1 1 0

0 0 0.02

0.001

0 1 1

0.01 -0.01 -0.01

Body : x y z | vx vy vz

Cycle 1

Body 1 : 0.010177 0.000179 0.000002 | 0.010354 0.000357 0.000004

Body 2 : 0.998230 0.998232 0.020002 | -0.003539 -0.003536 0.020004

Body 3 : 0.010177 0.988232 0.988055 | 0.010354 -0.013536 -0.013889

Cycle 2

Body 1 : 0.020709 0.000718 0.000011 | 0.010710 0.000721 0.000014

Body 2 : 0.992907 0.992896 0.039971 | -0.007109 -0.007138 0.019935

Body 3 : 0.020717 0.972888 0.972173 | 0.010727 -0.017153 -0.017876

Cycle 3

Body 1 : 0.031600 0.001625 0.000034 | 0.011072 0.001094 0.000033

Body 2 : 0.983985 0.983910 0.059834 | -0.010735 -0.010835 0.019790

Body 3 : 0.031643 0.953868 0.952235 | 0.011125 -0.020886 -0.021999

Cycle 4

Body 1 : 0.042858 0.002913 0.000081 | 0.011443 0.001481 0.000060

Body 2 : 0.971393 0.971163 0.079509 | -0.014448 -0.014659 0.019561

Body 3 : 0.042981 0.931039 0.928087 | 0.011552 -0.024772 -0.026299

Cycle 5

Body 1 : 0.054492 0.004595 0.000160 | 0.011826 0.001884 0.000097

Body 2 : 0.955030 0.954509 0.098909 | -0.018278 -0.018649 0.019238

Body 3 : 0.054766 0.904225 0.899522 | 0.012018 -0.028857 -0.030829

Cycle 6

Body 1 : 0.066517 0.006691 0.000281 | 0.012224 0.002308 0.000145

Body 2 : 0.934759 0.933760 0.117931 | -0.022265 -0.022849 0.018806

Body 3 : 0.067040 0.873197 0.866280 | 0.012530 -0.033199 -0.035655

Cycle 7

Body 1 : 0.078950 0.009225 0.000456 | 0.012642 0.002759 0.000206

Body 2 : 0.910400 0.908677 0.136456 | -0.026454 -0.027316 0.018244

Body 3 : 0.079856 0.837662 0.828023 | 0.013101 -0.037871 -0.040861

Cycle 8

Body 1 : 0.091815 0.012227 0.000702 | 0.013086 0.003245 0.000284

Body 2 : 0.881722 0.878958 0.154340 | -0.030902 -0.032122 0.017523

Body 3 : 0.093281 0.797239 0.784313 | 0.013749 -0.042975 -0.046559

Cycle 9

Body 1 : 0.105140 0.015737 0.001035 | 0.013564 0.003775 0.000383

Body 2 : 0.848429 0.844216 0.171401 | -0.035684 -0.037362 0.016600

Body 3 : 0.107405 0.751427 0.734579 | 0.014498 -0.048649 -0.052908

Cycle 10

Body 1 : 0.118964 0.019805 0.001481 | 0.014085 0.004362 0.000509

Body 2 : 0.810137 0.803953 0.187408 | -0.040900 -0.043166 0.015414

Body 3 : 0.122346 0.699554 0.678056 | 0.015384 -0.055097 -0.060138

Cycle 11

Body 1 : 0.133337 0.024498 0.002071 | 0.014662 0.005025 0.000672

Body 2 : 0.766343 0.757509 0.202050 | -0.046687 -0.049720 0.013868

Body 3 : 0.138268 0.640690 0.613685 | 0.016460 -0.062633 -0.068603

Cycle 12

Body 1 : 0.148327 0.029907 0.002851 | 0.015317 0.005792 0.000888

Body 2 : 0.716377 0.703998 0.214889 | -0.053246 -0.057302 0.011810

Body 3 : 0.155406 0.573482 0.539941 | 0.017816 -0.071782 -0.078886

Cycle 13

Body 1 : 0.164025 0.036157 0.003887 | 0.016079 0.006709 0.001184

Body 2 : 0.659310 0.642172 0.225282 | -0.060887 -0.066351 0.008976

Body 3 : 0.174112 0.495836 0.454475 | 0.019596 -0.083511 -0.092045

Cycle 14

Body 1 : 0.180564 0.043437 0.005286 | 0.017000 0.007852 0.001613

Body 2 : 0.593807 0.570186 0.232208 | -0.070119 -0.077621 0.004875

Body 3 : 0.194929 0.404136 0.353320 | 0.022038 -0.099890 -0.110265

Cycle 15

Body 1 : 0.198150 0.052049 0.007234 | 0.018171 0.009372 0.002283

Body 2 : 0.517817 0.485100 0.233878 | -0.081861 -0.092550 -0.001535

Body 3 : 0.218605 0.290860 0.228583 | 0.025314 -0.126661 -0.139210

Cycle 16

Body 1 : 0.217126 0.062542 0.010117 | 0.019781 0.011614 0.003484

Body 2 : 0.427899 0.381659 0.226654 | -0.097974 -0.114332 -0.012913

Body 3 : 0.244268 0.131956 0.057562 | 0.026013 -0.191148 -0.202831

Cycle 17

Body 1 : 0.238346 0.076539 0.015221 | 0.022658 0.016380 0.006723

Body 2 : 0.317489 0.248502 0.200967 | -0.122846 -0.151982 -0.038461

Body 3 : 0.075592 -0.559591 -0.487315 | -0.363366 -1.191945 -0.886924

Cycle 18

Body 1 : 0.263123 0.097523 0.026918 | 0.026898 0.025587 0.016672

Body 2 : 0.173428 0.050424 0.112716 | -0.165275 -0.244174 -0.138041

Body 3 : -0.286241 -1.745597 -1.369528 | -0.360299 -1.180066 -0.877501

Cycle 19

Body 1 : 0.270854 0.113045 0.061923 | -0.011436 0.005457 0.053339

Body 2 : 0.199821 -0.093105 -0.208666 | 0.218061 -0.042882 -0.504723

Body 3 : -0.646318 -2.924909 -2.246453 | -0.359856 -1.178559 -0.876350

Cycle 20

Body 1 : 0.258572 0.116046 0.112038 | -0.013129 0.000544 0.046890

Body 2 : 0.426346 -0.111425 -0.681150 | 0.234987 0.006241 -0.440245

Body 3 : -1.006089 -4.103186 -3.122591 | -0.359686 -1.177995 -0.875924</pre>

=={{header|Tcl}}==