N-body problem: Difference between revisions
Added Go
Thundergnat (talk | contribs) (→{{header|Perl 6}}: Correct syntax errors, limit output (to match what is displayed)) |
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More generally, when two bodies approach closely the resulting curvature forces a smaller step size, which is wasted when calculating details for widely-separated bodies. One ploy is to treat such pairs via two-body formulae (in their centre-of-mass coordinates) for the time of their closeness, retaining a larger time step for the rest of the calculation. This can be further generalised into clumping nearby bodies into a single mass when considering their effect on far-distant bodies. In all of this, the administration requirements become ever-more complex.
=={{header|Go}}==
{{trans|C}}
<lang go>package main
import (
"fmt"
"math"
"os"
)
type vector struct{ x, y, z float64 }
func (v vector) add(w vector) vector {
return vector{v.x + w.x, v.y + w.y, v.z + w.z}
}
func (v vector) sub(w vector) vector {
return vector{v.x - w.x, v.y - w.y, v.z - w.z}
}
func (v vector) scale(m float64) vector {
return vector{v.x * m, v.y * m, v.z * m}
}
func (v vector) mod() float64 {
return math.Sqrt(v.x*v.x + v.y*v.y + v.z*v.z)
}
var (
bodies, timeSteps int
masses []float64
gc float64
positions, velocities, accelerations []vector
)
func initiateSystem(fileName string) error {
file, err := os.Open(fileName)
if err != nil {
return err
}
defer file.Close()
fmt.Fscanf(file, "%f%d%d", &gc, &bodies, &timeSteps)
masses = make([]float64, bodies)
positions = make([]vector, bodies)
velocities = make([]vector, bodies)
accelerations = make([]vector, bodies)
for i := 0; i < bodies; i++ {
fmt.Fscanf(file, "%f", &masses[i])
fmt.Fscanf(file, "%f%f%f", &positions[i].x, &positions[i].y, &positions[i].z)
fmt.Fscanf(file, "%f%f%f", &velocities[i].x, &velocities[i].y, &velocities[i].z)
}
return nil
}
func resolveCollisions() {
for i := 0; i < bodies-1; i++ {
for j := i + 1; j < bodies; j++ {
if positions[i] == positions[j] {
velocities[i], velocities[j] = velocities[j], velocities[i]
}
}
}
}
func computeAccelerations() {
for i := 0; i < bodies; i++ {
accelerations[i] = vector{0, 0, 0}
for j := 0; j < bodies; j++ {
if i != j {
temp := gc * masses[j] / math.Pow(positions[i].sub(positions[j]).mod(), 3)
accelerations[i] = accelerations[i].add(positions[j].sub(positions[i]).scale(temp))
}
}
}
}
func computeVelocities() {
for i := 0; i < bodies; i++ {
velocities[i] = velocities[i].add(accelerations[i])
}
}
func computePositions() {
for i := 0; i < bodies; i++ {
positions[i] = positions[i].add(velocities[i].add(accelerations[i].scale(0.5)))
}
}
func simulate() {
computeAccelerations()
computePositions()
computeVelocities()
resolveCollisions()
}
func printResults() {
f := "Body %d : % 8.6f % 8.6f % 8.6f | % 8.6f % 8.6f % 8.6f\n"
for i := 0; i < bodies; i++ {
fmt.Printf(
f, i+1,
positions[i].x, positions[i].y, positions[i].z,
velocities[i].x, velocities[i].y, velocities[i].z,
)
}
}
func main() {
if len(os.Args) != 2 {
fmt.Printf("Usage : %s <file name containing system configuration data>\n", os.Args[0])
} else {
err := initiateSystem(os.Args[1])
if err != nil {
fmt.Println(err)
return
}
fmt.Print("Body : x y z |")
fmt.Println(" vx vy vz")
for i := 0; i < timeSteps; i++ {
fmt.Printf("\nCycle %d\n", i+1)
simulate()
printResults()
}
}
}</lang>
Contents of nbody.txt:
<pre>
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
</pre>
{{out}}
<pre>
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|J}}==
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