N-body problem: Difference between revisions
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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. |
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. |
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=={{header|Go}}== |
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{{trans|C}} |
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<lang go>package main |
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import ( |
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"fmt" |
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"math" |
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"os" |
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) |
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type vector struct{ x, y, z float64 } |
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func (v vector) add(w vector) vector { |
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return vector{v.x + w.x, v.y + w.y, v.z + w.z} |
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} |
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func (v vector) sub(w vector) vector { |
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return vector{v.x - w.x, v.y - w.y, v.z - w.z} |
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} |
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func (v vector) scale(m float64) vector { |
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return vector{v.x * m, v.y * m, v.z * m} |
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} |
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func (v vector) mod() float64 { |
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return math.Sqrt(v.x*v.x + v.y*v.y + v.z*v.z) |
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} |
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var ( |
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bodies, timeSteps int |
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masses []float64 |
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gc float64 |
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positions, velocities, accelerations []vector |
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) |
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func initiateSystem(fileName string) error { |
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file, err := os.Open(fileName) |
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if err != nil { |
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return err |
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} |
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defer file.Close() |
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fmt.Fscanf(file, "%f%d%d", &gc, &bodies, &timeSteps) |
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masses = make([]float64, bodies) |
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positions = make([]vector, bodies) |
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velocities = make([]vector, bodies) |
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accelerations = make([]vector, bodies) |
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for i := 0; i < bodies; i++ { |
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fmt.Fscanf(file, "%f", &masses[i]) |
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fmt.Fscanf(file, "%f%f%f", &positions[i].x, &positions[i].y, &positions[i].z) |
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fmt.Fscanf(file, "%f%f%f", &velocities[i].x, &velocities[i].y, &velocities[i].z) |
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} |
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return nil |
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} |
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func resolveCollisions() { |
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for i := 0; i < bodies-1; i++ { |
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for j := i + 1; j < bodies; j++ { |
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if positions[i] == positions[j] { |
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velocities[i], velocities[j] = velocities[j], velocities[i] |
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} |
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} |
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} |
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} |
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func computeAccelerations() { |
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for i := 0; i < bodies; i++ { |
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accelerations[i] = vector{0, 0, 0} |
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for j := 0; j < bodies; j++ { |
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if i != j { |
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temp := gc * masses[j] / math.Pow(positions[i].sub(positions[j]).mod(), 3) |
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accelerations[i] = accelerations[i].add(positions[j].sub(positions[i]).scale(temp)) |
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} |
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} |
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} |
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} |
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func computeVelocities() { |
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for i := 0; i < bodies; i++ { |
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velocities[i] = velocities[i].add(accelerations[i]) |
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} |
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} |
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func computePositions() { |
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for i := 0; i < bodies; i++ { |
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positions[i] = positions[i].add(velocities[i].add(accelerations[i].scale(0.5))) |
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} |
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} |
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func simulate() { |
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computeAccelerations() |
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computePositions() |
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computeVelocities() |
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resolveCollisions() |
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} |
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func printResults() { |
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f := "Body %d : % 8.6f % 8.6f % 8.6f | % 8.6f % 8.6f % 8.6f\n" |
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for i := 0; i < bodies; i++ { |
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fmt.Printf( |
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f, i+1, |
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positions[i].x, positions[i].y, positions[i].z, |
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velocities[i].x, velocities[i].y, velocities[i].z, |
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) |
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} |
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} |
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func main() { |
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if len(os.Args) != 2 { |
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fmt.Printf("Usage : %s <file name containing system configuration data>\n", os.Args[0]) |
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} else { |
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err := initiateSystem(os.Args[1]) |
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if err != nil { |
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fmt.Println(err) |
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return |
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} |
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fmt.Print("Body : x y z |") |
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fmt.Println(" vx vy vz") |
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for i := 0; i < timeSteps; i++ { |
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fmt.Printf("\nCycle %d\n", i+1) |
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simulate() |
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printResults() |
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} |
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} |
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}</lang> |
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Contents of nbody.txt: |
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<pre> |
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0.01 3 20 |
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1 |
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0 0 0 |
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0.01 0 0 |
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0.1 |
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1 1 0 |
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0 0 0.02 |
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0.001 |
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0 1 1 |
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0.01 -0.01 -0.01 |
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</pre> |
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{{out}} |
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<pre> |
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Body : x y z | vx vy vz |
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Cycle 1 |
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Body 1 : 0.010177 0.000179 0.000002 | 0.010354 0.000357 0.000004 |
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Body 2 : 0.998230 0.998232 0.020002 | -0.003539 -0.003536 0.020004 |
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Body 3 : 0.010177 0.988232 0.988055 | 0.010354 -0.013536 -0.013889 |
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Cycle 2 |
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Body 1 : 0.020709 0.000718 0.000011 | 0.010710 0.000721 0.000014 |
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Body 2 : 0.992907 0.992896 0.039971 | -0.007109 -0.007138 0.019935 |
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Body 3 : 0.020717 0.972888 0.972173 | 0.010727 -0.017153 -0.017876 |
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Cycle 3 |
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Body 1 : 0.031600 0.001625 0.000034 | 0.011072 0.001094 0.000033 |
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Body 2 : 0.983985 0.983910 0.059834 | -0.010735 -0.010835 0.019790 |
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Body 3 : 0.031643 0.953868 0.952235 | 0.011125 -0.020886 -0.021999 |
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Cycle 4 |
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Body 1 : 0.042858 0.002913 0.000081 | 0.011443 0.001481 0.000060 |
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Body 2 : 0.971393 0.971163 0.079509 | -0.014448 -0.014659 0.019561 |
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Body 3 : 0.042981 0.931039 0.928087 | 0.011552 -0.024772 -0.026299 |
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Cycle 5 |
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Body 1 : 0.054492 0.004595 0.000160 | 0.011826 0.001884 0.000097 |
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Body 2 : 0.955030 0.954509 0.098909 | -0.018278 -0.018649 0.019238 |
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Body 3 : 0.054766 0.904225 0.899522 | 0.012018 -0.028857 -0.030829 |
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Cycle 6 |
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Body 1 : 0.066517 0.006691 0.000281 | 0.012224 0.002308 0.000145 |
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Body 2 : 0.934759 0.933760 0.117931 | -0.022265 -0.022849 0.018806 |
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Body 3 : 0.067040 0.873197 0.866280 | 0.012530 -0.033199 -0.035655 |
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Cycle 7 |
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Body 1 : 0.078950 0.009225 0.000456 | 0.012642 0.002759 0.000206 |
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Body 2 : 0.910400 0.908677 0.136456 | -0.026454 -0.027316 0.018244 |
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Body 3 : 0.079856 0.837662 0.828023 | 0.013101 -0.037871 -0.040861 |
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Cycle 8 |
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Body 1 : 0.091815 0.012227 0.000702 | 0.013086 0.003245 0.000284 |
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Body 2 : 0.881722 0.878958 0.154340 | -0.030902 -0.032122 0.017523 |
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Body 3 : 0.093281 0.797239 0.784313 | 0.013749 -0.042975 -0.046559 |
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Cycle 9 |
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Body 1 : 0.105140 0.015737 0.001035 | 0.013564 0.003775 0.000383 |
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Body 2 : 0.848429 0.844216 0.171401 | -0.035684 -0.037362 0.016600 |
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Body 3 : 0.107405 0.751427 0.734579 | 0.014498 -0.048649 -0.052908 |
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Cycle 10 |
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Body 1 : 0.118964 0.019805 0.001481 | 0.014085 0.004362 0.000509 |
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Body 2 : 0.810137 0.803953 0.187408 | -0.040900 -0.043166 0.015414 |
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Body 3 : 0.122346 0.699554 0.678056 | 0.015384 -0.055097 -0.060138 |
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Cycle 11 |
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Body 1 : 0.133337 0.024498 0.002071 | 0.014662 0.005025 0.000672 |
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Body 2 : 0.766343 0.757509 0.202050 | -0.046687 -0.049720 0.013868 |
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Body 3 : 0.138268 0.640690 0.613685 | 0.016460 -0.062633 -0.068603 |
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Cycle 12 |
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Body 1 : 0.148327 0.029907 0.002851 | 0.015317 0.005792 0.000888 |
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Body 2 : 0.716377 0.703998 0.214889 | -0.053246 -0.057302 0.011810 |
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Body 3 : 0.155406 0.573482 0.539941 | 0.017816 -0.071782 -0.078886 |
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Cycle 13 |
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Body 1 : 0.164025 0.036157 0.003887 | 0.016079 0.006709 0.001184 |
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Body 2 : 0.659310 0.642172 0.225282 | -0.060887 -0.066351 0.008976 |
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Body 3 : 0.174112 0.495836 0.454475 | 0.019596 -0.083511 -0.092045 |
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Cycle 14 |
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Body 1 : 0.180564 0.043437 0.005286 | 0.017000 0.007852 0.001613 |
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Body 2 : 0.593807 0.570186 0.232208 | -0.070119 -0.077621 0.004875 |
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Body 3 : 0.194929 0.404136 0.353320 | 0.022038 -0.099890 -0.110265 |
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Cycle 15 |
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Body 1 : 0.198150 0.052049 0.007234 | 0.018171 0.009372 0.002283 |
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Body 2 : 0.517817 0.485100 0.233878 | -0.081861 -0.092550 -0.001535 |
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Body 3 : 0.218605 0.290860 0.228583 | 0.025314 -0.126661 -0.139210 |
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Cycle 16 |
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Body 1 : 0.217126 0.062542 0.010117 | 0.019781 0.011614 0.003484 |
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Body 2 : 0.427899 0.381659 0.226654 | -0.097974 -0.114332 -0.012913 |
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Body 3 : 0.244268 0.131956 0.057562 | 0.026013 -0.191148 -0.202831 |
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Cycle 17 |
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Body 1 : 0.238346 0.076539 0.015221 | 0.022658 0.016380 0.006723 |
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Body 2 : 0.317489 0.248502 0.200967 | -0.122846 -0.151982 -0.038461 |
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Body 3 : 0.075592 -0.559591 -0.487315 | -0.363366 -1.191945 -0.886924 |
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Cycle 18 |
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Body 1 : 0.263123 0.097523 0.026918 | 0.026898 0.025587 0.016672 |
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Body 2 : 0.173428 0.050424 0.112716 | -0.165275 -0.244174 -0.138041 |
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Body 3 : -0.286241 -1.745597 -1.369528 | -0.360299 -1.180066 -0.877501 |
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Cycle 19 |
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Body 1 : 0.270854 0.113045 0.061923 | -0.011436 0.005457 0.053339 |
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Body 2 : 0.199821 -0.093105 -0.208666 | 0.218061 -0.042882 -0.504723 |
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Body 3 : -0.646318 -2.924909 -2.246453 | -0.359856 -1.178559 -0.876350 |
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Cycle 20 |
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Body 1 : 0.258572 0.116046 0.112038 | -0.013129 0.000544 0.046890 |
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Body 2 : 0.426346 -0.111425 -0.681150 | 0.234987 0.006241 -0.440245 |
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Body 3 : -1.006089 -4.103186 -3.122591 | -0.359686 -1.177995 -0.875924 |
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</pre> |
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=={{header|J}}== |
=={{header|J}}== |