N-body problem: Difference between revisions
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(Corrected acceleration function.) |
(Added Kotlin) |
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cs:{(cos 2*pi*x%y;sin 2*pi*x%y;0)} / z-axis |
cs:{(cos 2*pi*x%y;sin 2*pi*x%y;0)} / z-axis |
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sc:{(sin 2*pi*x%y;-cos 2*pi*x%y;0)} / objects on screen go round and round</lang> |
sc:{(sin 2*pi*x%y;-cos 2*pi*x%y;0)} / objects on screen go round and round</lang> |
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=={{header|Kotlin}}== |
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{{trans|C}} |
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<lang scala>// version 1.2.0 |
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import java.io.File |
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import kotlin.math.sqrt |
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import kotlin.math.pow |
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class Vector3D(val x: Double, val y: Double, val z: Double) { |
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operator fun plus(v: Vector3D) = Vector3D(x + v.x, y + v.y, z + v.z) |
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operator fun minus(v: Vector3D) = Vector3D(x - v.x, y - v.y, z - v.z) |
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operator fun times(s: Double) = Vector3D(s * x, s * y, s * z) |
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val mod = sqrt(x * x + y * y + z * z) |
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} |
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val origin = Vector3D(0.0, 0.0, 0.0) |
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class NBody(fileName: String) { |
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val gc: Double |
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val bodies: Int |
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val timeSteps: Int |
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val masses: DoubleArray |
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val positions: Array<Vector3D> |
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val velocities: Array<Vector3D> |
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val accelerations: Array<Vector3D> |
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init { |
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val f = File(fileName) |
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val lines = f.readLines() |
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val (g, b, t) = lines[0].split(' ') |
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gc = g.toDouble() |
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bodies = b.toInt() |
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timeSteps = t.toInt() |
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masses = DoubleArray(bodies) |
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positions = Array<Vector3D>(bodies) { origin } |
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velocities = Array<Vector3D>(bodies) { origin } |
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accelerations = Array<Vector3D>(bodies) { origin } |
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for (i in 0 until bodies) { |
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masses[i] = lines[i * 3 + 1].toDouble() |
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positions[i] = decompose(lines[i * 3 + 2]) |
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velocities[i] = decompose(lines[i * 3 + 3]) |
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} |
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println("Contents of $fileName") |
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println(f.readText()) |
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print("Body : x y z |") |
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println(" vx vy vz") |
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} |
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private fun decompose(line: String): Vector3D { |
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val (x, y, z) = line.split(' ').map { it.toDouble() } |
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return Vector3D(x, y, z) |
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} |
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private fun resolveCollisions() { |
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for (i in 0 until bodies) { |
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for (j in i + 1 until bodies) { |
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if (positions[i].x == positions[j].x && |
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positions[i].y == positions[j].y && |
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positions[i].z == positions[j].z) { |
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val temp = velocities[i] |
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velocities[i] = velocities[j] |
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velocities[j] = temp |
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} |
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} |
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} |
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} |
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private fun computeAccelerations() { |
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for (i in 0 until bodies) { |
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accelerations[i] = origin |
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for (j in 0 until bodies) { |
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if (i != j) { |
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val temp = gc * masses[j] / (positions[i] - positions[j]).mod.pow(3) |
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accelerations[i] += (positions[j] - positions[i]) * temp |
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} |
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} |
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} |
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} |
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private fun computeVelocities() { |
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for (i in 0 until bodies) velocities[i] += accelerations[i] |
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} |
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private fun computePositions() { |
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for (i in 0 until bodies) { |
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positions[i] += velocities[i] + accelerations[i] * 0.5 |
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} |
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} |
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fun 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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fun printResults() { |
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val fmt = "Body %d : % 8.6f % 8.6f % 8.6f | % 8.6f % 8.6f % 8.6f" |
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for (i in 0 until bodies) { |
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println(fmt.format( |
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i + 1, |
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positions[i].x, |
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positions[i].y, |
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positions[i].z, |
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velocities[i].x, |
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velocities[i].y, |
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velocities[i].z |
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)) |
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} |
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} |
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} |
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fun main(args: Array<String>) { |
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val fileName = "nbody.txt" |
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val nb = NBody(fileName) |
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for (i in 1..nb.timeSteps) { |
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println("\nCycle $i") |
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nb.simulate() |
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nb.printResults() |
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} |
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}</lang> |
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{{out}} |
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<pre> |
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Contents of nbody.txt |
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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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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|Octave}}== |
=={{header|Octave}}== |