Added Verlet integration in Kotlin (#535)

Author: sklan

contents/verlet_integration/code/kotlin/verlet.kt

@@ -0,0 +1,55 @@
+data class VerletValues(val time: Double, val vel: Double)
+
+fun verlet(_pos: Double, acc: Double, dt: Double): Double {
+    var pos = _pos  // Since function parameter are val and can't be modified
+    var prevPos = pos
+    var time = 0.0
+
+    while (pos > 0) {
+        time += dt
+        val nextPos = pos * 2 - prevPos + acc * dt * dt
+        prevPos = pos
+        pos = nextPos
+    }
+    return time
+}
+
+fun stormerVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {
+    var pos = _pos
+    var prevPos = pos
+    var time = 0.0
+    var vel = 0.0
+    while (pos > 0) {
+        time += dt
+        val nextPos = pos * 2 - prevPos + acc * dt * dt
+        prevPos = pos
+        pos = nextPos
+        vel += acc * dt
+    }
+    return VerletValues(time, vel)
+}
+
+fun velocityVerlet(_pos: Double, acc: Double, dt: Double): VerletValues {
+    var pos = _pos
+    var time = 0.0
+    var vel = 0.0
+    while (pos > 0) {
+        time += dt
+        pos += vel * dt + 0.5 * acc * dt * dt
+        vel += acc * dt
+    }
+    return VerletValues(time, vel)
+}
+
+fun main(args: Array<String>) {
+    val verletTime = verlet(5.0, -10.0, 0.01)
+    println("Time for Verlet integration is: $verletTime")
+
+    val stormerVerlet = stormerVerlet(5.0, -10.0, 0.01)
+    println("Time for Stormer Verlet integration is: $stormerVerlet.time")
+    println("Velocity for Stormer Verlet integration is: $stormerVerlet.vel")
+
+    val velocityVerlet = velocityVerlet(5.0, -10.0, 0.01)
+    println("Time for Velocity Verlet integration is: $velocityVerlet.time")
+    println("Velocity for Velocity Verlet integration is: $velocityVerlet.vel")
+}

contents/verlet_integration/verlet_integration.md

@@ -65,6 +65,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:5-16, lang:"go"](code/golang/verlet.go)
 {% sample lang="asm-x64" %}
 [import:18-42, lang:"asm-x64"](code/asm-x64/verlet.s)
+{% sample lang="kotlin" %}
+[import:3-15, lang:"kotlin"](code/kotlin/verlet.kt)
 {% endmethod %}
 
 Now, obviously this poses a problem; what if we want to calculate a term that requires velocity, like the kinetic energy, $$\frac{1}{2}mv^2$$? In this case, we certainly cannot get rid of the velocity! Well, we can find the velocity to $$\mathcal{O}(\Delta t^2)$$ accuracy by using the Stormer-Verlet method, which is the same as before, but we calculate velocity like so
@@ -117,6 +119,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:18-30, lang:"go"](code/golang/verlet.go)
 {% sample lang="asm-x64" %}
 [import:44-71, lang:"asm-x64"](code/asm-x64/verlet.s)
+{% sample lang="kotlin" %}
+[import:17-30, lang:"kotlin"](code/kotlin/verlet.kt)
 {% endmethod %}
 
 
@@ -183,6 +187,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:32-42, lang:"go"](code/golang/verlet.go)
 {% sample lang="asm-x64" %}
 [import:73-101, lang:"asm-x64"](code/asm-x64/verlet.s)
+{% sample lang="kotlin" %}
+[import:32-42, lang:"kotlin"](code/kotlin/verlet.kt)
 {% endmethod %}
 
 Even though this method is more widely used than the simple Verlet method mentioned above, it unforunately has an error term of $$\mathcal{O}(\Delta t^2)$$, which is two orders of magnitude worse. That said, if you want to have a simulaton with many objects that depend on one another --- like a gravity simulation --- the Velocity Verlet algorithm is a handy choice; however, you may have to play further tricks to allow everything to scale appropriately. These types of simulatons are sometimes called *n-body* simulations and one such trick is the Barnes-Hut algorithm, which cuts the complexity of n-body simulations from $$\sim \mathcal{O}(n^2)$$ to $$\sim \mathcal{O}(n\log(n))$$.
@@ -231,6 +237,8 @@ Submitted by P. Mekhail
 [import, lang:"go"](code/golang/verlet.go)
 {% sample lang="asm-x64" %}
 [import, lang:"asm-x64"](code/asm-x64/verlet.s)
+{% sample lang="kotlin" %}
+[import, lang:"kotlin"](code/kotlin/verlet.kt)
 {% endmethod %}