Add verlet integration in golang (#484)

* add verlet integration in golang

* change the name golang to go

Author: Julian

contents/verlet_integration/code/golang/verlet.go

@@ -0,0 +1,60 @@
+package main
+
+import "fmt"
+
+func verlet(pos, acc, dt float64) (time float64) {
+	prevPos := pos
+	time = 0
+
+	for pos > 0 {
+		time += dt
+		nextPos := pos*2 - prevPos + acc*dt*dt
+		prevPos, pos = pos, nextPos
+	}
+
+	return
+}
+
+func stormerVerlet(pos, acc, dt float64) (time, vel float64) {
+	prevPos := pos
+	time, vel = 0, 0
+
+	for pos > 0 {
+		time += dt
+		vel += acc * dt
+		nextPos := pos*2 - prevPos + acc*dt*dt
+		prevPos, pos = pos, nextPos
+	}
+
+	return
+}
+
+func velocityVerlet(pos, acc, dt float64) (time, vel float64) {
+	time, vel = 0, 0
+
+	for pos > 0 {
+		time += dt
+		pos += vel*dt + .5*acc*dt*dt
+		vel += acc * dt
+	}
+
+	return
+}
+
+func main() {
+	time := verlet(5., -10., .01)
+	fmt.Println("Verlet")
+	fmt.Println("Time:", time)
+	fmt.Println()
+
+	time, vel := stormerVerlet(5., -10., .01)
+	fmt.Println("Stormer-Verlet")
+	fmt.Println("Time:", time)
+	fmt.Println("Velocity:", vel)
+	fmt.Println()
+
+	time, vel = velocityVerlet(5., -10., .01)
+	fmt.Println("Velocity Verlet")
+	fmt.Println("Time:", time)
+	fmt.Println("Velocity:", vel)
+}

contents/verlet_integration/verlet_integration.md

@@ -59,6 +59,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:1-15, lang:"swift"](code/swift/verlet.swift)
 {% sample lang="f90" %}
 [import:1-20, lang:"fortran"](code/fortran/verlet.f90)
+{% sample lang="go" %}
+[import:5-16, lang:"go"](code/golang/verlet.go)
 {% 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
@@ -105,6 +107,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:17-34, lang:"swift"](code/swift/verlet.swift)
 {% sample lang="f90" %}
 [import:22-42, lang:"fortran"](code/fortran/verlet.f90)
+{% sample lang="go" %}
+[import:18-30, lang:"go"](code/golang/verlet.go)
 {% endmethod %}
 
 
@@ -165,6 +169,8 @@ Unfortunately, this has not yet been implemented in LabVIEW, so here's Julia cod
 [import:36-49, lang:"swift"](code/swift/verlet.swift)
 {% sample lang="f90" %}
 [import:44-60, lang:"fortran"](code/fortran/verlet.f90)
+{% sample lang="go" %}
+[import:32-42, lang:"go"](code/golang/verlet.go)
 {% 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 $$\sim \mathcal{O}(n\log(n))$$.
@@ -207,6 +213,8 @@ Submitted by P. Mekhail
 [import, lang:"swift"](code/swift/verlet.swift)
 {% sample lang="f90" %}
 [import, lang:"fortran"](code/fortran/verlet.f90)
+{% sample lang="go" %}
+[import, lang:"go"](code/golang/verlet.go)
 {% endmethod %}