adding example verlet implementation in c++

Author: leios

chapters/computational_physics/verlet.md

@@ -99,4 +99,80 @@ Even though this method is more used than the simple Verlet method mentioned abo
 
 Both of these methods work simply by iterating timestep-by-timestep and can be written straightforwardly in any language. For reference, here are snippets of code that use both the classic and velocity Verlet methods to find the time it takes for a ball to hit the ground after being dropped from a given height.
 
-TODO
+#### C++
+```c++
+/*------------verlet.cpp------------------------------------------------------//
+*
+* Purpose: Simple demonstration of verlet algorithm
+*
+*-----------------------------------------------------------------------------*/
+
+#include <iostream>
+
+// Simple function for velocity-verlet
+void verlet(double pos, double acc, double dt){
+
+    // Note that we are using a temp variable for the previous position
+    double prev_pos, temp_pos, time;
+    prev_pos = pos;
+    time = 0;
+
+    while (pos > 0){
+        time += dt;
+        temp_pos = pos;
+        pos = pos*2 - prev_pos + acc * dt * dt;
+        prev_pos = temp_pos;
+    }
+
+   std::cout << time << '\n';
+
+}
+
+// Simple function for stormer-verlet
+void stormer_verlet(double pos, double acc, double dt){
+
+    // Note that we are using a temp variable for the previous position
+    double prev_pos, temp_pos, time, vel;
+    prev_pos = pos;
+    vel = 0;
+    time = 0;
+    while (pos > 0){
+        time += dt;
+        temp_pos = pos;
+        pos = pos*2 - prev_pos + acc * dt * dt;
+        prev_pos = temp_pos;
+
+        // The acceleration is constant, so the velocity is straightforward
+        vel += acc*dt;
+    }
+
+   std::cout << time << '\n';
+
+}
+
+// Simple function for velocity-verlet
+void velocity_verlet(double pos, double acc, double dt){
+
+    // Note that we are using a temp variable for the previous position
+    double time, vel;
+    vel = 0;
+    time = 0;
+    while (pos > 0){
+        time += dt;
+        pos += vel*dt + 0.5*acc * dt * dt;
+        vel += acc*dt;
+    }
+
+   std::cout << time << '\n';
+
+}
+
+int main(){
+
+    verlet(5.0, -10, 0.01);
+    stormer_verlet(5.0, -10, 0.01);
+    velocity_verlet(5.0, -10, 0.01);
+
+}
+
+```