corrected velocity verlet

config.js

@@ -6,20 +6,21 @@ export const DISPLAY_CURRENT_MODE = false;
 export const DISPLAY_VELOCITY_VECTORS = true;
 export const DISPLAY_ACCELERATION_VECTORS = true;
 
-export const MASS_CREATION_RATE = 0.001;
+export const MASS_CREATION_RATE = 1E1;
 export const POINTER_HISTORY_SIZE = 15;
 
-export const VELOCITY_VECTOR_SCALE = 0.1;
+export const VELOCITY_VECTOR_SCALE = 5E0;
 export const VELOCITY_VECTOR_COLOR = 'rgb(150, 150, 150)'; // optionally set to 'object color'
 export const VELOCITY_VECTOR_WIDTH = 1.5;
 export const VELOCITY_VECTOR_ARROWHEAD = true;
 
-export const ACCELERATION_VECTOR_SCALE = 1E-1;
+export const ACCELERATION_VECTOR_SCALE = 5E0;
 export const ACCELERATION_VECTOR_COLOR = 'rgb(0, 255, 0)'; // optionally set to 'object color'
+// export const ACCELERATION_VECTOR_COLOR = 'object color';
 export const ACCELERATION_VECTOR_WIDTH = 1.5;
 export const ACCELERATION_VECTOR_ARROWHEAD = true;
 
-export const MOTION_TIME_SCALE = 5E-5;
+export const MOTION_TIME_SCALE = 1E-4;
 export const PAN_VELOCITY_SCALE_FACTOR = 1E-3;
 
 export const ARROWHEAD_LENGTH = 7;

display.js

@@ -147,10 +147,11 @@ export class Display {
 
     // Draw arrow for the velocity
     if (DISPLAY_VELOCITY_VECTORS) {
-      const endVx = x + VELOCITY_VECTOR_SCALE * vx;
+      const speed = Math.sqrt(vx ** 2 + vy ** 2);
-      const endVy = y + VELOCITY_VECTOR_SCALE * vy;
+      const endVx = x + VELOCITY_VECTOR_SCALE * vx / speed * Math.log(speed);
+      const endVy = y + VELOCITY_VECTOR_SCALE * vy / speed * Math.log(speed);
       const style = VELOCITY_VECTOR_COLOR === 'object color' ? 
-        ctx.fillStyle : VELOCITY_VECTOR_COLOR;
+         `rgb(${r}, ${g}, ${b})` : VELOCITY_VECTOR_COLOR;
       this.drawArrow(x, y, endVx, endVy, {
         style, 
         width: VELOCITY_VECTOR_WIDTH,
@@ -162,10 +163,13 @@ export class Display {
 
     // Draw arrow for acceleration
     if (DISPLAY_ACCELERATION_VECTORS) {
-      const endAx = x + ACCELERATION_VECTOR_SCALE * acceleration.x;
+      const accelerationMagnitude = Math.sqrt(acceleration.x ** 2 + acceleration.y ** 2);
-      const endAy = y + ACCELERATION_VECTOR_SCALE * acceleration.y;
+      const endAx = x + ACCELERATION_VECTOR_SCALE * acceleration.x /
+        accelerationMagnitude * Math.log(accelerationMagnitude);
+      const endAy = y + ACCELERATION_VECTOR_SCALE * acceleration.y /
+        accelerationMagnitude * Math.log(accelerationMagnitude);
       const style = ACCELERATION_VECTOR_COLOR === 'object color' ? 
-        ctx.fillStyle : ACCELERATION_VECTOR_COLOR;
+        `rgb(${r}, ${g}, ${b})` : ACCELERATION_VECTOR_COLOR;
       this.drawArrow(x, y, endAx, endAy, {
         style, 
         width: ACCELERATION_VECTOR_WIDTH,

object.js

@@ -4,6 +4,7 @@ export class MassObject {
   density = 1;
   position = {x: undefined, y: undefined};
   velocity = {x: 0, y: 0};
+  acceleration = {x: 0, y: 0};
   color = {r: undefined, g: undefined, b: undefined};
   created = undefined;
   forces = []; // [{x, y}]
@@ -28,7 +29,7 @@ export class MassObject {
     return Math.pow(this.mass / this.density, 1/3);
   }
 
-  get acceleration() {
+  getAcceleration() {
     let ax = 0;
     let ay = 0;
     for (let {x, y} of this.forces) {

objects.js

@@ -114,7 +114,7 @@ export class Objects {
     }
   }
 
-  computeForces(elapsedTime) {
+  computeForces() {
     if (this.objects.length < 2) return;
     for (let i = 0; i < this.objects.length; i++) {
       this.objects[i].forces = [];
@@ -138,6 +138,7 @@ export class Objects {
   }
 
   computeFrame(elapsedTime) {
+    elapsedTime = elapsedTime * MOTION_TIME_SCALE;
     // If we're creating an object, increment its mass
     // with the mass creation rate accelerating over time
     if (this.creatingObject !== undefined) {
@@ -146,42 +147,39 @@ export class Objects {
       obj.mass += rate * elapsedTime;
     }
 
-    if (this.sim.playing) {
+    // Calculate forces due to gravity. 
-      // Calculate forces due to gravity. 
+    this.computeForces();
-      this.computeForces(elapsedTime);
 
+    if (this.sim.playing) {
       // Generate predicted positions (Velocity verlet method)
       for (let i = 0; i < this.objects.length; i++) {
         const obj = this.objects[i];
-        obj.currentAcceleration = {...obj.acceleration};
+        obj.currentAcceleration = obj.getAcceleration();
-        obj.projectedPosition = {
+        obj.position.x += elapsedTime *
-          x: obj.position.x + MOTION_TIME_SCALE * elapsedTime *
+            (obj.velocity.x + 1/2 * obj.currentAcceleration.x * elapsedTime);
-            (obj.velocity.x + 1/2 * obj.currentAcceleration.x * elapsedTime),
+        obj.position.y += elapsedTime *
-          y: obj.position.y + MOTION_TIME_SCALE * elapsedTime *
+            (obj.velocity.y + 1/2 * obj.currentAcceleration.y * elapsedTime);
-            (obj.velocity.y + 1/2 * obj.currentAcceleration.y * elapsedTime),
-        };
-        obj.currentPosition = {...obj.position};
-        obj.position = obj.projectedPosition;
       }
       
       // Recompute forces
       this.computeForces();
 
-      // Average first and second predicted accelerations
+      // Generated predicted velocities
       for (let i = 0; i < this.objects.length; i++) {
         const obj = this.objects[i];
-        const acceleration = {...obj.acceleration};
+        const acceleration = obj.getAcceleration();
-        const meanAcceleration = {
+        obj.acceleration = {
           x: (obj.currentAcceleration.x + acceleration.x) / 2,
           y: (obj.currentAcceleration.y + acceleration.y) / 2,
         };
-        obj.velocity.x += meanAcceleration.x * MOTION_TIME_SCALE * elapsedTime;
+        obj.velocity.x += obj.acceleration.x * elapsedTime;
-        obj.velocity.y += meanAcceleration.y * MOTION_TIME_SCALE * elapsedTime;
+        obj.velocity.y += obj.acceleration.y * elapsedTime;
-
+      }
-        obj.position.x = obj.currentPosition.x + obj.velocity.x * MOTION_TIME_SCALE * elapsedTime;
+    } else {
-        obj.position.y = obj.currentPosition.y + obj.velocity.y * MOTION_TIME_SCALE * elapsedTime;
+      for (let i = 0; i < this.objects.length; i++) {
+        const obj = this.objects[i];
+        obj.acceleration = obj.getAcceleration();
       }
-
     }
 
     // Display objects info