first working version of physics model

Physics/MovingParticles.mch

 MACHINE MovingParticles
 INCLUDES Vectors
 DEFINITIONS
-  "LibraryReals.def";
+  "LibraryReals.def"; "SORT.def"; 
   MASS == FLOAT;
   POS == FLOAT;
   SPEED == FLOAT;
@@ -10,13 +10,25 @@ DEFINITIONS
   SCALE == 1.25e11; // 100 % in visualisation
   SCALE100 == (SCALE/100.0);
   SPEED_MULTIPLIER == 1000000.0;
-  MAXMASS == 1.989e30
+  GRAV_MULTIPLIER == 1000000000000.0;
+  MAXMASS == 1.989e30;
   
+  gravitation == %i.(i:OBJ | sigma_vecs(
+                              SQUASH(
+                               %j.(j:OBJ & j/=i |
+                                times_vec( force_between(i,j,pos(i),pos(j)) / mass(i) ,
+                                           unit_vec(delta_vec(pos(j),pos(i)))))
+                                     )  ) ) // acceleration
+ABSTRACT_CONSTANTS
+  force_between
 CONSTANTS mass, nobjs
 PROPERTIES
   nobjs : 1..10 &
   mass : OBJ --> MASS &
   
+  force_between = %(a,b,pa,pb).(a:OBJ & b:OBJ & a/=b | (G * mass(a) * mass(b)) / (distance(pa,pb)**2))
+  
+  &
   n = 2 & // two dimensional space
   nobjs = 3 & mass = [5.97e24, 1.989e30, 1.989e30]
 VARIABLES pos, speed
@@ -27,9 +39,10 @@ INITIALISATION pos :=   [ [0.0,0.0]  ,  [0.0,4.5e10] ,   [0.0,-4.5e10 ] ] ||
                speed := [ [0.05e04,0.0],  [3.0e04,0.0],  [-3.0e04,0.0]  ] 
 OPERATIONS
   r <-- ForceBetween(a,b) = PRE a:OBJ & b:OBJ & a/= b THEN
-            r := (G * mass(a) * mass(b)) / (distance(pos(a),pos(b))**2)
+            r := force_between(a,b,pos(a),pos(b))
          END;
-  Move(delta) = PRE delta:REAL & delta = 100000.0 THEN
+  Move(delta) = PRE delta:REAL & delta = 10000.0 THEN
+            speed := %i.(i:OBJ | add_vec(speed(i),times_vec(delta,gravitation(i)) )) ||
             pos := %i.(i:OBJ | add_vec(pos(i),times_vec(delta,speed(i))) )
          END
 END

Physics/Vectors.mch

@@ -13,7 +13,9 @@ ABSTRACT_CONSTANTS
   distance,
   
   add_first,
-  sigma_reals
+  sigma_reals,
+  add_firstv,
+  sigma_vecs
 PROPERTIES
   n:NATURAL1 &
   DIM = (1..n) &
@@ -22,6 +24,9 @@ PROPERTIES
   add_first = %v.(v:seq1(REAL) | (v(1)+v(2)) -> tail(tail(v))) &
   sigma_reals = %v.(v:VEC | (iterate(add_first,n-1)(v))(1)) &
   
+  add_firstv = %v.(v:seq1(VEC) | add_vec(v(1),v(2)) -> tail(tail(v))) &
+  sigma_vecs = %v.(v:seq1(VEC) | (iterate(add_firstv,size(v)-1)(v))(1)) &
+  
   add_vec = %(v1,v2).(v1:VEC & v2:VEC | %i.(i:DIM| v1(i)+v2(i))) &
   delta_vec = %(v1,v2).(v1:VEC & v2:VEC | %i.(i:DIM| v1(i)-v2(i))) &
   // dot_product = %(v1,v2).(v1:VEC & v2:VEC | SIGMA(i).(i:DIM| v1(i)*v2(i))) &

Physics/three_bodies.json

@@ -44,6 +44,31 @@
       "id": "speed%0",
       "attr": "y2",
       "value" : "(pos(%0)(2)+ SPEED_MULTIPLIER*speed(%0)(2)) / SCALE100"
+    },
+    
+	{
+	  "for": {"from":1, "to":3},
+      "id": "gravitation%0",
+      "attr": "x1",
+      "value" : "pos(%0)(1) / SCALE100"
+    },
+	{
+	  "for": {"from":1, "to":3},
+      "id": "gravitation%0",
+      "attr": "y1",
+      "value" : "pos(%0)(2) / SCALE100"
+    },
+	{
+	  "for": {"from":1, "to":3},
+      "id": "gravitation%0",
+      "attr": "x2",
+      "value" : "(pos(%0)(1)+ GRAV_MULTIPLIER*gravitation(%0)(1)) / SCALE100"
+    },
+	{
+	  "for": {"from":1, "to":3},
+      "id": "gravitation%0",
+      "attr": "y2",
+      "value" : "(pos(%0)(2)+ GRAV_MULTIPLIER*gravitation(%0)(2)) / SCALE100"
     }
   ],
   "events": [

Physics/three_bodies.svg

@@ -14,12 +14,12 @@
     
     <marker id="startarrow" markerWidth="10" markerHeight="7" 
     refX="10" refY="3.5" orient="auto">
-      <polygon points="10 0, 10 7, 0 3.5" fill="blue" />
+      <polygon points="10 0, 10 7, 0 3.5" fill="green" />
     </marker>
     
     <marker id="endarrow" markerWidth="10" markerHeight="7" 
     refX="0" refY="3.5" orient="auto">
-      <polygon points="0 0, 10 3.5, 0 7"  fill="blue" />
+      <polygon points="0 0, 10 3.5, 0 7"  fill="green" />
     </marker>
   </defs>
   
@@ -47,4 +47,17 @@
    id = "speed3"
    />
    
+  <line x1="45" y1="15" x2="55" y2="15" stroke="green" 
+  stroke-width="0.3" marker-end="url(#endarrow)"
+   id = "gravitation1"
+   />
+  <line x1="5" y1="15" x2="0" y2="0" stroke="green" 
+  stroke-width="0.3" marker-end="url(#endarrow)"
+   id = "gravitation2"
+   />
+  <line x1="35" y1="45" x2="35" y2="55" stroke="green" 
+  stroke-width="0.3" marker-end="url(#endarrow)"
+   id = "gravitation3"
+   />
+    
 </svg>