From 86d5ca98bfbf6a2e97af8920687857164f3e0fc8 Mon Sep 17 00:00:00 2001
From: Michael Bradley <michaelmbrad@gmail.com>
Date: Sat, 7 Oct 2023 21:42:30 -0400
Subject: [PATCH] Add constrained physics sim

Performs slightly worse, sends less bodies flying off.
---
 data.py    |  4 ++--
 physics.py | 21 +++++++++++++++++++++
 2 files changed, 23 insertions(+), 2 deletions(-)

diff --git a/data.py b/data.py
index 29df928..5098d0f 100644
--- a/data.py
+++ b/data.py
@@ -3,7 +3,7 @@ import matplotlib.cm as cm
 import matplotlib.pyplot as plt
 import numpy as np
 
-from physics import n_body_matrix
+import physics
 
 
 def parse_csv(filename: str):
@@ -54,7 +54,7 @@ class Animator:
         return self.scat,
 
     def update(self, *_args, **_kwargs):
-        n_body_matrix(self.pos, self.vel, self.mass)
+        physics.n_body_matrix_constrained(self.pos, self.vel, self.mass)
         self.scat.set_offsets(self.pos)
         return self.scat,
 
diff --git a/physics.py b/physics.py
index ac0b2a5..232520c 100644
--- a/physics.py
+++ b/physics.py
@@ -34,3 +34,24 @@ def n_body_matrix(pos: np.ndarray, vel: np.ndarray, mass: np.ndarray):
     )
 
     pos += vel
+
+
+def n_body_matrix_constrained(pos: np.ndarray, vel: np.ndarray, mass: np.ndarray, close=2.):
+    dist = np.zeros((len(pos) - 1, len(pos), 2))
+    rot_mass = np.zeros((len(mass) - 1, len(mass), 1))
+
+    pos2 = np.concatenate((pos, pos))
+    mass2 = np.concatenate((mass, mass))
+
+    for i in range(1, len(pos)):
+        dist[i - 1] = pos2[i: i + len(pos)] - pos
+        rot_mass[i - 1] = mass2[i: i + len(mass)]
+
+    a = np.linalg.norm(dist, axis=2)
+    a[a < close] = close
+    vel += G * np.sum(
+        dist * rot_mass / (a ** 3)[:, :, np.newaxis],
+        axis=0
+    )
+
+    pos += vel