From 96ce11a8c568477349baf95e545949a1971c1a93 Mon Sep 17 00:00:00 2001
From: Jay Singh <jayrakeshsingh8796@gmail.com>
Date: Sun, 7 Jun 2026 01:15:06 +0530
Subject: [PATCH 1/2] fix: add fixed timestep accumulator to prevent energy
 drift in BouncingBall

---
 simulations/BouncingBall.jsx | 14 ++++++++++++--
 1 file changed, 12 insertions(+), 2 deletions(-)

diff --git a/simulations/BouncingBall.jsx b/simulations/BouncingBall.jsx
index 051a21cf..bb74dab1 100644
--- a/simulations/BouncingBall.jsx
+++ b/simulations/BouncingBall.jsx
@@ -55,6 +55,7 @@ export default function BouncingBall() {
   const dragControllerRef = useRef(null);
   const maxHeightRef = useRef(0);
   const fallStartTimeRef = useRef(0);
+  const accumulatorRef = useRef(0);
 
   // Sim info
   const { simData, updateSimInfo } = useSimInfo({
@@ -145,8 +146,17 @@ export default function BouncingBall() {
       p.draw = () => {
         if (!bodyRef.current || !trailLayer) return;
 
-        const dt = computeDelta(p);
-        if (dt === 0) return;
+        const rawDt = computeDelta(p);
+        if (rawDt === 0) return;
+
+        // Fixed timestep accumulator — prevents energy drift from variable frame rate
+        const FIXED_DT = 1 / 120; // 120Hz physics steps
+        accumulatorRef.current += rawDt;
+        // Cap accumulator to prevent spiral of death
+        if (accumulatorRef.current > 0.1) accumulatorRef.current = 0.1;
+        const dt = FIXED_DT;
+        if (accumulatorRef.current < FIXED_DT) return;
+        accumulatorRef.current -= FIXED_DT;
 
         const { size, gravity, trailEnabled, ballColor, mass, restitution } =
           inputsRef.current;

From ede209f05a63a0cf6212a160a10b82caf36f1de2 Mon Sep 17 00:00:00 2001
From: Jay Singh <jayrakeshsingh8796@gmail.com>
Date: Sun, 7 Jun 2026 15:02:56 +0530
Subject: [PATCH 2/2] fix: centralize fixed timestep accumulator in Time.js to
 prevent energy drift across all simulations

---
 app/(core)/constants/Time.js | 20 +++++++++++++++++---
 1 file changed, 17 insertions(+), 3 deletions(-)

diff --git a/app/(core)/constants/Time.js b/app/(core)/constants/Time.js
index c4ba3f37..56b9c37f 100644
--- a/app/(core)/constants/Time.js
+++ b/app/(core)/constants/Time.js
@@ -3,6 +3,8 @@ let timeScale = 1;
 let paused = false;
 let manualStepDelta = 0;
 let simulationInstances = new Map(); // Mappa per tenere traccia di ogni istanza
+let accumulators = new Map(); // Fixed timestep accumulators per instance
+const FIXED_DT = 1 / 120; // 120Hz fixed physics timestep
 
 /**
  * Returns dt in seconds, limited to a max step for stability.
@@ -26,16 +28,25 @@ export function computeDelta(p) {
   }
 
   let lastInstanceMillis = simulationInstances.get(instanceId);
-  let dt = (now - lastInstanceMillis) / 1000; // seconds
+  let rawDt = (now - lastInstanceMillis) / 1000; // seconds
 
   // Aggiorna lastMillis per questa istanza
   simulationInstances.set(instanceId, now);
 
   // limit burst (e.g. when tab regains focus)
   const maxStep = 1 / 30; // ~33ms
-  if (dt > maxStep) dt = maxStep;
+  if (rawDt > maxStep) rawDt = maxStep;
 
-  return dt * timeScale;
+  rawDt *= timeScale;
+
+  // Fixed timestep accumulator — prevents energy drift from variable frame rate
+  const acc = (accumulators.get(instanceId) || 0) + rawDt;
+  if (acc < FIXED_DT) {
+    accumulators.set(instanceId, acc);
+    return 0;
+  }
+  accumulators.set(instanceId, acc - FIXED_DT);
+  return FIXED_DT;
 }
 
 export function setTimeScale(scale) {
@@ -47,6 +58,7 @@ export function togglePause() {
   // Quando mettiamo in pausa, resettiamo i lastMillis per evitare salti al resume
   if (paused) {
     simulationInstances.clear();
+    accumulators.clear();
   }
 }
 
@@ -54,6 +66,7 @@ export function setPause(value) {
   paused = value;
   if (paused) {
     simulationInstances.clear();
+    accumulators.clear();
   }
 }
 
@@ -66,6 +79,7 @@ export function stepSimulation(delta) {
 export function resetTime() {
   paused = false;
   simulationInstances.clear(); // Pulisci tutte le istanze
+  accumulators.clear();
 }
 
 export function isPaused() {