From c798cc8547b59b57fdae106d82bb084ca9ac7d73 Mon Sep 17 00:00:00 2001
From: Leon Liu <leon.liuyang.d@gmail.com>
Date: Thu, 14 Aug 2025 16:52:35 +0900
Subject: [PATCH] update

---
 src/main.rs | 45 ++++++++++++++++++++++++++-------------------
 1 file changed, 26 insertions(+), 19 deletions(-)

diff --git a/src/main.rs b/src/main.rs
index a6fa09e..02b16b7 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -3,7 +3,7 @@ use bevy::{
     input::mouse::{MouseScrollUnit, MouseWheel},
     math::DVec3,
     prelude::*,
-    window::{WindowMode, WindowResolution},
+    window::{WindowMode, WindowResized, WindowResolution},
 };
 use bevy_inspector_egui::{bevy_egui::EguiPlugin, quick::WorldInspectorPlugin};
 use iyes_perf_ui::{PerfUiPlugin, prelude::*};
@@ -206,7 +206,6 @@ fn sync_name_labels(
     mut commands: Commands,
     objects_with_names: Query<(Entity, &Name, &Position), Changed<Name>>,
     existing_labels: Query<&ObjectLabel>,
-    ui_scale: Res<UiScale>,
 ) {
     for (entity, name, _position) in objects_with_names.iter() {
         // Check if label already exists for this entity
@@ -243,7 +242,6 @@ fn update_label_positions(
     mut label_query: Query<(&mut Node, &ObjectLabel, &mut Text), With<ObjectLabel>>,
     objects_query: Query<(&GlobalTransform, &Name, &Radius)>,
     camera_query: Query<(&Camera, &GlobalTransform)>,
-    ui_scale: Res<UiScale>,
 ) {
     let Ok((camera, camera_transform)) = camera_query.single() else {
         return;
@@ -491,11 +489,10 @@ fn n_body(mut query: Query<(&Mass, &mut Position, &mut Velocity)>) {
         .map(|(mass, pos, vel)| (mass.0.0, pos.0.0, vel.0.0))
         .collect();
 
-    // Perform integration steps
-    for _ in 0..STEPS {
-        // Calculate forces for all bodies
+    // Helper function to calculate gravitational forces
+    let calculate_forces = |bodies: &Vec<(f64, DVec3, DVec3)>| -> Vec<DVec3> {
         let mut forces: Vec<DVec3> = vec![DVec3::ZERO; bodies.len()];
-
+        
         for i in 0..bodies.len() {
             for j in 0..bodies.len() {
                 if i != j {
@@ -504,26 +501,36 @@ fn n_body(mut query: Query<(&Mass, &mut Position, &mut Velocity)>) {
 
                     if r_mag_au > 1e-10 {
                         // Avoid division by zero
-                        // Calculate force directly in AU/day² units
-                        let force_magnitude =
-                            G_AU * bodies[i].0 * bodies[j].0 / (r_mag_au * r_mag_au);
-                        let acceleration = force_magnitude / bodies[i].0; // F/m = a
-                        let force_vec = r_vec.normalize() * acceleration;
-
-                        forces[i] += force_vec;
+                        // Calculate gravitational acceleration in AU/day² units
+                        let acceleration_magnitude = G_AU * bodies[j].0 / (r_mag_au * r_mag_au);
+                        let acceleration_vec = r_vec.normalize() * acceleration_magnitude;
+                        forces[i] += acceleration_vec;
                     }
                 }
             }
         }
+        forces
+    };
 
-        // Update velocities and positions using Verlet integration
+    // Perform integration steps using Leapfrog (Verlet) symplectic integrator
+    for _ in 0..STEPS {
+        // Step 1: Half-step momentum update - p ← p - (h/2)∇U(q)
+        let forces = calculate_forces(&bodies);
         for i in 0..bodies.len() {
-            // Update velocity: v += a * dt
-            bodies[i].2 += forces[i] * DT;
+            bodies[i].2 += forces[i] * (DT * 0.5); // Update velocity (momentum/mass)
+        }
 
-            // Update position: x += v * dt
+        // Step 2: Full-step position update - q ← q + h∇T(p)
+        // For classical mechanics, ∇T(p) = p/m = v (velocity)
+        for i in 0..bodies.len() {
             let velocity = bodies[i].2;
-            bodies[i].1 += velocity * DT;
+            bodies[i].1 += velocity * DT; // Update position
+        }
+
+        // Step 3: Half-step momentum update - p ← p - (h/2)∇U(q)
+        let forces = calculate_forces(&bodies);
+        for i in 0..bodies.len() {
+            bodies[i].2 += forces[i] * (DT * 0.5); // Update velocity again
         }
     }