yangxiangyuan
ea379116cc
- 新增5个物理仿真实验室：黑洞模拟、日地轨道、3D太阳系、π推导、拉格朗日点 - 新增思想实验室后端路由与鉴权逻辑 - 首页新增思想实验室页签与前端渲染逻辑 - 修复中韩半导体监控标的配置错误 - 新增市场技能推送白名单过滤逻辑与单元测试
314 lines
15 KiB
HTML
314 lines
15 KiB
HTML
<!-- ============================================================
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思想实验室 · labs/lagrange_points · 拉格朗日点
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圆形限制性三体问题（CR3BP）交互演示：有效势 / 零速度曲线 / 测试粒子。
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独立 lab：单文件自包含，不引用其他 lab 的任何资源。
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服务端配置：src/server/thought_lab/labs/lagrange_points/config.json
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============================================================ -->
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<!DOCTYPE html>
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<html lang="zh-CN">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>拉格朗日点 · 限制性三体问题交互演示</title>
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<style>
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:root { --bg:#0a0e1a; --panel:#101830; --line:rgba(255,255,255,.10); --txt:#d8dee9; --dim:#8fa0bd; --acc:#8fb3ff; --warn:#e8b84a; }
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* { margin:0; padding:0; box-sizing:border-box; }
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body { background:var(--bg); color:var(--txt); font-family:"PingFang SC","Microsoft YaHei",sans-serif; padding:18px; }
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h1 { font-size:21px; color:#fff; }
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.sub { color:var(--dim); font-size:12.5px; margin:4px 0 14px; }
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.wrap { display:flex; gap:16px; flex-wrap:wrap; align-items:flex-start; }
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#stage { position:relative; background:#05070d; border:1px solid var(--line); border-radius:12px; overflow:hidden; }
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canvas#cv { display:block; cursor:crosshair; }
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#hud { position:absolute; top:10px; left:12px; font-size:12px; line-height:1.7; color:var(--dim);
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background:rgba(10,14,26,.62); border:1px solid var(--line); border-radius:8px; padding:8px 12px; pointer-events:none; max-width:340px; }
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#hud b { color:#fff; }
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.panel { width:430px; background:var(--panel); border:1px solid var(--line); border-radius:12px; padding:16px; }
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.panel h2 { font-size:14px; color:var(--acc); margin:14px 0 8px; }
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.panel h2:first-child { margin-top:0; }
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.panel p, .panel li { font-size:12.8px; line-height:1.75; color:#aeb8cc; }
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.panel ul { padding-left:20px; }
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.row { display:flex; gap:8px; align-items:center; margin:8px 0; flex-wrap:wrap; }
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select, button { background:rgba(143,179,255,.12); border:1px solid rgba(143,179,255,.4); color:#d8e5ff;
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padding:6px 10px; border-radius:8px; font-size:12.5px; cursor:pointer; }
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button:hover, select:hover { background:rgba(143,179,255,.28); }
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input[type=range] { flex:1; accent-color:var(--acc); min-width:140px; }
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label { font-size:12.5px; color:var(--dim); display:flex; gap:6px; align-items:center; cursor:pointer; }
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code { background:rgba(255,255,255,.08); color:#ffd479; padding:1px 6px; border-radius:4px; font-size:12px; }
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table { width:100%; border-collapse:collapse; font-size:12.3px; }
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td, th { border:1px solid var(--line); padding:5px 8px; text-align:left; color:#aeb8cc; }
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th { color:var(--acc); background:rgba(143,179,255,.08); }
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.warn { color:var(--warn); }
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.mono { font-family:Consolas,monospace; font-size:12px; }
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</style>
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</head>
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<body>
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<h1>拉格朗日点 · 圆形限制性三体问题（CR3BP）交互演示</h1>
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<div class="sub">旋转坐标系下的有效势、零速度曲线与测试粒子运动 · 全部物理来自经典力学，无虚构成分 · 点击画面可放置测试粒子</div>
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<div class="wrap">
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<div id="stage">
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<canvas id="cv" width="820" height="700"></canvas>
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<div id="hud"></div>
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</div>
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<div class="panel">
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<h2>系统与控制</h2>
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<div class="row">
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<span style="font-size:12.5px;color:var(--dim)">天体系统</span>
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<select id="mu">
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<option value="0.01215" selected>地-月 μ=0.01215</option>
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<option value="0.0009537">日-木 μ=0.000954</option>
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<option value="0.000003003">日-地 μ=3.0e-6</option>
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<option value="0.109">冥-卡 μ=0.109（L4/L5 不稳定）</option>
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</select>
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</div>
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<div class="row">
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<span style="font-size:12.5px;color:var(--dim)">雅可比常数 C</span>
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<input type="range" id="cj" min="2.95" max="4.2" step="0.005" value="3.10">
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<span class="mono" id="cj-val">3.100</span>
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</div>
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<div class="row">
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<button id="p-tad4">L4 马蹄/蝌蚪</button>
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<button id="p-tad5">L5 蝌蚪</button>
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<button id="p-l2">L2 准轨道</button>
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<button id="p-trans">L1 颈部穿越</button>
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<button id="p-out">外侧偏心轨道</button>
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<button id="p-clear">清除粒子</button>
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</div>
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<div class="row">
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<label><input type="checkbox" id="tg-trail" checked> 轨迹拖尾</label>
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<label><input type="checkbox" id="tg-forbid" checked> 禁行区/零速度曲线</label>
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<span style="font-size:11.5px;color:var(--dim)">（白线=滑块 C 的零速度曲线，暗红=其禁行区；黄线=粒子自身 C₀ 的零速度曲线，粒子永不可越）</span>
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</div>
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<div class="mono" id="lp-info"></div>
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<h2>物理原理（旋转坐标系，归一化 G=M=ω=a=1）</h2>
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<ul>
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<li>有效势：<code>Ω = ½(x²+y²) + (1−μ)/r₁ + μ/r₂</code>（离心势+双星引力势）</li>
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<li>运动方程：<code>ẍ = 2ẏ + Ω/∂x</code>，<code>ÿ = −2ẋ + ∂Ω/∂y</code>（科里奥利力使轨迹弯曲）</li>
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<li>唯一守恒量——雅可比常数：<code>C = 2Ω − (ẋ²+ẏ²)</code>。因 v²≥0，<code>2Ω < C</code> 的区域粒子永远无法进入（零速度曲线为边界）</li>
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<li>五个平衡点 L1–L5：∇Ω=0。L1–L3 为鞍点（不稳定）；L4/L5 虽是极大值点，但当 <code>μ < 0.03852</code>（Routh 判据，1875）时科里奥利力使其稳定</li>
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</ul>
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<h2>真实世界的拉格朗日点（非虚构）</h2>
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<table>
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<tr><th>点</th><th>真实驻留者</th></tr>
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<tr><td>日-地 L1</td><td>SOHO、ACE、DSCOVR、WIND 太阳观测器</td></tr>
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<tr><td>日-地 L2</td><td>JWST、Gaia、Planck、WMAP、Herschel</td></tr>
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<tr><td>地-月 L2</td><td>中国"鹊桥"中继星（嫦娥四号，2018）；ARTEMIS 探测器曾驻留地-月 L1/L2</td></tr>
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<tr><td>日-木 L4/L5</td><td>木星特洛伊小行星群（已确认上万颗）</td></tr>
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<tr><td>日-地 L4/L5</td><td>地球特洛伊 2010 TK7、2020 XL5；地-月 L4/L5 的 Kordylewski 尘埃云</td></tr>
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<tr><td>L3</td><td>不稳定且被太阳遮挡，无已知驻留天体（科幻"反地球"不存在）</td></tr>
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</table>
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<h2>诚实声明</h2>
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<p class="warn">演示为理想化 CR3BP：忽略其他天体摄动、太阳光压、轨道偏心率。真实任务（如 JWST 的 Lissajous/halo 轨道）需在此模型上叠加摄动与轨道维持。画面中双星在旋转系中固定，这是坐标系选择而非物理近似。</p>
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</div>
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</div>
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<script>
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'use strict';
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/* ============ 物理内核：CR3BP（归一化单位） ============ */
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let MU = 0.01215;
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const R1 = (x,y)=>Math.hypot(x+MU, y);
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const R2 = (x,y)=>Math.hypot(x-1+MU, y);
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// 有效势 Ω 与加速度
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function Omega(x,y){ return 0.5*(x*x+y*y) + (1-MU)/R1(x,y) + MU/R2(x,y); }
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function acc(x,y,vx,vy){
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const r1=R1(x,y), r2=R2(x,y);
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const r13=r1*r1*r1, r23=r2*r2*r2;
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const ax = 2*vy + x - (1-MU)*(x+MU)/r13 - MU*(x-1+MU)/r23;
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const ay = -2*vx + y - (1-MU)*y/r13 - MU*y/r23;
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return [ax,ay];
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}
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function jacobi(x,y,vx,vy){ return 2*Omega(x,y) - (vx*vx+vy*vy); }
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// RK4 单步
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function rk4(st, dt){
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const f = s => { const a = acc(s[0],s[1],s[2],s[3]); return [s[2],s[3],a[0],a[1]]; };
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const k1=f(st);
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const k2=f(st.map((v,i)=>v+dt/2*k1[i]));
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const k3=f(st.map((v,i)=>v+dt/2*k2[i]));
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const k4=f(st.map((v,i)=>v+dt*k3[i]));
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return st.map((v,i)=>v+dt/6*(k1[i]+2*k2[i]+2*k3[i]+k4[i]));
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}
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// 共线拉格朗日点：f(x)=∂Ω/x|_{y=0}=0 的三个根
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function collinear(){
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const f = x => {
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const r1=Math.abs(x+MU), r2=Math.abs(x-1+MU);
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return x - (1-MU)*(x+MU)/(r1*r1*r1) - MU*(x-1+MU)/(r2*r2*r2);
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};
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const roots=[];
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const zones=[[-1.5,-MU-1e-6],[-MU+1e-6,1-MU-1e-6],[1-MU+1e-6,1.8]];
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for(const [a0,b0] of zones){
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let a=a0,b=b0,fa=f(a);
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for(let i=0;i<200;i++){
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const m=(a+b)/2, fm=f(m);
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if(fa*fm<=0){ b=m; } else { a=m; fa=fm; }
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}
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roots.push((a+b)/2);
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}
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return roots; // [L3, L1, L2]
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}
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function lagrangePoints(){
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const [l3,l1,l2]=collinear();
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return { L1:[l1,0], L2:[l2,0], L3:[l3,0], L4:[0.5-MU, Math.sqrt(3)/2], L5:[0.5-MU, -Math.sqrt(3)/2] };
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}
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/* ============ 视口与势场底图 ============ */
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const cv=document.getElementById('cv'), ctx=cv.getContext('2d');
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const X0=-1.7, X1=1.9, Y0=-1.527, Y1=1.527;
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const GW=410, GH=350; // 势场网格分辨率
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const off=document.createElement('canvas'); off.width=GW; off.height=GH;
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const octx=off.getContext('2d');
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let baseCol=null, valArr=null; // 每像素底色与 2Ω 值
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const w2px=(x,y)=>[ (x-X0)/(X1-X0)*cv.width, (1-(y-Y0)/(Y1-Y0))*cv.height ];
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const px2w=(px,py)=>[ X0+px/cv.width*(X1-X0), Y0+(1-py/cv.height)*(Y1-Y0) ];
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function palette(t){
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const stops=[[6,10,34],[16,42,96],[32,96,160],[90,170,200],[240,210,140]];
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const s=Math.min(0.999,Math.max(0,t))*(stops.length-1);
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const i=Math.floor(s), k=s-i, A=stops[i], B=stops[i+1];
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return [A[0]+(B[0]-A[0])*k, A[1]+(B[1]-A[1])*k, A[2]+(B[2]-A[2])*k];
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}
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function buildBase(){
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const img=octx.createImageData(GW,GH);
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baseCol=new Float32Array(GW*GH*3); valArr=new Float32Array(GW*GH);
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for(let j=0;j<GH;j++){
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const y=Y0+(1-j/GH)*(Y1-Y0);
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for(let i=0;i<GW;i++){
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const x=X0+(i/GW)*(X1-X0);
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const v=2*Omega(x,y); valArr[j*GW+i]=v;
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const t=Math.pow(Math.min(1,Math.max(0,(v-2.9)/4)),0.5);
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const c=palette(t);
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baseCol[(j*GW+i)*3]=c[0]; baseCol[(j*GW+i)*3+1]=c[1]; baseCol[(j*GW+i)*3+2]=c[2];
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}
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}
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composite();
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}
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let CJ=3.10;
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let C0p=null; // 当前粒子的雅可比常数（画其专属零速度曲线）
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function composite(){
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const img=octx.createImageData(GW,GH);
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const showF=document.getElementById('tg-forbid').checked;
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const mask=new Uint8Array(GW*GH);
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for(let k=0;k<GW*GH;k++) mask[k]=valArr[k]<CJ?1:0; // 禁行区: 2Ω<C
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const mask0=C0p!=null?new Uint8Array(GW*GH):null;
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if(mask0) for(let k=0;k<GW*GH;k++) mask0[k]=valArr[k]<C0p?1:0;
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for(let j=0;j<GH;j++)for(let i=0;i<GW;i++){
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const k=j*GW+i; let r=baseCol[k*3],g=baseCol[k*3+1],b=baseCol[k*3+2];
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if(showF&&mask[k]){ r=r*0.12+34; g=g*0.10+4; b=b*0.10+6; } // 暗红禁行区
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// 零速度曲线：分类边界画亮线
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if(showF&&(i+1<GW&&mask[k+1]!==mask[k] || j+1<GH&&mask[k+GW]!==mask[k])){ r=235;g=240;b=250; }
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// 粒子自身 C0 的零速度曲线（黄线，粒子永不可越）
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if(showF&&mask0&&(i+1<GW&&mask0[k+1]!==mask0[k] || j+1<GH&&mask0[k+GW]!==mask0[k])){ r=255;g=214;b=110; }
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img.data[k*4]=r; img.data[k*4+1]=g; img.data[k*4+2]=b; img.data[k*4+3]=255;
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}
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octx.putImageData(img,0,0);
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}
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/* ============ 粒子与动画 ============ */
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let st=null, trail=[], C0=0, pStatus='', pLabel='', hasZVC=false;
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function spawn(x,y,vx,vy,label){
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st=[x,y,vx,vy]; trail=[]; C0=jacobi(x,y,vx,vy); C0p=C0;
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hasZVC = C0 > jacobi(LP.L4[0],LP.L4[1],0,0) + 1e-12; // C0 高于全局最小才有禁行区
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pStatus='运行中'; pLabel=label;
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composite();
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}
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const PRESETS={
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'p-tad4': ()=>spawn(LP.L4[0], LP.L4[1], 0.025, 0, 'L4 蝌蚪轨道（特洛伊型）'),
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'p-tad5': ()=>spawn(LP.L5[0], LP.L5[1], -0.025, 0, 'L5 蝌蚪轨道'),
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'p-l2' : ()=>spawn(LP.L2[0]+0.07, 0.05, 0, -0.10, 'L2 准轨道（不稳定，会漂移）'),
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'p-trans':()=>spawn(0.72, 0.015, 0, 0, 'L1 颈部穿越（混沌）'),
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'p-out' : ()=>spawn(-1.32, 0.0, 0, 0.40, '外侧偏心轨道（旋转系摆线）'),
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'p-clear':()=>{ st=null; trail=[]; pStatus=''; pLabel=''; C0p=null; composite(); }
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};
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let LP=lagrangePoints();
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const DT=0.002, SUB=12;
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function step(){
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if(!st) return;
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for(let i=0;i<SUB;i++){
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st=rk4(st,DT);
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const [x,y]=st;
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if(R1(x,y)<0.03){ pStatus='撞入主星'; st=null; break; }
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if(R2(x,y)<0.015){ pStatus='撞入伴星'; st=null; break; }
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if(Math.abs(x)>4||Math.abs(y)>4){ pStatus='逃逸出系统'; st=null; break; }
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}
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if(st){ trail.push([st[0],st[1]]); if(trail.length>3600) trail.shift(); }
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}
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function draw(){
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ctx.clearRect(0,0,cv.width,cv.height);
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ctx.imageSmoothingEnabled=true;
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ctx.drawImage(off,0,0,cv.width,cv.height);
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// 双星（旋转系中固定）
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const [p1x,p1y]=w2px(-MU,0), [p2x,p2y]=w2px(1-MU,0);
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const g1=ctx.createRadialGradient(p1x,p1y,0,p1x,p1y,26);
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g1.addColorStop(0,'#fff7d6'); g1.addColorStop(.4,'#ffd75e'); g1.addColorStop(1,'rgba(255,157,60,0)');
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ctx.fillStyle=g1; ctx.beginPath(); ctx.arc(p1x,p1y,26,0,7); ctx.fill();
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ctx.fillStyle='#ffd75e'; ctx.beginPath(); ctx.arc(p1x,p1y,11,0,7); ctx.fill();
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ctx.fillStyle='#c9ccd4'; ctx.beginPath(); ctx.arc(p2x,p2y,5,0,7); ctx.fill();
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ctx.fillStyle='#d8dee9'; ctx.font='12px sans-serif';
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ctx.fillText(MU>0.05?'冥王星':'地球', p1x-14, p1y+24);
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ctx.fillText(MU>0.05?'卡戎':'月球', p2x-10, p2y-10);
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// 拉格朗日点标记
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ctx.strokeStyle='#fff'; ctx.fillStyle='#fff'; ctx.font='bold 12px sans-serif';
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for(const [name,[lx,ly]] of Object.entries(LP)){
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const [px,py]=w2px(lx,ly);
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ctx.beginPath(); ctx.moveTo(px-5,py); ctx.lineTo(px+5,py); ctx.moveTo(px,py-5); ctx.lineTo(px,py+5); ctx.stroke();
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ctx.fillText(name, px+7, py-6);
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}
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// 拖尾
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if(document.getElementById('tg-trail').checked && trail.length>1){
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for(let i=1;i<trail.length;i++){
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||
const a=i/trail.length;
|
||
ctx.strokeStyle=`rgba(96,200,250,${0.15+0.6*a})`;
|
||
ctx.lineWidth=1.4;
|
||
const [x1,y1]=w2px(trail[i-1][0],trail[i-1][1]), [x2,y2]=w2px(trail[i][0],trail[i][1]);
|
||
ctx.beginPath(); ctx.moveTo(x1,y1); ctx.lineTo(x2,y2); ctx.stroke();
|
||
}
|
||
}
|
||
// 粒子
|
||
if(st){
|
||
const [px,py]=w2px(st[0],st[1]);
|
||
const g=ctx.createRadialGradient(px,py,0,px,py,9);
|
||
g.addColorStop(0,'rgba(255,255,255,1)'); g.addColorStop(1,'rgba(120,220,255,0)');
|
||
ctx.fillStyle=g; ctx.beginPath(); ctx.arc(px,py,9,0,7); ctx.fill();
|
||
}
|
||
|
||
// HUD
|
||
const drift = st? Math.abs(jacobi(st[0],st[1],st[2],st[3])-C0) : 0;
|
||
document.getElementById('hud').innerHTML =
|
||
`<b>旋转坐标系</b>（双星固定）· μ=${MU}<br>` +
|
||
(pLabel? `粒子：${pLabel} · C₀=${C0.toFixed(4)}${hasZVC?'（黄线为其零速度曲线）':'（C₀<C(L4)，全平面无禁行区）'}<br>` : '') +
|
||
(pStatus? `状态：<b>${pStatus}</b>` + (st? ` · 雅可比漂移 |ΔC|=${drift.toExponential(2)}（RK4 精度自检）`:'') + '<br>' : '') +
|
||
`C 滑块=${CJ.toFixed(3)} · 点击画面放置静止粒子`;
|
||
step();
|
||
requestAnimationFrame(draw);
|
||
}
|
||
|
||
/* ============ 交互 ============ */
|
||
document.getElementById('mu').onchange=e=>{ MU=parseFloat(e.target.value); LP=lagrangePoints(); buildBase(); showLP(); PRESETS['p-clear'](); };
|
||
document.getElementById('cj').oninput=e=>{ CJ=parseFloat(e.target.value); document.getElementById('cj-val').textContent=CJ.toFixed(3); composite(); };
|
||
document.getElementById('tg-forbid').onchange=composite;
|
||
for(const id of Object.keys(PRESETS)) document.getElementById(id).onclick=PRESETS[id];
|
||
cv.addEventListener('click', e=>{
|
||
const r=cv.getBoundingClientRect();
|
||
const [x,y]=px2w((e.clientX-r.left)*(cv.width/r.width), (e.clientY-r.top)*(cv.height/r.height));
|
||
spawn(x,y,0,0,'自定义（旋转系静止释放）');
|
||
});
|
||
function showLP(){
|
||
const c=n=>jacobi(LP[n][0],LP[n][1],0,0);
|
||
document.getElementById('lp-info').innerHTML =
|
||
`L1 x=${LP.L1[0].toFixed(4)} (C=${c('L1').toFixed(4)}) · L2 x=${LP.L2[0].toFixed(4)} (C=${c('L2').toFixed(4)})<br>` +
|
||
`L3 x=${LP.L3[0].toFixed(4)} (C=${c('L3').toFixed(4)}) · L4/L5 C=${c('L4').toFixed(4)}<br>` +
|
||
`Routh 判据 μ<0.03852 → L4/L5 ${MU<0.0385208965?'<b style="color:#7ee2a8">稳定</b>':'<b style="color:#ff8080">不稳定</b>'}`;
|
||
}
|
||
buildBase(); showLP(); requestAnimationFrame(draw);
|
||
</script>
|
||
</body>
|
||
</html>
|