pendulum.html

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<title>Маятник — фазовые портреты</title>
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<div class="app">
  <header>
    <div class="brand">
      <div class="eyebrow">danySSG · 2023 → 2026</div>
      <h1>Ма<em>я</em>тник</h1>
      <p class="sub">наследник <code>pendulum</code> · <code>double-pendulum</code> · <code>my-first-binder</code> — теперь в реальном времени</p>
    </div>
    <nav class="tabs" aria-label="Режим">
      <button data-mode="single" aria-pressed="true">Автономный</button>
      <button data-mode="forced" aria-pressed="false">Вынужденный</button>
      <button data-mode="double" aria-pressed="false">Двойной</button>
    </nav>
  </header>

  <main>
    <section class="stage">
      <div class="panel">
        <div class="panel-head">
          <span class="panel-title">Маятник</span>
          <label class="toggle" id="ghostsWrap" hidden title="8 клонов с отличием в θ₁ на 10⁻⁶ рад — чувствительность к начальным условиям"><input type="checkbox" id="ghosts"> призраки</label>
          <span class="spacer"></span>
          <span class="hint">грузик можно перетаскивать и бросать</span>
        </div>
        <canvas id="cv-pend" aria-label="Анимация маятника"></canvas>
      </div>
      <div class="panel">
        <div class="panel-head">
          <span class="panel-title">Фазовый портрет</span>
          <span class="legend" id="legend"></span>
          <span class="spacer"></span>
          <label class="toggle" id="fieldWrap" title="Векторное поле направлений и сепаратриса"><input type="checkbox" id="field" checked> поле</label>
          <div class="seg" id="viewSeg" role="group" aria-label="Вид фазового пространства">
            <button type="button" data-v="flat" aria-pressed="true">плоскость</button>
            <button type="button" data-v="wrap" aria-pressed="false" title="Обещание из ноутбука 2023 года: θ mod 2π">цилиндр</button>
            <button type="button" data-v="cyl3d" aria-pressed="false" title="Траектория наматывается на настоящий цилиндр">3D</button>
          </div>
        </div>
        <canvas id="cv-phase" aria-label="Фазовый портрет"></canvas>
      </div>
      <div class="panel energy-panel">
        <div class="panel-head">
          <span class="panel-title">Энергия E(t)</span>
        </div>
        <canvas id="cv-energy" aria-label="График полной энергии"></canvas>
      </div>
    </section>

    <section class="deck">
      <div class="card">
        <div class="presets" id="presets"></div>
        <div class="sliders" id="sliders"></div>
      </div>
      <div class="side">
        <div class="card">
          <div class="playback">
            <button class="btn btn-accent" id="btnPlay">Пауза</button>
            <button class="btn btn-ghost" id="btnReset">Сброс</button>
          </div>
          <div class="srow" style="margin-top:12px">
            <label for="speed">Скорость времени <output id="speedOut">×1.00</output></label>
            <input type="range" id="speed" min="0.1" max="3" step="0.05" value="1">
          </div>
          <div class="playback" style="margin-top:12px">
            <button class="btn btn-ghost" id="btnRec">⏺ Записать видео</button>
            <button class="btn btn-ghost" id="btnShare">Ссылка</button>
          </div>
          <p class="kbd-hint"><kbd>Пробел</kbd> — пауза · <kbd>R</kbd> — сброс</p>
        </div>
        <div class="card">
          <dl class="readouts" id="readouts"></dl>
        </div>
      </div>
    </section>

    <details class="theory">
      <summary>Читать теорию</summary>
      <div class="theory-body">
        <h3>Автономный маятник</h3>
        <p>Груз массы <i>m</i> на невесомом стержне длины <i>l</i> в среде с вязкостью <i>b</i>:</p>
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        <h3>Маятник с периодическим возмущением</h3>
        <p>К автономному уравнению добавляется вынуждающий момент с экспоненциально меняющейся амплитудой:</p>
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        <h3>Двойной маятник</h3>
        <p>Углы θ₁, θ₂ отсчитываются от вертикали; уравнения получаются из лагранжиана (вывод — в theory.pdf оригинального репозитория):</p>
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        <h3>Численное решение</h3>
        <p>Система интегрируется методом Рунге–Кутты 4-го порядка с шагом 2 мс — прямо во время движения. В 2023-м это делал <code style="font-family:var(--mono);font-size:12.5px">scipy.solve_ivp</code> (DOP853), после чего Manim минутами рендерил видео. Теперь между «подвинул слайдер» и «увидел» — один кадр.</p>
        <h3>Фазовый цилиндр</h3>
        <p>Последняя ячейка ноутбука 2023 года обещала: «в следующей версии фазовое пространство будет представлено цилиндром». Виды «цилиндр» и «3D» выполняют это обещание: в первом угол берётся по модулю 2π и вращение («солнышко») перестаёт убегать за край портрета, а во втором траектория буквально наматывается на цилиндр. Пунктирная кривая на плоском портрете — сепаратриса, граница между колебаниями и вращением:</p>
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transform="translate(258.962084 0.75)"/> <use xlink:href="#Cmex10-15" transform="translate(308.962084 104.078125) scale(0.72923)"/> <use xlink:href="#Cmmi10-2f" transform="translate(394.383959 0.75)"/> <use xlink:href="#Cmmi10-62" transform="translate(442.089037 0.75)"/> <use xlink:href="#Cmmi10-71" transform="translate(492.089037 0.75)"/> <use xlink:href="#Cmr10-7b" transform="translate(562.152273 0.75)"/> <use xlink:href="#Cmr10-42" transform="translate(606.537038 0.75)"/> <use xlink:href="#Cmr10-52" transform="translate(656.537038 0.75)"/> <use xlink:href="#Cmmi10-12" transform="translate(719.858383 35.9125) scale(0.7)"/> <use xlink:href="#Cmr10-31" transform="translate(718.858383 -30.251563) scale(0.7)"/> <path d="M 381.883959 106.75 L 381.883959 113 L 534.374193 113 L 534.374193 106.75 L 381.883959 106.75 z "/> <path d="M 718.858383 22.625 L 718.858383 28.875 L 753.858383 28.875 L 753.858383 22.625 L 718.858383 22.625 z "/> </g> </g> </g> </svg></div>
      </div>
    </details>
  </main>

  <footer>
    <span>Кадр считается за <span class="ms" id="frameMs">—</span> мс. В 2023-м ролик на 30 секунд рендерился минутами.</span>
    <span>g по умолчанию — 2.0 м/с², как в оригинале · θ₀ = 2.71 ≈ e</span>
  </footer>
</div>
<div class="toast" id="toast" role="status"></div>

<script>
(() => {
  'use strict';
  const TAU = Math.PI * 2;
  const wrapPi = a => { a = (a + Math.PI) % TAU; if (a < 0) a += TAU; return a - Math.PI; };
  const C = {
    yellow: '#ffff00', blue: '#58c4dd', red: '#fc6255', orange: '#ff862f',
    white: '#ececec', grey: '#8a8279', canvas: '#0f0e0d',
  };

  // ---------- режимы ----------
  const S = (key, label, min, max, step, def, opts = {}) => ({ key, label, min, max, step, def, ...opts });
  const gSlider = S('g', 'Ускорение g', 0.1, 20, 0.1, 2.0, { unit: 'м/с²', preset: 9.8 });

  const MODES = {
    single: {
      sliders: [
        S('th0', 'Начальный угол θ₀', -3.14, 3.14, 0.01, 2.71, { unit: 'рад', resets: true }),
        S('w0', 'Начальная скорость θ̇₀', -10, 10, 0.1, 0, { unit: 'рад/с', resets: true }),
        S('b', 'Вязкость b', 0, 5, 0.01, 0.35),
        gSlider,
        S('l', 'Длина стержня l', 0.1, 5, 0.1, 1.0, { unit: 'м' }),
        S('m', 'Масса груза m', 0.1, 10, 0.1, 5.0, { unit: 'кг' }),
      ],
      init: p => [p.th0, p.w0],
      deriv: (t, y, p) => [y[1], -(p.g / p.l) * Math.sin(y[0]) - (p.b / (p.m * p.l)) * y[1]],
      reach: p => p.l,
      series: [{ i: 0, color: C.yellow, label: null }],
      bobs: [{ color: C.red, trail: C.orange, l: p => p.l, m: p => p.m, sub: '' }],
      energy: (y, p) => 0.5 * p.m * (p.l * y[1]) ** 2 + p.m * p.g * p.l * (1 - Math.cos(y[0])),
      readouts: ['t', 'th', 'w', 'E'],
    },
    forced: {
      sliders: [
        S('th0', 'Начальный угол θ₀', -3.14, 3.14, 0.01, 2.71, { unit: 'рад', resets: true }),
        S('w0', 'Начальная скорость θ̇₀', -10, 10, 0.1, 0, { unit: 'рад/с', resets: true }),
        S('b', 'Вязкость b', 0, 5, 0.01, 0.35),
        gSlider,
        S('l', 'Длина стержня l', 0.1, 5, 0.1, 1.0, { unit: 'м' }),
        S('m', 'Масса груза m', 0.1, 10, 0.1, 5.0, { unit: 'кг' }),
        S('a1', 'Эксп. коэффициент a₁', -2, 2, 0.05, 1.0),
        S('a2', 'Период. коэффициент a₂', 0, 10, 0.05, 2.0),
      ],
      init: p => [p.th0, p.w0],
      deriv: (t, y, p) => [y[1],
        Math.exp(p.a1 * t / 30) * Math.cos(p.a2 * t)
        - (p.g / p.l) * Math.sin(y[0]) - (p.b / (p.m * p.l)) * y[1]],
      reach: p => p.l,
      series: [{ i: 0, color: C.yellow, label: null }],
      bobs: [{ color: C.red, trail: C.orange, l: p => p.l, m: p => p.m, sub: '' }],
      energy: (y, p) => 0.5 * p.m * (p.l * y[1]) ** 2 + p.m * p.g * p.l * (1 - Math.cos(y[0])),
      readouts: ['t', 'th', 'w', 'F', 'E'],
    },
    double: {
      sliders: [
        S('th10', 'Начальный угол θ₁', -3.14, 3.14, 0.01, 2.71, { unit: 'рад', resets: true }),
        S('w10', 'Нач. скорость θ̇₁', -10, 10, 0.1, 0, { unit: 'рад/с', resets: true }),
        S('th20', 'Начальный угол θ₂', -3.14, 3.14, 0.01, 2.71, { unit: 'рад', resets: true }),
        S('w20', 'Нач. скорость θ̇₂', -10, 10, 0.1, 0, { unit: 'рад/с', resets: true }),
        S('l1', 'Длина стержня l₁', 0.1, 5, 0.1, 1.0, { unit: 'м' }),
        S('l2', 'Длина стержня l₂', 0.1, 5, 0.1, 1.0, { unit: 'м' }),
        S('m1', 'Масса груза m₁', 0.1, 10, 0.1, 5.0, { unit: 'кг' }),
        S('m2', 'Масса груза m₂', 0.1, 10, 0.1, 5.0, { unit: 'кг' }),
        gSlider,
      ],
      init: p => [p.th10, p.w10, p.th20, p.w20],
      deriv: (t, y, p) => {
        const [a1, w1, a2, w2] = y, { m1, m2, l1, l2, g } = p;
        const d = a1 - a2, sd = Math.sin(d), cd = Math.cos(d);
        const den = 2 * m1 + m2 - m2 * Math.cos(2 * d);
        const dw1 = (-g * (2 * m1 + m2) * Math.sin(a1) - m2 * g * Math.sin(a1 - 2 * a2)
          - 2 * sd * m2 * (l2 * w2 * w2 + l1 * w1 * w1 * cd)) / (l1 * den);
        const dw2 = (2 * sd * (l1 * w1 * w1 * (m1 + m2) + g * (m1 + m2) * Math.cos(a1)
          + l2 * w2 * w2 * m2 * cd)) / (l2 * den);
        return [w1, dw1, w2, dw2];
      },
      reach: p => p.l1 + p.l2,
      series: [
        { i: 0, color: C.yellow, label: 'θ₁' },
        { i: 2, color: C.blue, label: 'θ₂' },
      ],
      bobs: [
        { color: C.yellow, trail: C.yellow, l: p => p.l1, m: p => p.m1, sub: '1' },
        { color: C.blue, trail: C.blue, l: p => p.l2, m: p => p.m2, sub: '2' },
      ],
      energy: (y, p) => {
        const [a1, w1, a2, w2] = y, { m1, m2, l1, l2, g } = p;
        return 0.5 * (m1 + m2) * l1 * l1 * w1 * w1 + 0.5 * m2 * l2 * l2 * w2 * w2
          + m2 * l1 * l2 * w1 * w2 * Math.cos(a1 - a2)
          - (m1 + m2) * g * l1 * Math.cos(a1) - m2 * g * l2 * Math.cos(a2)
          + (m1 + m2) * g * l1 + m2 * g * l2;
      },
      readouts: ['t', 'th1', 'th2', 'w1', 'w2', 'E'],
    },
  };

  const READOUT_DEFS = {
    t:   { label: 't',  fmt: s => s.t.toFixed(2) + ' с' },
    th:  { label: 'θ',  fmt: s => s.y[0].toFixed(2) + ' рад' },
    w:   { label: 'θ̇',  fmt: s => s.y[1].toFixed(2) + ' рад/с' },
    th1: { label: 'θ₁', fmt: s => s.y[0].toFixed(2) + ' рад' },
    th2: { label: 'θ₂', fmt: s => s.y[2].toFixed(2) + ' рад' },
    w1:  { label: 'θ̇₁', fmt: s => s.y[1].toFixed(2) + ' рад/с' },
    w2:  { label: 'θ̇₂', fmt: s => s.y[3].toFixed(2) + ' рад/с' },
    F:   { label: 'F',  fmt: s => (Math.exp(P.a1 * s.t / 30) * Math.cos(P.a2 * s.t)).toFixed(2) },
    E:   { label: 'E',  fmt: s => MODES[s.mode].energy(s.y, P).toFixed(2) + ' Дж' },
  };

  // ---------- пресеты ----------
  const PRESETS = [
    { label: 'Солнышко', mode: 'single', view: 'wrap', params: { th0: 0, w0: 4.5, b: 0.1, g: 2, l: 1, m: 5 } },
    { label: 'Сепаратриса', mode: 'single', view: 'flat', field: true, params: { th0: 3.1, w0: 0, b: 0, g: 2, l: 1, m: 5 } },
    { label: 'Резонанс', mode: 'forced', view: 'flat', params: { th0: 0.1, w0: 0, b: 0.1, g: 2, l: 1, m: 5, a1: 0, a2: 1.4 } },
    { label: 'Хаос', mode: 'double', view: 'flat', ghosts: true, params: { th10: 2.71, w10: 0, th20: 2.71, w20: 0, l1: 1, l2: 1, m1: 5, m2: 5, g: 2 } },
  ];

  // ---------- состояние ----------
  const P = {};
  const REDUCED = matchMedia('(prefers-reduced-motion: reduce)').matches;
  const sim = {
    mode: 'single', y: [], t: 0,
    running: !REDUCED,
    view: 'flat', energy: [], ghosts: null, yaw: 0.6, pitch: 0.35,
    dragging: -1, speed: 1,
    phase: [],            // по одному плоскому массиву [θ,ω,θ,ω,…] на серию
    bobTrail: [],         // [{t, ang:[…]}]
    maxTh: 1, maxW: 1, rTh: 1.4, rW: 1.4,
    bobPx: [], pivotPx: null,
  };
  const H = 0.002, PUSH_EVERY = 3, TRAIL_CAP = 24000, BOB_FADE = 0.55;
  let pushCnt = 0;

  function rk4(t, y, h, f) {
    const k1 = f(t, y, P);
    const y2 = y.map((v, i) => v + 0.5 * h * k1[i]);
    const k2 = f(t + h / 2, y2, P);
    const y3 = y.map((v, i) => v + 0.5 * h * k2[i]);
    const k3 = f(t + h / 2, y3, P);
    const y4 = y.map((v, i) => v + h * k3[i]);
    const k4 = f(t + h, y4, P);
    return y.map((v, i) => v + h / 6 * (k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i]));
  }

  function recomputeMax() {
    let mt = 0.8, mw = 0.8;
    for (const arr of sim.phase) {
      for (let i = 0; i < arr.length; i += 2) {
        if (!Number.isFinite(arr[i]) || !Number.isFinite(arr[i + 1])) continue;
        const a = Math.abs(arr[i]), b = Math.abs(arr[i + 1]);
        if (a > mt) mt = a;
        if (b > mw) mw = b;
      }
    }
    sim.maxTh = mt;
    sim.maxW = mw;
  }

  function pushPhase() {
    const md = MODES[sim.mode];
    let trimmed = false;
    md.series.forEach((s, k) => {
      const th = sim.y[s.i], w = sim.y[s.i + 1];
      const arr = sim.phase[k];
      arr.push(th, w);
      if (arr.length > TRAIL_CAP) { arr.splice(0, TRAIL_CAP / 4); trimmed = true; }
      const a = Math.abs(th), b = Math.abs(w);
      if (Number.isFinite(a) && a > sim.maxTh) sim.maxTh = a;
      if (Number.isFinite(b) && b > sim.maxW) sim.maxW = b;
    });
    if (trimmed) recomputeMax();
    sim.energy.push(sim.t, md.energy(sim.y, P));
    if (sim.energy.length > TRAIL_CAP / 2) sim.energy.splice(0, TRAIL_CAP / 8);
  }

  function stepSim(dt) {
    const md = MODES[sim.mode];
    const n = Math.max(1, Math.ceil(dt / H)), h = dt / n;
    for (let i = 0; i < n; i++) {
      if (sim.ghosts) for (let gi = 0; gi < sim.ghosts.length; gi++) sim.ghosts[gi] = rk4(sim.t, sim.ghosts[gi], h, md.deriv);
      sim.y = rk4(sim.t, sim.y, h, md.deriv);
      sim.t += h;
      if (++pushCnt >= PUSH_EVERY) { pushCnt = 0; pushPhase(); }
    }
    sim.bobTrail.push({ t: sim.t, ang: md.series.map(s => sim.y[s.i]) });
    while (sim.bobTrail.length && sim.t - sim.bobTrail[0].t > BOB_FADE) sim.bobTrail.shift();
  }

  function resetSim() {
    const md = MODES[sim.mode];
    sim.y = md.init(P);
    sim.t = 0;
    sim.phase = md.series.map(() => []);
    sim.energy = [];
    sim.bobTrail = [];
    sim.maxTh = Math.max(...md.series.map(s => Math.abs(sim.y[s.i])), 0.8);
    sim.maxW = 0.8;
    pushCnt = 0;
    sim.dragging = -1;
    pushPhase();
    initGhosts();
  }

  // ---------- DOM ----------
  const $ = id => document.getElementById(id);
  const slidersEl = $('sliders'), readoutsEl = $('readouts'), legendEl = $('legend');
  const btnPlay = $('btnPlay'), btnReset = $('btnReset');
  const viewSeg = $('viewSeg'), fieldEl = $('field'), fieldWrap = $('fieldWrap');
  const ghostsEl = $('ghosts'), ghostsWrap = $('ghostsWrap');
  let readoutSpans = [];
  let sliderCtl = {};

  function initGhosts() {
    if (sim.mode === 'double' && ghostsEl.checked) {
      sim.ghosts = Array.from({ length: 8 }, (_, k) => {
        const y = sim.y.slice();
        y[0] += (k + 1) * 1e-6;
        return y;
      });
    } else sim.ghosts = null;
  }

  function buildSliders() {
    slidersEl.innerHTML = '';
    sliderCtl = {};
    for (const cfg of MODES[sim.mode].sliders) {
      P[cfg.key] = cfg.def;
      const row = document.createElement('div');
      row.className = 'srow';
      const label = document.createElement('label');
      const name = document.createElement('span');
      name.textContent = cfg.label;
      const out = document.createElement('output');
      const fmt = v => v.toFixed(2) + (cfg.unit ? ' ' + cfg.unit : '');
      out.textContent = fmt(cfg.def);
      label.append(name, out);
      if (cfg.preset != null) {
        const chip = document.createElement('button');
        chip.type = 'button'; chip.className = 'preset'; chip.textContent = String(cfg.preset);
        chip.title = 'Земное значение';
        name.append(' ', chip);
        chip.addEventListener('click', () => { input.value = cfg.preset; input.dispatchEvent(new Event('input')); });
      }
      const input = document.createElement('input');
      input.type = 'range';
      input.min = cfg.min; input.max = cfg.max; input.step = cfg.step; input.value = cfg.def;
      input.setAttribute('aria-label', cfg.label);
      input.addEventListener('input', () => {
        P[cfg.key] = parseFloat(input.value);
        out.textContent = fmt(P[cfg.key]);
        if (cfg.resets) resetSim();
        updateHash();
      });
      label.htmlFor = input.id = 'sl-' + cfg.key;
      row.append(label, input);
      slidersEl.append(row);
      sliderCtl[cfg.key] = { input, out, fmt };
    }
  }

  function buildPresets() {
    const el = $('presets');
    for (const p of PRESETS) {
      const b = document.createElement('button');
      b.type = 'button';
      b.textContent = p.label;
      b.addEventListener('click', () => applyPreset(p));
      el.append(b);
    }
  }

  function applyParams(params) {
    for (const [k, v] of Object.entries(params)) {
      const ctl = sliderCtl[k];
      if (!ctl) continue;
      P[k] = v;
      ctl.input.value = v;
      ctl.out.textContent = ctl.fmt(v);
    }
  }

  function applyPreset(p) {
    setMode(p.mode);
    applyParams(p.params);
    setView(p.view || 'flat');
    ghostsEl.checked = !!p.ghosts;
    if ('field' in p) fieldEl.checked = p.field;
    resetSim();
    updateHash();
  }

  function buildReadouts() {
    readoutsEl.innerHTML = '';
    readoutSpans = [];
    for (const key of MODES[sim.mode].readouts) {
      const def = READOUT_DEFS[key];
      const dt = document.createElement('dt');
      dt.textContent = def.label;
      const dd = document.createElement('dd');
      readoutsEl.append(dt, dd);
      readoutSpans.push([dd, def.fmt]);
    }
  }

  function buildLegend() {
    legendEl.innerHTML = '';
    for (const s of MODES[sim.mode].series) {
      if (!s.label) continue;
      const chip = document.createElement('span');
      chip.className = 'chip';
      const i = document.createElement('i');
      i.style.background = s.color;
      chip.append(i, s.label);
      legendEl.append(chip);
    }
  }

  function setMode(mode) {
    sim.mode = mode;
    document.querySelectorAll('.tabs button').forEach(b =>
      b.setAttribute('aria-pressed', String(b.dataset.mode === mode)));
    buildSliders();
    buildReadouts();
    buildLegend();
    ghostsWrap.hidden = mode !== 'double';
    fieldWrap.hidden = MODES[mode].series.length !== 1;
    resetSim();
  }

  function setView(v) {
    sim.view = v;
    viewSeg.querySelectorAll('button').forEach(b =>
      b.setAttribute('aria-pressed', String(b.dataset.v === v)));
    cvF.style.touchAction = v === 'cyl3d' ? 'none' : '';
  }

  // ---------- канвасы ----------
  const cvP = $('cv-pend'), cvF = $('cv-phase'), cvE = $('cv-energy');
  const ctxP = cvP.getContext('2d'), ctxF = cvF.getContext('2d'), ctxE = cvE.getContext('2d');
  const dpr = Math.min(devicePixelRatio || 1, 2);
  function fitCanvas(cv) {
    const w = cv.clientWidth, h = cv.clientHeight;
    if (cv.width !== Math.round(w * dpr)) { cv.width = Math.round(w * dpr); cv.height = Math.round(h * dpr); }
  }
  new ResizeObserver(() => { fitCanvas(cvP); fitCanvas(cvF); fitCanvas(cvE); }).observe(cvP);

  function mathText(ctx, ch, sub, x, y, size, color) {
    ctx.fillStyle = color;
    ctx.font = 'italic ' + size + 'px ' + 'Georgia, "Times New Roman", serif';
    ctx.fillText(ch, x, y);
    if (sub) {
      const w = ctx.measureText(ch).width;
      ctx.font = 'italic ' + (size * 0.62) + 'px Georgia, "Times New Roman", serif';
      ctx.fillText(sub, x + w + 1, y + size * 0.22);
    }
  }

  function drawAngleArc(ctx, px, py, theta, r, sub) {
    const w = wrapPi(theta);
    if (Math.abs(w) < 0.03) return;
    const to = Math.atan2(Math.cos(w), Math.sin(w));
    ctx.beginPath();
    ctx.strokeStyle = C.grey;
    ctx.lineWidth = 1.4;
    ctx.arc(px, py, r, Math.PI / 2, to, w > 0);
    ctx.stroke();
    const scale = Math.min(1, Math.abs(w) ** (1 / 3));
    const mid = Math.PI / 2 - w / 2;
    const lr = r + 15;
    ctx.textAlign = 'center'; ctx.textBaseline = 'middle';
    mathText(ctx, 'θ', sub, px + lr * Math.cos(mid), py + lr * Math.sin(mid), 18 * scale, C.white);
    ctx.textAlign = 'left'; ctx.textBaseline = 'alphabetic';
  }

  function drawPend() {
    fitCanvas(cvP);
    const W = cvP.width / dpr, Hh = cvP.height / dpr;
    ctxP.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctxP.fillStyle = C.canvas;
    ctxP.fillRect(0, 0, W, Hh);
    const md = MODES[sim.mode];
    const reach = md.reach(P);
    const s = 0.42 * Math.min(W, Hh) / reach;
    const cx = W / 2, cy = Hh / 2;
    sim.pivotPx = { x: cx, y: cy };

    // штриховая вертикаль
    ctxP.setLineDash([6, 6]);
    ctxP.strokeStyle = '#4a453f';
    ctxP.lineWidth = 1.2;
    ctxP.beginPath();
    ctxP.moveTo(cx, cy);
    ctxP.lineTo(cx, cy + s * md.bobs[0].l(P) * 0.95);
    ctxP.stroke();
    ctxP.setLineDash([]);

    // позиции грузов
    const pts = [{ x: cx, y: cy }];
    let px = cx, py = cy;
    md.bobs.forEach((b, k) => {
      const th = sim.y[md.series[k].i];
      px += s * b.l(P) * Math.sin(th);
      py += s * b.l(P) * Math.cos(th);
      pts.push({ x: px, y: py });
    });

    // затухающие следы грузов
    for (let k = 0; k < md.bobs.length; k++) {
      const tr = sim.bobTrail;
      if (tr.length < 2) break;
      ctxP.lineWidth = 2.4;
      ctxP.lineCap = 'round';
      for (let i = 1; i < tr.length; i++) {
        const posAt = rec => {
          let x = cx, y = cy;
          for (let j = 0; j <= k; j++) {
            x += s * md.bobs[j].l(P) * Math.sin(rec.ang[j]);
            y += s * md.bobs[j].l(P) * Math.cos(rec.ang[j]);
          }
          return { x, y };
        };
        const a = posAt(tr[i - 1]), b = posAt(tr[i]);
        const alpha = Math.max(0, 1 - (sim.t - tr[i].t) / BOB_FADE);
        ctxP.globalAlpha = alpha * 0.75;
        ctxP.strokeStyle = md.bobs[k].trail;
        ctxP.beginPath(); ctxP.moveTo(a.x, a.y); ctxP.lineTo(b.x, b.y); ctxP.stroke();
      }
      ctxP.globalAlpha = 1;
    }

    // призрачные клоны: чувствительность к начальным условиям
    if (sim.ghosts) {
      for (const gs of sim.ghosts) {
        let gpx = cx, gpy = cy;
        ctxP.strokeStyle = 'rgba(236,236,236,0.10)';
        ctxP.lineWidth = 1.2;
        ctxP.beginPath();
        ctxP.moveTo(gpx, gpy);
        const ends = [];
        for (let j = 0; j < md.bobs.length; j++) {
          gpx += s * md.bobs[j].l(P) * Math.sin(gs[md.series[j].i]);
          gpy += s * md.bobs[j].l(P) * Math.cos(gs[md.series[j].i]);
          ctxP.lineTo(gpx, gpy);
          ends.push([gpx, gpy, md.bobs[j].color]);
        }
        ctxP.stroke();
        ctxP.globalAlpha = 0.3;
        for (const [ex, ey, ec] of ends) {
          ctxP.fillStyle = ec;
          ctxP.beginPath(); ctxP.arc(ex, ey, 3.4, 0, TAU); ctxP.fill();
        }
        ctxP.globalAlpha = 1;
      }
    }

    // стержни
    ctxP.strokeStyle = C.white;
    ctxP.lineWidth = 2.2;
    ctxP.beginPath();
    for (let i = 0; i < pts.length - 1; i++) {
      ctxP.moveTo(pts[i].x, pts[i].y);
      ctxP.lineTo(pts[i + 1].x, pts[i + 1].y);
    }
    ctxP.stroke();

    // точка подвеса
    ctxP.fillStyle = C.white;
    ctxP.beginPath(); ctxP.arc(cx, cy, 3.2, 0, TAU); ctxP.fill();

    // дуги углов (θ₂ — от вертикали в точке сочленения)
    drawAngleArc(ctxP, cx, cy, sim.y[0], Math.min(34, s * md.bobs[0].l(P) * 0.45), md.bobs.length > 1 ? '1' : '');
    if (md.bobs.length > 1) {
      const j = pts[1];
      ctxP.setLineDash([4, 5]);
      ctxP.strokeStyle = '#4a453f';
      ctxP.beginPath(); ctxP.moveTo(j.x, j.y); ctxP.lineTo(j.x, j.y + s * P.l2 * 0.6); ctxP.stroke();
      ctxP.setLineDash([]);
      drawAngleArc(ctxP, j.x, j.y, sim.y[2], Math.min(28, s * P.l2 * 0.4), '2');
    }

    // грузы
    sim.bobPx = [];
    md.bobs.forEach((b, k) => {
      const p = pts[k + 1];
      const r = 7 * Math.cbrt(b.m(P)) + 2;
      ctxP.fillStyle = b.color;
      ctxP.beginPath(); ctxP.arc(p.x, p.y, r, 0, TAU); ctxP.fill();
      ctxP.strokeStyle = C.canvas;
      ctxP.lineWidth = 2;
      ctxP.stroke();
      sim.bobPx.push({ x: p.x, y: p.y, r: Math.max(r, 16) });
    });
  }

  const niceStep = raw => {
    if (!Number.isFinite(raw) || raw <= 0) return 1;
    const p = Math.pow(10, Math.floor(Math.log10(raw)));
    const m = raw / p;
    return (m <= 1 ? 1 : m <= 2 ? 2 : m <= 5 ? 5 : 10) * p;
  };

  function drawPhase() {
    fitCanvas(cvF);
    const W = cvF.width / dpr, Hh = cvF.height / dpr;
    ctxF.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctxF.fillStyle = C.canvas;
    ctxF.fillRect(0, 0, W, Hh);
    const md = MODES[sim.mode];
    const wrap = sim.view === 'wrap';

    const tTh = wrap ? Math.PI : Math.min(Math.max(sim.maxTh * 1.15, 1.2), 1e4);
    const tW = Math.min(Math.max(sim.maxW * 1.15, 1.2), 1e4);
    sim.rTh += (tTh - sim.rTh) * 0.12;
    sim.rW += (tW - sim.rW) * 0.12;

    if (sim.view === 'cyl3d') { drawPhase3D(W, Hh); return; }

    const pad = 30;
    const cx = W / 2, cy = Hh / 2;
    const sx = (W / 2 - pad) / sim.rTh, sy = (Hh / 2 - pad) / sim.rW;
    const X = th => cx + th * sx, Y = w => cy - w * sy;

    // оси со стрелками
    ctxF.strokeStyle = C.grey;
    ctxF.fillStyle = C.grey;
    ctxF.lineWidth = 1.3;
    ctxF.beginPath();
    ctxF.moveTo(pad * 0.4, cy); ctxF.lineTo(W - pad * 0.4, cy);
    ctxF.moveTo(cx, Hh - pad * 0.4); ctxF.lineTo(cx, pad * 0.4);
    ctxF.stroke();
    ctxF.beginPath();
    ctxF.moveTo(W - pad * 0.4, cy); ctxF.lineTo(W - pad * 0.4 - 9, cy - 4); ctxF.lineTo(W - pad * 0.4 - 9, cy + 4); ctxF.fill();
    ctxF.beginPath();
    ctxF.moveTo(cx, pad * 0.4); ctxF.lineTo(cx - 4, pad * 0.4 + 9); ctxF.lineTo(cx + 4, pad * 0.4 + 9); ctxF.fill();

    // деления
    ctxF.font = '10.5px ' + 'ui-monospace, Menlo, monospace';
    ctxF.textAlign = 'center'; ctxF.textBaseline = 'top';
    if (wrap) {
      const t = [[-Math.PI, '−π'], [-Math.PI / 2, '−π/2'], [Math.PI / 2, 'π/2'], [Math.PI, 'π']];
      for (const [v, lb] of t) {
        ctxF.beginPath(); ctxF.moveTo(X(v), cy - 4); ctxF.lineTo(X(v), cy + 4); ctxF.stroke();
        ctxF.fillText(lb, X(v), cy + 7);
      }
    } else {
      const st = niceStep(sim.rTh / 2.2);
      for (let v = st; v <= sim.rTh; v += st) {
        for (const vv of [v, -v]) {
          ctxF.beginPath(); ctxF.moveTo(X(vv), cy - 4); ctxF.lineTo(X(vv), cy + 4); ctxF.stroke();
          ctxF.fillText(String(parseFloat(vv.toFixed(2))), X(vv), cy + 7);
        }
      }
    }
    const stw = niceStep(sim.rW / 2.2);
    ctxF.textAlign = 'left'; ctxF.textBaseline = 'middle';
    for (let v = stw; v <= sim.rW; v += stw) {
      for (const vv of [v, -v]) {
        ctxF.beginPath(); ctxF.moveTo(cx - 4, Y(vv)); ctxF.lineTo(cx + 4, Y(vv)); ctxF.stroke();
        ctxF.fillText(String(parseFloat(vv.toFixed(2))), cx + 8, Y(vv));
      }
    }

    // подписи осей
    ctxF.textAlign = 'left'; ctxF.textBaseline = 'alphabetic';
    mathText(ctxF, 'θ', '', W - pad * 0.4 - 4, cy - 10, 17, C.white);
    mathText(ctxF, 'θ̇', '', cx + 10, pad * 0.4 + 14, 17, C.white);

    // векторное поле и сепаратриса (только одномаятниковые режимы)
    if (fieldEl.checked && md.series.length === 1) {
      ctxF.strokeStyle = C.grey;
      ctxF.fillStyle = C.grey;
      ctxF.lineWidth = 1;
      ctxF.globalAlpha = 0.16;
      const stepPx = 36;
      for (let gx = pad; gx <= W - pad; gx += stepPx) {
        for (let gy = pad; gy <= Hh - pad; gy += stepPx) {
          const th = (gx - cx) / sx, w = (cy - gy) / sy;
          const d = md.deriv(sim.t, [th, w], P);
          const vx = d[0] * sx, vy = -d[1] * sy;
          const n = Math.hypot(vx, vy) || 1;
          ctxF.beginPath();
          ctxF.moveTo(gx - vx / n * 4, gy - vy / n * 4);
          ctxF.lineTo(gx + vx / n * 4, gy + vy / n * 4);
          ctxF.stroke();
          ctxF.beginPath(); ctxF.arc(gx + vx / n * 4, gy + vy / n * 4, 1.1, 0, TAU); ctxF.fill();
        }
      }
      // сепаратриса θ̇ = ±2·√(g/l)·|cos(θ/2)| — точна только для консервативного маятника
      if (sim.mode === 'single' && P.b < 0.005) {
        ctxF.globalAlpha = 0.5;
        ctxF.strokeStyle = '#17a8a8';
        ctxF.setLineDash([5, 5]);
        const sepK = 2 * Math.sqrt(P.g / P.l);
        for (const sgn of [1, -1]) {
          ctxF.beginPath();
          let first = true;
          for (let th = -sim.rTh; th <= sim.rTh; th += sim.rTh / 160) {
            const x = X(th), y = Y(sgn * sepK * Math.abs(Math.cos(th / 2)));
            if (first) { ctxF.moveTo(x, y); first = false; } else ctxF.lineTo(x, y);
          }
          ctxF.stroke();
        }
        ctxF.setLineDash([]);
        ctxF.globalAlpha = 1;
      }
    }

    // траектории
    md.series.forEach((sr, k) => {
      const arr = sim.phase[k];
      if (arr.length >= 4) {
        ctxF.strokeStyle = sr.color;
        ctxF.lineWidth = 1.8;
        ctxF.globalAlpha = 0.85;
        ctxF.beginPath();
        let prev = null;
        for (let i = 0; i < arr.length; i += 2) {
          let th = arr[i];
          if (!Number.isFinite(th)) { prev = null; continue; }
          if (wrap) th = wrapPi(th);
          const x = X(th), y = Y(arr[i + 1]);
          if (prev === null || (wrap && Math.abs(th - prev) > Math.PI)) ctxF.moveTo(x, y);
          else ctxF.lineTo(x, y);
          prev = th;
        }
        ctxF.stroke();
        ctxF.globalAlpha = 1;
      }
      // текущая точка с кольцом цвета фона — рисуется всегда, даже без следа
      let th = sim.y[sr.i];
      if (wrap) th = wrapPi(th);
      const x = X(th), y = Y(sim.y[sr.i + 1]);
      ctxF.beginPath(); ctxF.arc(x, y, 6.5, 0, TAU); ctxF.fillStyle = C.canvas; ctxF.fill();
      ctxF.beginPath(); ctxF.arc(x, y, 4.5, 0, TAU); ctxF.fillStyle = sr.color; ctxF.fill();
    });

    // призраки на портрете
    if (sim.ghosts) {
      ctxF.globalAlpha = 0.35;
      for (const gs of sim.ghosts) {
        for (const sr of md.series) {
          let th = gs[sr.i];
          if (wrap) th = wrapPi(th);
          ctxF.fillStyle = sr.color;
          ctxF.beginPath(); ctxF.arc(X(th), Y(gs[sr.i + 1]), 2.4, 0, TAU); ctxF.fill();
        }
      }
      ctxF.globalAlpha = 1;
    }
  }

  function drawPhase3D(W, Hh) {
    const md = MODES[sim.mode];
    const cx = W / 2, cy = Hh / 2;
    const L = 1.7, R = 1, D = 4.2;
    const S3 = Math.min(W, Hh) * 0.3;
    const cp = Math.cos(sim.pitch), sp = Math.sin(sim.pitch);
    const cw = Math.cos(sim.yaw), sw = Math.sin(sim.yaw);
    const proj = (x, y, z) => {
      const x1 = x * cw + z * sw, z1 = -x * sw + z * cw;
      const y2 = y * cp - z1 * sp, z2 = y * sp + z1 * cp;
      const f = D / (D - z2);
      return [cx + x1 * f * S3, cy - y2 * f * S3];
    };
    const P3 = (th, w) => proj(Math.max(-1, Math.min(1, w / sim.rW)) * L, -Math.cos(th) * R, Math.sin(th) * R);

    // каркас цилиндра: два обода и четыре образующие
    ctxF.strokeStyle = C.grey;
    ctxF.lineWidth = 1;
    ctxF.globalAlpha = 0.35;
    for (const ex of [-L, L]) {
      ctxF.beginPath();
      for (let i = 0; i <= 72; i++) {
        const a = i * TAU / 72;
        const [x, y] = proj(ex, -Math.cos(a) * R, Math.sin(a) * R);
        i === 0 ? ctxF.moveTo(x, y) : ctxF.lineTo(x, y);
      }
      ctxF.stroke();
    }
    ctxF.globalAlpha = 0.15;
    for (let k = 0; k < 4; k++) {
      const a = k * Math.PI / 2;
      const [x1, y1] = proj(-L, -Math.cos(a) * R, Math.sin(a) * R);
      const [x2, y2] = proj(L, -Math.cos(a) * R, Math.sin(a) * R);
      ctxF.beginPath(); ctxF.moveTo(x1, y1); ctxF.lineTo(x2, y2); ctxF.stroke();
    }
    ctxF.globalAlpha = 1;
    ctxF.textAlign = 'left'; ctxF.textBaseline = 'middle';
    const [lx, ly] = proj(L * 1.22, 0, 0);
    mathText(ctxF, 'θ̇', '', lx, ly, 16, C.grey);

    // траектории, намотанные на цилиндр
    md.series.forEach((sr, k) => {
      const arr = sim.phase[k];
      if (arr.length >= 4) {
        ctxF.strokeStyle = sr.color;
        ctxF.lineWidth = 1.5;
        ctxF.globalAlpha = 0.8;
        ctxF.beginPath();
        let started = false;
        for (let i = 0; i < arr.length; i += 2) {
          if (!Number.isFinite(arr[i])) { started = false; continue; }
          const [x, y] = P3(arr[i], arr[i + 1]);
          if (!started) { ctxF.moveTo(x, y); started = true; } else ctxF.lineTo(x, y);
        }
        ctxF.stroke();
        ctxF.globalAlpha = 1;
      }
      const [x, y] = P3(sim.y[sr.i], sim.y[sr.i + 1]);
      ctxF.beginPath(); ctxF.arc(x, y, 6, 0, TAU); ctxF.fillStyle = C.canvas; ctxF.fill();
      ctxF.beginPath(); ctxF.arc(x, y, 4.2, 0, TAU); ctxF.fillStyle = sr.color; ctxF.fill();
    });

    // призраки и в 3D
    if (sim.ghosts) {
      ctxF.globalAlpha = 0.35;
      for (const gs of sim.ghosts) {
        for (const sr of md.series) {
          const [x, y] = P3(gs[sr.i], gs[sr.i + 1]);
          ctxF.fillStyle = sr.color;
          ctxF.beginPath(); ctxF.arc(x, y, 2.4, 0, TAU); ctxF.fill();
        }
      }
      ctxF.globalAlpha = 1;
    }

    ctxF.font = '11px ui-monospace, Menlo, monospace';
    ctxF.fillStyle = C.grey;
    ctxF.textAlign = 'left'; ctxF.textBaseline = 'alphabetic';
    ctxF.fillText((REDUCED ? '' : 'крутится само · ') + 'перетащите, чтобы повернуть', 12, Hh - 12);
  }

  function drawEnergy() {
    fitCanvas(cvE);
    const W = cvE.width / dpr, Hh = cvE.height / dpr;
    ctxE.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctxE.fillStyle = C.canvas;
    ctxE.fillRect(0, 0, W, Hh);
    const arr = sim.energy;
    if (arr.length < 4) return;
    let t0 = Infinity, t1 = -Infinity, eMax = 0;
    for (let i = 0; i < arr.length; i += 2) {
      if (!Number.isFinite(arr[i]) || !Number.isFinite(arr[i + 1])) continue;
      if (arr[i] < t0) t0 = arr[i];
      if (arr[i] > t1) t1 = arr[i];
      if (arr[i + 1] > eMax) eMax = arr[i + 1];
    }
    if (!(t1 > t0)) return;
    eMax = Math.max(eMax, 1e-6);
    const padX = 46, padY = 12;
    const X = t => padX + (t - t0) / (t1 - t0) * (W - padX - 14);
    const Y = e => Hh - padY - e / (eMax * 1.08) * (Hh - 2 * padY);
    ctxE.strokeStyle = '#3b3733';
    ctxE.lineWidth = 1;
    ctxE.beginPath(); ctxE.moveTo(padX, Hh - padY); ctxE.lineTo(W - 10, Hh - padY); ctxE.stroke();
    ctxE.font = '10.5px ui-monospace, Menlo, monospace';
    ctxE.fillStyle = C.grey;
    ctxE.textAlign = 'left'; ctxE.textBaseline = 'middle';
    ctxE.fillText(eMax.toFixed(1), 8, Y(eMax));
    ctxE.fillText('0', 8, Hh - padY);
    ctxE.textBaseline = 'bottom';
    ctxE.fillText(t0.toFixed(0) + ' с', padX + 4, Hh - padY - 3);
    ctxE.textAlign = 'right';
    ctxE.fillText(t1.toFixed(0) + ' с', W - 14, Hh - padY - 3);
    ctxE.textAlign = 'left'; ctxE.textBaseline = 'middle';
    ctxE.strokeStyle = C.orange;
    ctxE.lineWidth = 1.6;
    ctxE.beginPath();
    let started = false;
    for (let i = 0; i < arr.length; i += 2) {
      if (!Number.isFinite(arr[i])) { started = false; continue; }
      const x = X(arr[i]), y = Y(arr[i + 1]);
      if (!started) { ctxE.moveTo(x, y); started = true; } else ctxE.lineTo(x, y);
    }
    ctxE.stroke();
  }

  // ---------- перетаскивание ----------
  cvP.addEventListener('pointerdown', e => {
    if (e.button !== 0 || sim.dragging >= 0) return;
    const rect = cvP.getBoundingClientRect();
    const x = e.clientX - rect.left, y = e.clientY - rect.top;
    for (let k = sim.bobPx.length - 1; k >= 0; k--) {
      const b = sim.bobPx[k];
      if ((x - b.x) ** 2 + (y - b.y) ** 2 <= b.r * b.r) {
        sim.dragging = k;
        sim.dragPointer = e.pointerId;
        const ci = MODES[sim.mode].series[k].i;
        sim.dragUnwrap = sim.y[ci];
        sim.dragLastRaw = wrapPi(sim.y[ci]);
        sim.dragSamples = [];
        // разрыв следов: скачок состояния при перетаскивании — не траектория
        for (const arr of sim.phase) arr.push(NaN, NaN);
        sim.energy.push(NaN, NaN);
        try { cvP.setPointerCapture(e.pointerId); } catch (_) {}
        cvP.style.cursor = 'grabbing';
        dragTo(e);
        return;
      }
    }
  });
  function dragTo(e) {
    const md = MODES[sim.mode];
    const sr = md.series[sim.dragging];
    if (!sr || !sim.pivotPx) return;
    const rect = cvP.getBoundingClientRect();
    const x = e.clientX - rect.left, y = e.clientY - rect.top;
    const origin = sim.dragging === 0 ? sim.pivotPx
      : { x: sim.bobPx[sim.dragging - 1].x, y: sim.bobPx[sim.dragging - 1].y };
    const th = Math.atan2(x - origin.x, y - origin.y);
    // непрерывный угол: протаскивание через низ наматывает обороты
    sim.dragUnwrap += wrapPi(th - sim.dragLastRaw);
    sim.dragLastRaw = th;
    sim.y[sr.i] = sim.dragUnwrap;
    for (const s of md.series) sim.y[s.i + 1] = 0;
    sim.dragSamples.push({ tm: performance.now() / 1000, a: sim.dragUnwrap });
    if (sim.dragSamples.length > 8) sim.dragSamples.shift();
    sim.bobTrail = [];
  }
  cvP.addEventListener('pointermove', e => {
    if (sim.dragging >= 0) {
      if (e.pointerId === sim.dragPointer) dragTo(e);
      return;
    }
    const rect = cvP.getBoundingClientRect();
    const x = e.clientX - rect.left, y = e.clientY - rect.top;
    const over = sim.bobPx.some(b => (x - b.x) ** 2 + (y - b.y) ** 2 <= b.r * b.r);
    cvP.style.cursor = over ? 'grab' : 'default';
  });
  function endDrag(fling) {
    if (sim.dragging < 0) return;
    const sr = MODES[sim.mode].series[sim.dragging];
    sim.dragging = -1;
    cvP.style.cursor = 'grab';
    // бросок: угловая скорость из последних перемещений мыши
    if (fling && sr && sim.dragSamples.length >= 2) {
      const a = sim.dragSamples[0], b = sim.dragSamples[sim.dragSamples.length - 1];
      const dt = b.tm - a.tm;
      if (dt > 0.02 && performance.now() / 1000 - b.tm < 0.12) {
        // деление на sim.speed: экранная скорость после броска равна скорости руки
        sim.y[sr.i + 1] = Math.max(-25, Math.min(25, (b.a - a.a) / dt / sim.speed));
      }
    }
    initGhosts();
    pushPhase();
  }
  cvP.addEventListener('pointerup', e => { if (e.pointerId === sim.dragPointer) endDrag(true); });
  cvP.addEventListener('pointercancel', e => { if (e.pointerId === sim.dragPointer) endDrag(false); });
  cvP.addEventListener('lostpointercapture', e => { if (e.pointerId === sim.dragPointer) endDrag(false); });

  // вращение 3D-цилиндра
  let rot = null;
  cvF.addEventListener('pointerdown', e => {
    if (sim.view !== 'cyl3d' || e.button !== 0 || rot) return;
    rot = { x: e.clientX, y: e.clientY, id: e.pointerId };
    try { cvF.setPointerCapture(e.pointerId); } catch (_) {}
  });
  cvF.addEventListener('pointermove', e => {
    if (!rot || e.pointerId !== rot.id) return;
    sim.yaw += (e.clientX - rot.x) * 0.008;
    sim.pitch = Math.max(-1.3, Math.min(1.3, sim.pitch + (e.clientY - rot.y) * 0.008));
    rot = { x: e.clientX, y: e.clientY, id: rot.id };
  });
  const endRot = e => { if (rot && e.pointerId === rot.id) rot = null; };
  cvF.addEventListener('pointerup', endRot);
  cvF.addEventListener('pointercancel', endRot);

  // ---------- управление ----------
  function setRunning(v) {
    sim.running = v;
    btnPlay.textContent = v ? 'Пауза' : 'Пуск';
  }
  btnPlay.addEventListener('click', () => setRunning(!sim.running));
  btnReset.addEventListener('click', resetSim);
  $('speed').addEventListener('input', e => {
    sim.speed = parseFloat(e.target.value);
    $('speedOut').textContent = '×' + sim.speed.toFixed(2);
    updateHash();
  });
  document.querySelectorAll('.tabs button').forEach(b =>
    b.addEventListener('click', () => { setMode(b.dataset.mode); updateHash(); }));
  viewSeg.querySelectorAll('button').forEach(b =>
    b.addEventListener('click', () => { setView(b.dataset.v); updateHash(); }));
  ghostsEl.addEventListener('change', () => { initGhosts(); updateHash(); });
  fieldEl.addEventListener('change', updateHash);

  // ---------- ссылка на текущее состояние ----------
  function buildHash() {
    const q = new URLSearchParams();
    q.set('mode', sim.mode);
    for (const cfg of MODES[sim.mode].sliders) q.set(cfg.key, String(P[cfg.key]));
    q.set('view', sim.view);
    q.set('spd', String(sim.speed));
    q.set('field', fieldEl.checked ? '1' : '0');
    if (ghostsEl.checked) q.set('gh', '1');
    return '#' + q.toString();
  }
  let hashTimer = 0;
  function updateHash() {
    // дебаунс: Safari ограничивает replaceState ~100 вызовами за 30 с
    clearTimeout(hashTimer);
    hashTimer = setTimeout(() => {
      try { history.replaceState(null, '', buildHash()); } catch (_) {}
    }, 250);
  }
  function applyHash() {
    const q = new URLSearchParams(location.hash.slice(1));
    // старый ключ 'm' совпадал со слайдером массы — принимаем его как режим только если это имя режима
    const m = q.get('mode') || (MODES[q.get('m')] ? q.get('m') : null);
    setMode(m && MODES[m] ? m : 'single');
    const params = {};
    for (const cfg of MODES[sim.mode].sliders) {
      if (!q.has(cfg.key)) continue;
      const v = parseFloat(q.get(cfg.key));
      if (Number.isFinite(v)) params[cfg.key] = Math.min(cfg.max, Math.max(cfg.min, v));
    }
    applyParams(params);
    const view = q.get('view');
    if (['flat', 'wrap', 'cyl3d'].includes(view)) setView(view);
    if (q.get('field') === '0') fieldEl.checked = false;
    ghostsEl.checked = q.get('gh') === '1';
    const spd = parseFloat(q.get('spd'));
    if (Number.isFinite(spd) && spd >= 0.1 && spd <= 3) {
      sim.speed = spd;
      $('speed').value = spd;
      $('speedOut').textContent = '×' + spd.toFixed(2);
    }
    resetSim();
  }
  const toastEl = $('toast');
  let toastTimer = 0;
  function toast(msg) {
    toastEl.textContent = msg;
    toastEl.classList.add('show');
    clearTimeout(toastTimer);
    toastTimer = setTimeout(() => toastEl.classList.remove('show'), 1800);
  }
  $('btnShare').addEventListener('click', () => {
    try { history.replaceState(null, '', buildHash()); } catch (_) {}
    const href = location.href.split('#')[0] + buildHash();
    if (navigator.clipboard && navigator.clipboard.writeText) {
      navigator.clipboard.writeText(href).then(() => toast('Ссылка скопирована'), () => prompt('Скопируйте ссылку:', href));
    } else prompt('Скопируйте ссылку:', href);
  });
  window.addEventListener('hashchange', applyHash);

  // ---------- запись видео ----------
  const btnRec = $('btnRec');
  let rec = null;
  btnRec.addEventListener('click', () => {
    if (rec) { rec.mr.stop(); return; }
    if (typeof MediaRecorder === 'undefined') { toast('Запись видео не поддерживается браузером'); return; }
    const cnv = document.createElement('canvas');
    cnv.width = cvP.width + cvF.width;
    cnv.height = Math.max(cvP.height, cvF.height);
    const mime = ['video/webm;codecs=vp9', 'video/webm', 'video/mp4'].find(t => MediaRecorder.isTypeSupported(t)) || '';
    const mr = new MediaRecorder(cnv.captureStream(30), mime ? { mimeType: mime } : undefined);
    const chunks = [];
    mr.ondataavailable = e => { if (e.data.size) chunks.push(e.data); };
    mr.onstop = () => {
      const type = mr.mimeType || mime || 'video/webm';
      const url = URL.createObjectURL(new Blob(chunks, { type }));
      const a = document.createElement('a');
      a.href = url;
      a.download = 'mayatnik-' + sim.mode + (type.includes('mp4') ? '.mp4' : '.webm');
      a.click();
      setTimeout(() => URL.revokeObjectURL(url), 5000);
      rec = null;
      btnRec.classList.remove('rec');
      btnRec.textContent = '⏺ Записать видео';
      toast('Видео сохранено');
    };
    rec = { mr, cnv, ctx: cnv.getContext('2d'), w1: cvP.width };
    mr.start();
    btnRec.classList.add('rec');
    btnRec.textContent = '⏹ Стоп — сохранить';
  });
  window.addEventListener('keydown', e => {
    const tag = e.target.tagName;
    if (tag === 'INPUT' || tag === 'BUTTON' || tag === 'SUMMARY' || tag === 'A') return;
    if (e.code === 'Space') { e.preventDefault(); setRunning(!sim.running); }
    if (e.code === 'KeyR') resetSim();
  });

  // ---------- цикл ----------
  const frameMsEl = $('frameMs');
  let last = performance.now(), ema = 0;
  function frame(now) {
    const t0 = performance.now();
    const dt = Math.min((now - last) / 1000, 0.25);
    last = now;
    if (sim.running && sim.dragging < 0) stepSim(dt * sim.speed);
    if (sim.view === 'cyl3d' && !rot && !REDUCED) sim.yaw += dt * 0.25;
    drawPend();
    drawPhase();
    drawEnergy();
    if (rec) {
      rec.ctx.fillStyle = C.canvas;
      rec.ctx.fillRect(0, 0, rec.cnv.width, rec.cnv.height);
      rec.ctx.drawImage(cvP, 0, 0, rec.w1, rec.cnv.height);
      rec.ctx.drawImage(cvF, rec.w1, 0, rec.cnv.width - rec.w1, rec.cnv.height);
    }
    for (const [dd, fmt] of readoutSpans) dd.textContent = fmt(sim);
    ema = ema * 0.95 + (performance.now() - t0) * 0.05;
    frameMsEl.textContent = ema.toFixed(1);
    requestAnimationFrame(frame);
  }

  buildPresets();
  applyHash();
  setRunning(sim.running);
  requestAnimationFrame(frame);
  window.__sim = sim;
  window.__draw = () => { drawPend(); drawPhase(); drawEnergy(); };
  window.__preset = applyPreset;
  window.__setView = setView;
  window.__applyHash = applyHash;
  window.__step = dt => stepSim(dt);
})();
</script>