{
  "id": "spm-full-sector",
  "lesson_ids": [
    "II01.2",
    "II01.3",
    "II07.2"
  ],
  "title": "Собственная четырёхполюсная SPM: полный период, сектор и гармоники ЭДС",
  "intro": [
    "Эта машина отличается от 16-полюсного образца AGE: в собственной геометрии курса четыре полюса, 12 пазов и две пары полюсов. Период основной магнитной системы составляет 180 механических градусов. Ротор поворачивается как группа геометрии с перестроением сетки: отсутствующая в файле граница скользящего зазора не имитируется вызовом API.",
    "Сохранённая серия содержит 768 независимо решённых положений за один магнитный период. Подмножества на 48, 96 и 192 точках выделяются из этой серии; они не объявляются дополнительными полевыми решениями."
  ],
  "theory": [
    {
      "heading": "От потокосцепления к ЭДС",
      "paragraphs": [
        "Потокосцепление фазы есть сумма потоков всех её витков с учётом знаков сторон обмотки. Для синусоидального вращения удобно сначала определить Ψ(θ), затем применить закон Фарадея. При постоянной механической скорости производная по времени равна ωмех, умноженной на производную по углу.",
        "Если k-я электрическая гармоника потокосцепления имеет амплитуду Ψk, её частота равна kfэл. Поэтому действующая ЭДС содержит множитель k: малая высокая гармоника потокосцепления может дать заметную гармонику напряжения. Численное дифференцирование шумного ряда без проверки шага опасно.",
        "При исследовании зубцового момента следует анализировать отдельный ненагруженный ряд момента и проверять его гармоники. Сходимость основной ЭДС сама по себе не доказывает сходимость малого зубцового момента."
      ],
      "formulas": [
        {
          "latex": "e(\\theta)=-\\omega_{\\mathrm{мех}}\\frac{\\mathrm d\\Psi}{\\mathrm d\\theta},\\qquad E_{k,\\mathrm{д}}=\\frac{k\\omega_{\\mathrm{эл}}\\Psi_{k,\\mathrm{амп}}}{\\sqrt2}",
          "explanation": "Угол в производной выражается в радианах; знак зависит от принятого направления обхода обмотки."
        },
        {
          "latex": "\\Psi_{k,\\mathrm{амп}}=\\frac2N\\left|\\sum_{j=0}^{N-1}\\Psi_j\\exp\\!\\left(-\\mathrm i\\frac{2\\pi kj}{N}\\right)\\right|",
          "explanation": "Ряд охватывает один электрический период, последняя точка не повторяет первую."
        }
      ]
    },
    {
      "heading": "Сектор и два независимых уточнения",
      "paragraphs": [
        "Сектор 90° допустим только при согласованной антипериодичности геометрии, намагниченности, витков и текущего возбуждения. Для полной и секторной модели сравнивают одинаковые физические токи и положение; потокосцепление, энергию и момент проверяют отдельно.",
        "Угловое уточнение определяет достоверность спектра, пространственное — точность каждого полевого решения. В дополнительной серии 24 одинаковых угла рассчитаны на сетках зазора 0,4; 0,2; 0,1 мм. Допуск выбирается для конкретной величины до просмотра результата.",
        "Для постоянных магнитов энергия содержит источник намагниченности. Сырой интеграл энергии нельзя бездумно проверять равенством ½ΣIΨ: это равенство относится к линейной системе без независимого поля магнитов. В комплекте сохранена специальная проверка энергии возвратной ветви."
      ],
      "formulas": [
        {
          "latex": "\\varepsilon_q=\\frac{|q_{\\mathrm{уточн}}-q_{\\mathrm{база}}|}{\\max(|q_{\\mathrm{уточн}}|,q_{\\mathrm{масш}})}",
          "explanation": "Масштаб qмасш необходим около нуля; абсолютный допуск задают заранее."
        }
      ]
    }
  ],
  "parameters": [
    {
      "name": "Пары полюсов",
      "value": 2,
      "unit": ""
    },
    {
      "name": "Пазы",
      "value": 12,
      "unit": ""
    },
    {
      "name": "Положения",
      "value": 768,
      "unit": ""
    },
    {
      "name": "Механический период",
      "value": 180,
      "unit": "°"
    },
    {
      "name": "Последний угол",
      "value": 179.765625,
      "unit": "°"
    },
    {
      "name": "Частота для восстановления ЭДС",
      "value": 100,
      "unit": "Гц"
    }
  ],
  "steps": [
    "Распакуйте полный комплект. Сначала запустите reproduce.py для свежего контрольного поля.",
    "Откройте reference/measurements.json: таблица full_period содержит исходные токи, Ψ трёх фаз, момент и число элементов.",
    "Полные программы, названные далее, запускайте через run-series.py из корня распакованного комплекта: выберите SERIES_NUMBER по списку README.html. Диспетчер сам устанавливает подпапку и контекст исходной программы; прежний рабочий каталог FEMM не важен.",
    "Запустите reference/postprocess-full.py из его каталога для повторной обработки ряда. Для самостоятельного полного полевого прохода используйте angular-full.py; сектор проверяется sector-full.py.",
    "Сравните Ψ₁ и гармоники 3, 5, 7, 11 на вложенных подмножествах. Затем отдельно проверьте средний момент на трёх пространственных сетках из дополнительного каталога mesh.",
    "Нарушьте симметрию только в отдельной копии: при несимметричном возбуждении подтвердите необходимость полной геометрии."
  ],
  "table": {
    "columns": [
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        "key": "N",
        "label": "Отсчёты",
        "unit": ""
      },
      {
        "key": "psi1",
        "label": "Ψ₁ фазы А",
        "unit": "Вб"
      },
      {
        "key": "psi3",
        "label": "Ψ₃ фазы А",
        "unit": "Вб"
      },
      {
        "key": "psi5",
        "label": "Ψ₅ фазы А",
        "unit": "Вб"
      }
    ],
    "rows": [
      {
        "N": 48,
        "psi1": 0.3412694310264159,
        "psi3": 0.029787505128507644,
        "psi5": 0.007825469705106362
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        "N": 96,
        "psi1": 0.34126926941794394,
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        "psi1": 0.34126737896913445,
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        "psi5": 0.007825572748599094
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        "N": 768,
        "psi1": 0.3412664146893918,
        "psi3": 0.02978618706419339,
        "psi5": 0.007824825440830642
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  "series": [
    {
      "title": "Потокосцепление фазы А, полный период",
      "x_label": "Механический угол, °",
      "y_label": "Потокосцепление, Вб",
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