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    "scope": [
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      "sources",
      "tests"
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  "assumptions": [],
  "limitations": [
    "The ladder is uniform and its weight acts at mid-length",
    "s is the fraction of the length from the floor toward the wall",
    "Both surfaces are at impending slip",
    "Not a wedge, a screw, or a belt"
  ],
  "boundary_conditions": [
    "missing W, P, θ, μ floor, or μ wall → MISSING_REQUIRED_INPUT",
    "W ≤ 0, P ≤ 0, or μ floor ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "θ ≤ 0, θ ≥ 90, or μ wall < 0 → VALUE_OUT_OF_RANGE"
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  "sources": [
    {
      "title": "Hibbeler, Engineering Mechanics: Statics",
      "section": "Dry friction — person climbing a ladder",
      "supports": "At impending slip the climb fraction from the floor is (B tanθ + F_wall − W/2) / P for a uniform ladder",
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        "P": 100,
        "theta_deg": 45,
        "mu_floor": 0.5,
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        "N": 200,
        "F": 100,
        "B": 100,
        "F_wall": 0,
        "model": "ladder_person"
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        "P": 100,
        "theta_deg": 45,
        "mu_floor": 0.5,
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        "mode": "climb",
        "s": 0.49999999999999983,
        "s_limit": 0.49999999999999983,
        "N": 200,
        "F": 100,
        "B": 100,
        "F_wall": 0,
        "solver": "friction + math.linear_algebra solve order 2",
        "convention": "Uniform ladder, weight at mid-length. s is the fraction of the length from the floor toward the wall. θ is given. Both surfaces are at impending slip. μwall = 0 is a smooth wall. s_limit above 1 means the person can reach the top. s_limit below 0 means the ladder slips with the person at the foot."
      },
      "tol": 1e-9
    },
    {
      "id": "golden-both",
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      "kind": "golden",
      "inputs": {
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        "P": 200,
        "theta_deg": 45,
        "mu_floor": 0.4,
        "mu_wall": 0.3
      },
      "expect": {
        "mode": "climb",
        "s": 0.44642857142857145,
        "N": 267.85714285714283,
        "B": 107.14285714285714,
        "F_wall": 32.142857142857146
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      "actual": {
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        "W": 100,
        "P": 200,
        "theta_deg": 45,
        "mu_floor": 0.4,
        "mu_wall": 0.3,
        "mode": "climb",
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        "F_wall": 32.1428571429,
        "solver": "friction + math.linear_algebra solve order 2",
        "convention": "Uniform ladder, weight at mid-length. s is the fraction of the length from the floor toward the wall. θ is given. Both surfaces are at impending slip. μwall = 0 is a smooth wall. s_limit above 1 means the person can reach the top. s_limit below 0 means the ladder slips with the person at the foot."
      },
      "tol": 1e-9
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      "inputs": {
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        "P": 100,
        "theta_deg": 60,
        "mu_floor": 0.5,
        "mu_wall": 0
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        "s": 1,
        "s_limit": 1.2320508075688772,
        "N": 200,
        "B": 100
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        "convention": "Uniform ladder, weight at mid-length. s is the fraction of the length from the floor toward the wall. θ is given. Both surfaces are at impending slip. μwall = 0 is a smooth wall. s_limit above 1 means the person can reach the top. s_limit below 0 means the ladder slips with the person at the foot."
      },
      "tol": 1e-9
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      "inputs": {
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        "P": 100,
        "theta_deg": 45,
        "mu_floor": 0.5,
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