tether_slack_angle — DRIVE `kendama` op

• Data kinds: none → any (an op determined by its arguments alone — it takes no image or data input)

• Call: import fullseye as fs; fs.ledger.tether_slack_angle(theta0: 'float', L: 'float', g: 'float' = 9.81) (to call the implementation directly, import kendama; kendama.tether_slack_angle(theta0: 'float', L: 'float', g: 'float' = 9.81); from the registry, opsdrive.get("tether_slack_angle"))

Usage

Angle θ_s (from straight down) at which the string goes slack for a ball with speed v₀ = √(2gL(1 − cos θ₀)) at the bottom (the energy at which a rod would stop at θ₀).

Derivation: v² = 2gL(cos θ − cos θ₀), T = m(v²/L + g cos θ) = m g (3 cos θ − 2 cos θ₀) = 0 → cos θ_s = (2/3) cos θ₀. The upper half (cos θ_s < 0) is reached only when cos θ₀ < 0 ⇔ θ₀ > π/2. If θ₀ ≤ π/2 the tension only drops to m g cos θ₀ ≥ 0 at θ₀ and the string does not go slack → None. At θ₀ = π (energy just enough to reach the top), θ_s = arccos(−2/3) = 131.8°. θ₀ outside (0, π] raises ValueError. A ball with θ₀ > π/2 released from rest is slack from the start (tension m g cos θ₀ < 0), so θ₀ is given via the speed at the bottom.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• poc_kendama — py -3.11 examples/poc_kendama.py

Ops the type connects to (they accept `any` as input)

course_crank · course_s_curve · course_turnaround · course_slope · course_intersection · course_parallel_parking · course_crossing · course_road

Same category (`kendama`)

kendama_params · elliptic_k_agm · pendulum_period_exact · pendulum_launch_speed · pendulum_rod_simulate · tether_tension_fixed · swing_up_plan · swing_up_apex

*Provenance: kendama.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tether_slack_angle — DRIVE kendama op