{"uid":"cap_dt74rxKfsilt2v_YurrNR","slug":"inextensible-catenary-inverse-endpoint-slack-shape-tension-solver-126f7dcb","name":"Inextensible Catenary Inverse Endpoint Slack Shape & Tension Solver","description":"Recover an anonymous slack cable model and its local geometric/tension state.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/inextensible-catenary-inverse-endpoint-slack-shape-tension?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["catenary"],"properties":{"catenary":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["horizontal_span","vertical_offset","cable_length","weight_per_length","horizontal_samples"],"properties":{"cable_length":{"type":"number","maximum":100000,"minimum":0.001},"horizontal_span":{"type":"number","maximum":10000,"minimum":0.001},"vertical_offset":{"type":"number","maximum":10000,"minimum":-10000},"weight_per_length":{"type":"number","maximum":1000000,"minimum":0.000001},"horizontal_samples":{"type":"array","items":{"type":"number","maximum":10000,"minimum":0},"maxItems":32,"minItems":1}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_XZEj543o9reZWHhqYfTvG","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Given geometric and physical parameters of a slack cable, recovers the anonymous catenary model and computes its local geometric shape and tension state at sampled horizontal positions.","exampleAgentPrompt":"I have a slack cable spanning 80 meters horizontally with a 3-meter vertical offset between supports, total cable length of 83.5 meters, and a weight per unit length of 12.5 N/m — can you recover the catenary model and compute the local shape and tension at horizontal positions 0, 20, 40, 60, and 80 meters?","exampleUseCases":[{"title":"Overhead power line sag analysis","prompt":"I need to analyze a transmission cable with a 500-meter horizontal span, a vertical offset of 15 meters between towers, a total cable length of 507 meters, and a weight per unit length of 45 N/m. Recover the catenary model and give me the shape and tension at horizontal positions 0, 100, 200, 300, 400, and 500 meters."},{"title":"Suspension bridge cable profiling","prompt":"Model a hanging bridge cable with a 200-meter span, zero vertical offset (both endpoints at same height), a cable length of 206 meters, and a linear weight of 80 N/m. I want the catenary shape and tension values sampled at 0, 50, 100, 150, and 200 meters horizontally."},{"title":"Ski lift or ropeway cable geometry check","prompt":"I have a ski lift cable with a 350-meter horizontal span, a 60-meter vertical drop from start to end, total cable length of 362 meters, and weight per unit length of 22 N/m. Can you recover the catenary model and tell me the local shape and tension at 10 evenly spaced points from 0 to 350 meters?"}],"resultDescription":"Returns the recovered anonymous catenary model (including catenary constant and reference parameters) together with per-sample local geometric state (position, slope, curvature) and tension values at each requested horizontal sample position along the cable.","failureModes":["Cable length shorter than horizontal span — physically impossible, returns validation error","Horizontal samples outside the [0, horizontal_span] range may produce extrapolated or error responses","Extreme weight-per-length or span values near schema limits may cause numerical instability","Missing required fields (horizontal_span, cable_length, etc.) return schema validation errors","Claim field mismatch or invalid artifact structure returns a 400-level error"],"whenToPreferThis":"Choose this endpoint when you need to solve the inverse catenary problem — recovering the cable model and local physics from geometric and physical cable parameters — rather than a forward simulation. It is specifically suited for inextensible cable models (no elastic stretch), making it appropriate for heavy structural cables, transmission lines, and rigging where material extension is negligible. Prefer this over general numerical ODE solvers when you need fast, closed-form catenary results with per-point tension output.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:39:58.558Z","isFirstParty":false,"canonicalSlug":"inextensible-catenary-inverse-endpoint-slack-shape-tension-solver-126f7dcb"}