{"uid":"cap_JYnLVMvDA0J4FIlbupPKm","slug":"halowerk-free-asymmetric-euler-top-rigid-body-simulator-5de53a9f","name":"Halowerk Free Asymmetric Euler Top Rigid-Body Simulator","description":"Replay a supplied free rigid-body model with complete orientation and momentum diagnostics.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/free-asymmetric-euler-top-body-world-quaternion-invariant-ledger?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["eulerTop"],"properties":{"eulerTop":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["principal_inertias","initial_angular_velocity","initial_quaternion","timestep","sample_steps"],"properties":{"timestep":{"type":"number","maximum":0.1,"minimum":0.000001},"sample_steps":{"type":"array","items":{"type":"integer","maximum":512,"minimum":0},"maxItems":32,"minItems":1},"initial_quaternion":{"type":"array","items":{"type":"number","maximum":10000,"minimum":-10000},"maxItems":4,"minItems":4},"principal_inertias":{"type":"array","items":{"type":"number","maximum":1000000,"minimum":0.001},"maxItems":3,"minItems":3},"initial_angular_velocity":{"type":"array","items":{"type":"number","maximum":10000,"minimum":-10000},"maxItems":3,"minItems":3}},"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_bF3IpA63b64XkLLgdVLFP","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":"Simulates and replays a free rigid-body (asymmetric Euler top) given principal inertias, initial angular velocity, and quaternion orientation, returning full orientation and angular momentum diagnostics at specified time steps.","exampleAgentPrompt":"Simulate a free asymmetric rigid body with principal inertias [10, 20, 30] kg·m², initial angular velocity [0.5, 0.1, 2.0] rad/s, and initial quaternion [1, 0, 0, 0], using a timestep of 0.01 seconds, and sample at steps [0, 50, 100, 200, 512] to get the full orientation and momentum diagnostics.","exampleUseCases":[{"title":"Spacecraft attitude wobble analysis","prompt":"I have a satellite with principal moments of inertia [500, 800, 1200] kg·m², spinning with initial angular velocity [0.1, 0.0, 2.5] rad/s and initial quaternion [1, 0, 0, 0]. Use a timestep of 0.005 seconds and sample at steps [0, 100, 200, 300, 400, 500] to show me how the attitude and angular momentum evolve over that interval."},{"title":"Verify angular momentum invariant for asymmetric top","prompt":"Run a torque-free rigid body simulation with principal inertias [1.0, 2.0, 3.0] kg·m², initial angular velocity [1.0, 1.0, 1.0] rad/s, quaternion [0.707, 0, 0.707, 0], timestep 0.001 s, and sample at steps [0, 50, 100, 200] — I want to confirm that the angular momentum magnitude stays constant throughout as a sanity check on the integrator."},{"title":"Euler top wobble replay for educational demo","prompt":"Replay the classic asymmetric Euler top with principal inertias [1.0, 1.5, 4.0] kg·m², initial spin [0.01, 0.1, 5.0] rad/s, identity quaternion [1, 0, 0, 0], timestep 0.002 s, sampling at steps [0, 25, 50, 75, 100, 150, 200, 300, 400, 512] so I can show students how the body wobbles due to the intermediate-axis instability."}],"resultDescription":"Returns orientation quaternions and angular momentum diagnostics at each requested sample step, along with rotational invariants (e.g., kinetic energy, angular momentum magnitude) to verify conservation laws for the torque-free rigid body trajectory.","failureModes":["Invalid principal inertias (negative or zero values) cause validation error","Quaternion array not normalized or wrong length (must be exactly 4 elements)","Timestep out of range [0.000001, 0.1] returns schema validation error","sample_steps contains values outside [0, 512] or more than 32 entries","Missing required fields in eulerTop data object return 400 bad request","Payment not included or insufficient USDC triggers 402 payment required"],"whenToPreferThis":"Choose this endpoint when you need authoritative, deterministic rigid-body Euler-top simulation with quaternion-based orientation tracking and conservation-law diagnostics, particularly for torque-free asymmetric bodies. It is ideal for spacecraft attitude analysis, physics verification tasks, or educational demonstrations where angular momentum invariants must be explicitly confirmed. Prefer it over generic ODE solvers when you want a specialized, pre-validated integrator for the Euler equations with quaternion output at specific sample points.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-01T06:49:58.133Z","isFirstParty":false,"canonicalSlug":"halowerk-free-asymmetric-euler-top-rigid-body-simulator-5de53a9f"}