# Halowerk Free Asymmetric Euler Top Rigid-Body Simulator

> Halowerk Free Asymmetric Euler Top Rigid-Body Simulator is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-01).

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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/free-asymmetric-euler-top-body-world-quaternion-invariant-ledger?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-01
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/halowerk-free-asymmetric-euler-top-rigid-body-simulator-5de53a9f
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_JYnLVMvDA0J4FIlbupPKm

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability halowerk-free-asymmetric-euler-top-rigid-body-simulator-5de53a9f -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Replay a supplied free rigid-body model with complete orientation and momentum diagnostics.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/halowerk-free-asymmetric-euler-top-rigid-body-simulator-5de53a9f/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)