# ⚛  L1 Principle — Rotor Dynamics Aeroelastic Inversion

**ID:** `L1-456` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Robotics — *Aerial robotics*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** rotor parameter vector
> **📡 Carrier:** N/A · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555279

---

## 🧠 1. Introduction

**Rotor Dynamics Aeroelastic Inversion** is a **parameter-estimation problem** whose unknown lives in **rotor parameter vector** space, within the **Aerial robotics** sub-domain of **Robotics**.

Measurements consist of N/A via a **rotor thrust torque model** sensing mechanism.

The forward operator applies, in order: O · composite method operator; S · bvp · flapping equation operator; O · chi2 · thrust torque operator.

Observations are corrupted by additive Gaussian noise. Existence of the recovered rotor_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); dynamic_stall_effect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → O · composite method → S · bvp · flapping equation → O · chi2 · thrust torque → **y** (detector).

```
y = `O.chi2.thrust_torque` `S.bvp.flapping_equation` `O.composite_method` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `O.composite_method` | O · composite method operator |
| `S.bvp.flapping_equation` | S · bvp · flapping equation operator |
| `O.chi2.thrust_torque` | O · chi2 · thrust torque operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Robotics |
| Sub domain | Aerial robotics |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | rotor_parameter_vector |
| Noise model | gaussian |
| Integration axis | azimuth_angle |
| Difficulty delta | 5 |
| L dag | 4 |

## 📡 4. Measurement Model

Existence of the recovered rotor_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); dynamic_stall_effect dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | thrust_prediction_RMSE_N |
| Secondary | vibration_mode_error_Hz |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `rotor_thrust_torque_model`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Rotor rpm | — | 3000 |
| Altitude m | m | 0 |
| Advance ratio mu | — | 0 |
| Collective pitch deg | deg | 8 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Rotor rpm | — | 500 – 10000 |
| Altitude m | m | 0 – 5000 |
| Advance ratio mu | — | 0.0 – 0.4 |
| Collective pitch deg | deg | 0 – 20.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 5 thrust_prediction_RMSE_N

| Metric | Range |
|---|---|
| Thrust prediction rmse n | 0.5 – 50 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **thrust_prediction_RMSE_N**, with κ = `10000.0` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x28410d58466e8760437dad2358b166756a20da07497965653a3e7400be55c875`
- **Chain tx hash:** `0x2e808b4eafd884e77a97e05f7c6327b6e85bfc5c687686701e01b26ad306c66d`
- **Chain block:** `41555279`

---

## File Mapping

This bundle consists of: `L1-456.md`, `L1-456.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-456.md` | Source of truth — edit this | Human or LLM |
| `L1-456.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-456`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._