.. _python_API_dynamic_derivatives:

.. currentmodule:: flow360

**************************
Dynamic Derivatives
**************************

Dynamic derivatives are essential coefficients that characterize an aircraft's stability and control characteristics. Flow360 provides advanced capabilities for accurately computing these derivatives using time-accurate CFD simulations with prescribed motions. These derivatives are crucial inputs for flight dynamics models, control system design, and handling qualities assessment.

.. grid:: 1

    .. grid-item-card:: 🔄 Dynamic Simulation Methods
        :link: dynamic
        :link-type: doc
        
        Learn techniques for setting up prescribed motion simulations to compute pitch, roll, and yaw dynamic derivatives and other stability parameters.

Key Concepts in Dynamic Derivative Analysis
=======================================

* Static vs. dynamic stability coefficients
* Frequency-dependent aerodynamic behavior
* Small-perturbation vs. large-amplitude motions
* Forced oscillation techniques in CFD
* Linear vs. nonlinear aerodynamic modeling
* Time domain and frequency domain analysis methods

Applications
==========

Dynamic derivatives are essential for numerous aerospace applications:

* Flight dynamics model development and validation
* Control system design and analysis
* Flight simulator aerodynamic databases
* Aircraft certification and regulatory compliance
* Stability augmentation system design
* Flutter and aeroelastic analysis
* Handling qualities assessment

Simulation Approaches
=================

Flow360 supports various methods for computing dynamic derivatives:

**Forced Oscillation Technique:**

* Prescribe sinusoidal motions (pitch, roll, yaw)
* Extract in-phase and out-of-phase components
* Determine frequency-dependent derivatives

**Small Perturbation Method:**

* Apply small amplitude motions around trim conditions
* Compute linear stability derivatives
* Validate linear aerodynamic assumptions

**Time-Domain System Identification:**

* Process time-history data from dynamic simulations
* Extract derivatives using parameter estimation techniques
* Build reduced-order models from high-fidelity CFD

**Rotary Balance Simulation:**

* Model continuous rotation about body axes
* Capture nonlinear aerodynamic damping effects
* Predict spin characteristics and recovery

.. toctree::
   :hidden:

   dynamic