DOC: Add comprehensive documentation for acceleration-based parachute triggers

- Created docs/user/parachute_triggers.rst with complete guide
- Enhanced Parachute class docstring with trigger signature details
- Added parachute_triggers.rst to docs/user/index.rst

Documentation covers:
- Built-in triggers (burnout, apogee_acc, freefall, liftoff)
- Custom trigger examples (3, 4, and 5-parameter signatures)
- IMU noise simulation
- Performance considerations
- Best practices and complete dual-deploy example

Author: ViniciusCMB

docs/user/index.rst

@@ -24,6 +24,7 @@ RocketPy's User Guide
    :caption: Special Case Simulations
 
    Compare Flights Class<compare_flights.rst>
+   Parachute Triggers (Acceleration-Based) <parachute_triggers.rst>
    Deployable Payload <deployable.rst>
    Air Brakes Example <airbrakes.rst>
    ../notebooks/sensors.ipynb

docs/user/parachute_triggers.rst

@@ -0,0 +1,329 @@
+Acceleration-Based Parachute Triggers
+======================================
+
+RocketPy supports advanced parachute deployment logic using acceleration data
+from simulated IMU (Inertial Measurement Unit) sensors. This enables realistic
+avionics algorithms that mimic real-world flight computers.
+
+Overview
+--------
+
+Traditional parachute triggers rely on altitude and velocity. Acceleration-based
+triggers provide additional capabilities:
+
+- **Motor burnout detection**: Detect thrust termination via sudden deceleration
+- **Apogee detection**: Use acceleration and velocity together for precise apogee
+- **Freefall detection**: Identify ballistic coasting phases
+- **Liftoff detection**: Confirm motor ignition via high acceleration
+
+These triggers can optionally include sensor noise to simulate realistic IMU
+behavior, making simulations more representative of actual flight conditions.
+
+Built-in Triggers
+-----------------
+
+RocketPy provides four built-in acceleration-based triggers:
+
+Motor Burnout Detection
+~~~~~~~~~~~~~~~~~~~~~~~~
+
+Detects when the motor stops producing thrust by monitoring sudden drops in
+acceleration magnitude.
+
+.. code-block:: python
+
+    from rocketpy import Parachute
+
+    drogue = Parachute(
+        name="Drogue",
+        cd_s=1.0,
+        trigger="burnout",  # Built-in trigger
+        sampling_rate=100,
+        lag=1.5
+    )
+
+**Detection criteria:**
+- Vertical acceleration < -8.0 m/s² (end of thrust phase), OR
+- Total acceleration magnitude < 2.0 m/s² (coasting detected)
+- Rocket must be above 5m altitude and ascending (prevents false triggers at launch)
+
+Apogee Detection
+~~~~~~~~~~~~~~~~
+
+Detects apogee using both near-zero vertical velocity and negative vertical
+acceleration.
+
+.. code-block:: python
+
+    main = Parachute(
+        name="Main",
+        cd_s=10.0,
+        trigger="apogee_acc",  # Acceleration-based apogee
+        sampling_rate=100,
+        lag=0.5
+    )
+
+**Detection criteria:**
+- Absolute vertical velocity < 1.0 m/s
+- Vertical acceleration < -0.1 m/s² (downward)
+
+Freefall Detection
+~~~~~~~~~~~~~~~~~~
+
+Detects free-fall by monitoring very low total acceleration (near gravitational
+acceleration only).
+
+.. code-block:: python
+
+    drogue = Parachute(
+        name="Drogue",
+        cd_s=1.0,
+        trigger="freefall",
+        sampling_rate=100,
+        lag=1.0
+    )
+
+**Detection criteria:**
+- Total acceleration magnitude < 11.5 m/s²
+- Rocket descending (vz < -0.2 m/s)
+- Altitude > 5m (prevents ground-level false triggers)
+
+Liftoff Detection
+~~~~~~~~~~~~~~~~~
+
+Detects motor ignition via high total acceleration.
+
+.. code-block:: python
+
+    test_parachute = Parachute(
+        name="Test",
+        cd_s=0.5,
+        trigger="liftoff",
+        sampling_rate=100,
+        lag=0.0
+    )
+
+**Detection criteria:**
+- Total acceleration magnitude > 15.0 m/s²
+
+Custom Triggers
+---------------
+
+You can create custom triggers that use acceleration data:
+
+.. code-block:: python
+
+    def custom_trigger(pressure, height, state_vector, u_dot):
+        """
+        Custom trigger using acceleration data.
+
+        Parameters
+        ----------
+        pressure : float
+            Atmospheric pressure in Pa (with optional noise)
+        height : float
+            Height above ground level in meters (with optional noise)
+        state_vector : array
+            [x, y, z, vx, vy, vz, e0, e1, e2, e3, wx, wy, wz]
+        u_dot : array
+            Derivative: [vx, vy, vz, ax, ay, az, e0_dot, ...]
+            Accelerations are at indices [3:6]
+
+        Returns
+        -------
+        bool
+            True to trigger parachute deployment
+        """
+        # Extract acceleration components (m/s²)
+        ax = u_dot[3]
+        ay = u_dot[4]
+        az = u_dot[5]
+
+        # Calculate total acceleration magnitude
+        total_acc = (ax**2 + ay**2 + az**2)**0.5
+
+        # Custom logic: deploy if total acceleration < 5 m/s² while descending
+        vz = state_vector[5]
+        return total_acc < 5.0 and vz < -10.0
+
+    # Use custom trigger
+    parachute = Parachute(
+        name="Custom",
+        cd_s=2.0,
+        trigger=custom_trigger,
+        sampling_rate=100,
+        lag=1.0
+    )
+
+Sensor and Acceleration Triggers
+---------------------------------
+
+Triggers can also accept sensor data alongside acceleration:
+
+.. code-block:: python
+
+    def advanced_trigger(pressure, height, state_vector, sensors, u_dot):
+        """
+        Advanced trigger using both sensors and acceleration.
+
+        Parameters
+        ----------
+        sensors : list
+            List of sensor objects attached to the rocket
+        u_dot : array
+            State derivative including accelerations
+
+        Returns
+        -------
+        bool
+        """
+        # Access sensor measurements
+        if len(sensors) > 0:
+            imu_reading = sensors[0].measurement
+
+        # Use acceleration data
+        az = u_dot[5]
+
+        # Combine sensor and acceleration logic
+        return az < -5.0 and imu_reading > threshold
+
+    parachute = Parachute(
+        name="Advanced",
+        cd_s=1.5,
+        trigger=advanced_trigger,
+        sampling_rate=100
+    )
+
+Adding Acceleration Noise
+--------------------------
+
+To simulate realistic IMU behavior, you can add noise to acceleration data:
+
+.. code-block:: python
+
+    from rocketpy import Flight
+
+    flight = Flight(
+        rocket=my_rocket,
+        environment=env,
+        rail_length=5.2,
+        inclination=85,
+        heading=0,
+        acceleration_noise_function=lambda: np.random.normal(0, 0.5, 3)
+    )
+
+The ``acceleration_noise_function`` returns a 3-element array ``[noise_x, noise_y, noise_z]``
+that is added to the acceleration components before passing to the trigger function.
+
+**Example with time-correlated noise:**
+
+.. code-block:: python
+
+    class NoiseGenerator:
+        def __init__(self, stddev=0.5, correlation=0.9):
+            self.stddev = stddev
+            self.correlation = correlation
+            self.last_noise = np.zeros(3)
+
+        def __call__(self):
+            # Time-correlated noise (AR(1) process)
+            white_noise = np.random.normal(0, self.stddev, 3)
+            self.last_noise = (self.correlation * self.last_noise +
+                               np.sqrt(1 - self.correlation**2) * white_noise)
+            return self.last_noise
+
+    flight = Flight(
+        rocket=my_rocket,
+        environment=env,
+        rail_length=5.2,
+        inclination=85,
+        heading=0,
+        acceleration_noise_function=NoiseGenerator(stddev=0.3, correlation=0.95)
+    )
+
+Performance Considerations
+--------------------------
+
+Computing acceleration (``u_dot``) requires evaluating the equations of motion,
+which adds computational cost. RocketPy optimizes this by:
+
+1. **Lazy evaluation**: ``u_dot`` is only computed if the trigger actually needs it
+2. **Metadata detection**: The wrapper inspects trigger signatures to determine requirements
+3. **Caching**: Derivative evaluations are reused when possible
+
+**Trigger signature detection:**
+
+- 3 parameters ``(p, h, y)``: Legacy trigger, no ``u_dot`` computed
+- 4 parameters with ``u_dot``: Only acceleration computed
+- 4 parameters with ``sensors``: Only sensors passed
+- 5 parameters: Both sensors and acceleration provided
+
+Best Practices
+--------------
+
+1. **Choose appropriate sampling rates**: 50-200 Hz is typical for flight computers
+2. **Add realistic noise**: Real IMUs have noise; simulate it for validation
+3. **Test edge cases**: Verify triggers work at low altitudes, high speeds, etc.
+4. **Use built-in triggers**: They handle edge cases (NaN, Inf) automatically
+5. **Document custom triggers**: Include detection criteria in docstrings
+
+Example: Complete Dual-Deploy System
+-------------------------------------
+
+.. code-block:: python
+
+    from rocketpy import Rocket, Parachute, Flight, Environment
+    import numpy as np
+
+    # Environment and rocket setup
+    env = Environment(latitude=32.99, longitude=-106.97, elevation=1400)
+    env.set_atmospheric_model(type="standard_atmosphere")
+
+    my_rocket = Rocket(...)  # Define your rocket
+
+    # Drogue parachute: Deploy at motor burnout
+    drogue = Parachute(
+        name="Drogue",
+        cd_s=1.0,
+        trigger="burnout",
+        sampling_rate=100,
+        lag=1.5,
+        noise=(0, 8.3, 0.5)  # Pressure sensor noise
+    )
+    my_rocket.add_parachute(drogue)
+
+    # Main parachute: Deploy at 800m using custom trigger
+    def main_deploy_trigger(pressure, height, state_vector, u_dot):
+        """Deploy main at 800m while descending with positive vertical acceleration."""
+        vz = state_vector[5]
+        az = u_dot[5]
+        return height < 800 and vz < -5 and az > -15
+
+    main = Parachute(
+        name="Main",
+        cd_s=10.0,
+        trigger=main_deploy_trigger,
+        sampling_rate=100,
+        lag=0.5,
+        noise=(0, 8.3, 0.5)
+    )
+    my_rocket.add_parachute(main)
+
+    # Flight with IMU noise simulation
+    flight = Flight(
+        rocket=my_rocket,
+        environment=env,
+        rail_length=5.2,
+        inclination=85,
+        heading=0,
+        acceleration_noise_function=lambda: np.random.normal(0, 0.3, 3)
+    )
+
+    flight.all_info()
+
+See Also
+--------
+
+- :doc:`Parachute Class Reference </reference/rocket/parachute>`
+- :doc:`Flight Simulation </user/flight>`
+- :doc:`Sensors and Controllers </user/sensors>`