Added coordinate map.

exercises/21_six_axis/Discussion.md

@@ -54,7 +54,7 @@ Az = -0.003
 
 Device standing upright (antenna vertical)
 
-<img src="img/upright_DSC_5194.webp" alt="Upright Orientation" width="500">
+<img src="img/upright_DSC_5194.webp" alt="Upright Orientation"  height="350">
 
 
 Measured accelerometer values:
@@ -164,6 +164,39 @@ While raw values differ between orientations:
 - Results are consistent regardless of startup pose
 
 ---
+### 4. Coordinate Mapping
+
+From the observed accelerometer data:
+
+- Upright orientation: +Y_sensor ≈ UP
+- Sideways orientation: -X_sensor ≈ UP (after 90° rotation)
+
+We define a **device coordinate system** aligned with the AlleyCat enclosure:
+
+- Z_device = UP (antenna direction)
+- Y_device = FORWARD (normal to display, pointing outward)
+- X_device = RIGHT (along the long axis of the display)
+
+Mapping from sensor frame to device frame:
+
+    Z_device = +Y_sensor
+
+The remaining axes are determined by physical orientation and require sign validation:
+
+    X_device ≈ +Z_sensor
+    Y_device ≈ ±X_sensor
+
+Final sign conventions should be verified empirically by observing motion:
+
+- Rotate device forward/back → affects Y_device
+- Rotate device left/right → affects X_device
+
+This mapping separates:
+
+- Sensor frame (hardware-defined)
+- Device frame (application-defined)
+
+and provides a consistent basis for roll, pitch, and future magnetometer integration.
 
 ## Sources of Error