Yaw and Pitch
Yaw
Yaw rotation is the movement of a rigid body around its vertical axis. It changes the direction the object is pointing to the left or right relative to its forward motion.
The yaw rate (or yaw velocity) is defined as:
\(\omega_{\text{yaw}} = \frac{d\psi}{dt}\)
where \(\omega_{\text{yaw}}\) is the yaw rate and \(\psi\) is the heading angle.
The yawing moment is the torque component about the vertical axis:
\(M_{\text{yaw}} = I_z \cdot \alpha_{\text{yaw}}\)
where \(I_z\) is the moment of inertia about the vertical axis and \(\alpha_{\text{yaw}} = \frac{d\omega_{\text{yaw}}}{dt}\) is the angular acceleration.
Pitch
Pitch rotation is around the horizontal axis, changing the up or down orientation of the object.
The pitch rate is defined as:
\(\omega_{\text{pitch}} = \frac{d\theta}{dt}\)
where \(\theta\) is the pitch angle.
The pitch moment is:
\(M_{\text{pitch}} = I_y \cdot \alpha_{\text{pitch}}\)
where \(I_y\) is the moment of inertia about the pitch axis and \(\alpha_{\text{pitch}}\) is the pitch angular acceleration.
Summary Table
| Motion | Axis | Angle | Rate | Moment |
|---|---|---|---|---|
| Yaw | Vertical | \(\psi\) | \(\omega_{\text{yaw}} = \frac{d\psi}{dt}\) | \(M_{\text{yaw}} = I_z \cdot \alpha_{\text{yaw}}\) |
| Pitch | Horizontal | \(\theta\) | \(\omega_{\text{pitch}} = \frac{d\theta}{dt}\) | \(M_{\text{pitch}} = I_y \cdot \alpha_{\text{pitch}}\) |