Force-Free Motion

Nd787 C5 L3 A02 L Force Free Dynamics V3

Force-Free Motion

When tracking the longitudinal dynamics, we use the following state vector:

\mathbf{x} = \begin{bmatrix} x_I\\ z_I\\ \theta \\ u \\ w \\ q \end{bmatrix}

x_I and z_I are the position in the inertial frame (note that z is positive UPWARDS for this lesson).

\theta is the pitch angle.

u and w are the body frame velocities.

q is this pitch rate.

When there are no forces acting on the vehicle, the equations of motion are as follows:

\begin{aligned} \dot{x}_I &= u \cos \theta + w \sin \theta \\ \dot{z}_I &= -u \sin \theta + w \cos \theta \\ \dot{\theta} &= q \\ \dot{u} &=- qw \\ \dot{w} &= qu \\ \dot{q} &= 0 \\ \end{aligned}

Reminder: Fixed Wing Cheat Sheet

You can find all of the equations for this module in the Fixed Wing Cheat Sheet .

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