08. Linearization Intuition 1
L3 06 Linearization Intuition 1 V1
2D Drone Equations of Motion
\begin{aligned}
\\
\ddot{y} &= \frac{u_1}{m}\sin\phi
\\
\ddot{z} &= g - \frac{u_1}{m}\cos\phi
\\
\ddot{\phi} &= \frac{u_2}{I_{xx}}
\end{aligned}
At the equilibrium hover configuration, all of the above accelerations (\ddot{y}, \ddot{z}, \ddot{\phi}) must be zero. This imposes some constraints on what values the other variables can take.
Use the equations of motions above (and your intuition), to identify some of these constraints.
Recall that equilibrium is where we can find certain fixed and non-changing control inputs, where the velocities and accelerations in the y, z and psi dimensions are zero.
Intuitively, this is the state where the vehicle stays for an extended period of time. For a quadrotor, the only state that is in equilibrium is called hover.