# Doubt linearizing 2D planar quadrotor equation of motion

Equation of motion for 2D planar quadrotor are as follows

$$\ddot{x} = \frac{1}{m} (u1+u2)sin(\theta)$$

$$\ddot{y} = \frac{1}{m} (u1+u2)cos(\theta) - mg$$

$$\ddot{\theta} = \frac{r}{I} (u1+u2)$$

How to linearize this equation to get it in state space form x = Ax + Bu. Could someone please help me out?

• Could it be that there are a couple mistakes in your equations, namely in $\ddot{y}$ you both multiply and divide by $m$ and shouldn't $\ddot{\theta}$ be a function of the difference of the inputs? Also what have you tried? – fibonatic May 20 at 10:48
• yes you are right. Thanks. – npkp May 20 at 19:03