‫Welcome back, starting from this lecture, we will start driving the fundamental formulation for the
‫dynamics equations for six degrees of freedom system that we will later use on our specific quadcopter.
‫So if kinematics was a branch of mechanics which studied the motion of a body or system of bodies without
‫forces or talks, without considering them, then dynamics.
‫Thus consider forces and talks.
‫One crucial assumption that we will have is that our drone is a rigid body.
‫So what does it mean if you look at the drone from the side and you apply some thrust to it with the
‫propellers like this, then this is what will really happen.
‫The rods from the center of the drone to the propeller will slightly bend upwards.
‫The bending is very small and you will probably not see it in real life, but nevertheless, it's there.
‫And if you want to perform structural analysis on the body of the drone, meaning that you want to find
‫at which laws the rules break or you want to assess the stiffness of the rods, then you have to take
‫that bending into account.
‫And they are equations for that as well.
‫However, for controlling the drone, you don't need to take it into account so you can ignore bending
‫and make your life much simpler for yourself.
‫If you ignore bending, then you treat the drone as a rigid body.
‫It means that when you apply thrust, then your drone looks like this.
‫That's not the reality, but it's good enough for control purposes.
‫The same thing with a beam attached to a wall.
‫If you're on the edge of the beam, then it will slightly bend downwards.
‫In fact, it will bend downwards even if you are not there because there's force of gravity acting on
‫it.
‫However, let's ignore that for now.
‫But if bending is very small and not even visible, then we neglect it and we treat the beam as a rigid
‫body.
‫Then it looks like this and that's how we will treat our drone as a rigid body.