‫Welcome back.
‫In this section, we're going to start moving towards the derivation of a planned model for the use
‫quadcopter in the next section, we're going to derive a specific mathematical model for that.
‫However, in order to do it, we first need to lay the groundwork for that.
‫I first need to familiarize you with certain fundamental concepts that you need in order to understand
‫the stuff in the next section.
‫Now, our drone is a six degree of freedom system, meaning that we have six dimensions that completely
‫describe the drones position and it in space, three dimensions to describe its position with the inertial
‫X, Y, Z axis that we measure in meters and three dimensions to describe.
‫It's added to it with the angles, Phi Theta and PSI that we measure in radians.
‫Therefore, we're going to derive fundamental kinematic and dynamic mathematical equations for a general
‫six degree of freedom system.
‫And then when we have that in the next section, we are going to apply it to our drone specifically.
‫And now you might ask, of course, what's the difference between kinematics and dynamics?
‫Well, what you need to know is that both of them describe how an object moves in space.
‫However, kinematics does so without considering forces and moments that act on that object.
‫Kinematics relates position and velocity and acceleration variables and also angular position, angular
‫velocity and angular acceleration variables.
‫For example, this is a kinematic equation.
‫Velocity at certain time equals the initial velocity, meaning velocity at time equals zero seconds
‫plus the acceleration at that time, times that time and that time can be anything, can be, for example,
‫five seconds or 10 seconds.
‫So this is one example of a kinematic equation.
‫Dynamics, on the other hand, studies the effect of forces and moments on the motion of an object.
‫So you apply forces and moments to a body and you see how it moves.
‫For example, in the previous course in the series, we derive the equations of motion for a car that
‫was dynamic's.
‫You related the sum of the forces that was applied to a car, to the acceleration of the car.
‫And you also related the sum of the moments apply to a car to its angular acceleration.
‫And so X double dot is the double time derivative of X, so the linear acceleration and theta double
‫that is the double time derivative of theta, which is the angular acceleration.
‫So that is the difference.
‫We will start with kinematics in the next lecture and then we will cover equations in dynamics after
‫that.
‫Thank you very much and I'll see you in the next video.