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‫Welcome back.

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‫In this section, we're going to start moving towards the derivation of a planned model for the use

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‫quadcopter in the next section, we're going to derive a specific mathematical model for that.

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‫However, in order to do it, we first need to lay the groundwork for that.

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‫I first need to familiarize you with certain fundamental concepts that you need in order to understand

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‫the stuff in the next section.

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‫Now, our drone is a six degree of freedom system, meaning that we have six dimensions that completely

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‫describe the drones position and it in space, three dimensions to describe its position with the inertial

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‫X, Y, Z axis that we measure in meters and three dimensions to describe.

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‫It's added to it with the angles, Phi Theta and PSI that we measure in radians.

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‫Therefore, we're going to derive fundamental kinematic and dynamic mathematical equations for a general

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‫six degree of freedom system.

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‫And then when we have that in the next section, we are going to apply it to our drone specifically.

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‫And now you might ask, of course, what's the difference between kinematics and dynamics?

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‫Well, what you need to know is that both of them describe how an object moves in space.

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‫However, kinematics does so without considering forces and moments that act on that object.

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‫Kinematics relates position and velocity and acceleration variables and also angular position, angular

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‫velocity and angular acceleration variables.

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‫For example, this is a kinematic equation.

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‫Velocity at certain time equals the initial velocity, meaning velocity at time equals zero seconds

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‫plus the acceleration at that time, times that time and that time can be anything, can be, for example,

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‫five seconds or 10 seconds.

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‫So this is one example of a kinematic equation.

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‫Dynamics, on the other hand, studies the effect of forces and moments on the motion of an object.

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‫So you apply forces and moments to a body and you see how it moves.

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‫For example, in the previous course in the series, we derive the equations of motion for a car that

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‫was dynamic's.

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‫You related the sum of the forces that was applied to a car, to the acceleration of the car.

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‫And you also related the sum of the moments apply to a car to its angular acceleration.

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‫And so X double dot is the double time derivative of X, so the linear acceleration and theta double

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‫that is the double time derivative of theta, which is the angular acceleration.

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‫So that is the difference.

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‫We will start with kinematics in the next lecture and then we will cover equations in dynamics after

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‫that.

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‫Thank you very much and I'll see you in the next video.