Lesson Outline

In this lesson you will learn about the physics which underlies motion in one and two dimensions. We will cover 3D dynamics in the fourth lesson of this course.

Part 1 - Basic (1D) Quadrotor Physics

We're going to go quickly through this section. We assume you've taken basic physics before and this is mostly a review.

• Definition of Force
• Forces on a Quadrotor: gravity / weight, thrusts, drag (which we won't be modeling)
• Translational Equilibrium / Hover
• Rotational Equilibrium
• Definition of Moment / Torque
• Rotor Physics: F = k_f \omega^2 and M = k_m \omega^2
• F = m a and F_z = m \ddot{z}
• \tau = I \alpha and M_z = I_z \ddot{\psi}
• Programming Exercise: Coaxial Copter Dynamics

Part 2 - Quadrotor Math: Second Order Systems

This will be a brief introduction to some of the math and programming we use to keep track of the state of flying vehicles.

• Programming Exercise: Tracking Changes to State
• Second order systems / double integrated systems
• Using vectors to store state

Part 3 - Dynamics of Controlled Quadrotors (2D)

Now we will allow the vehicle to move in two dimensions. This part is meant to be a quick review of the trigonometry and physics required for 2D motion.

• Decomposing thrust vectors (review of trig: \sin and \cos )
• Calculating moments: \tau = d_\text{perp} \times F
• Converting propeller rotations to Forces and Moments
• Programming Exercise: 2D Controlled Quad