Explore rotational dynamics of rigid bodies using an arbitrary reference point in this comprehensive lecture on analytical dynamics. Delve into Euler's modified rotational dynamics equation, examining a car jumping off a ramp as a practical example. Learn about planar rigid body motion, simplified kinematics equations, and moment of inertia calculations for flat bodies. Discover the special form of the 3x3 moment of inertia matrix for thin, flat objects commonly encountered in engineering. Cover topics such as angular momentum, planar rigid bodies, and radius of gyration, with a focus on applying these concepts to real-world scenarios.