Euler angles are a set of three angles used to describe the orientation of a rigid body in a three-dimensional space with respect to a fixed coordinate system. The three angles are typically denoted as (θ), (φ), and (ψ), and represent rotations about the nutation, precession, and spin respectively. 

Matlab is an excellent tool for simulation because it has a wide range of built-in functions and libraries that can be used to create complex models and simulations quickly and easily. Its powerful numerical computation capabilities and visualization tools also make it easy to analyze and interpret simulation results.

This spinning top simulation with friction is modeled using the Euler equations of motion, which describe the motion of a rigid body in terms of its angular momentum and the torques acting on it. In this simulation, the frictional and gravitational forces would be included as a torque acting on the top, which would cause it to slow down and eventually come to a stop. This simulation also accounts for the effects of nutation, which causes the top to wobble and change direction slightly as it spins.

A spinning top simulation without friction is modeled using the Euler equations of motion, which describe the motion of a rigid body in terms of its angular momentum and the torques acting on it. In this simulation, the top is assumed to be a perfect, rigid object with a fixed axis of rotation and no external torques acting on it, and the effects of air resistance and other forms of friction are neglected which is the reason that is seems to spin on forever.