Model of ball and plate dynamics
This is a three-dimensional model so in this case it is preferable to get the movement equations by Lagrange's formulation of mechanics because it minimize the number of required coordinates to be used in the characterization of involved bodies kinematics. Firstly we get positions and velocities, secondly we write the conservative terms of energy and then we differentiate a set of Lagrange's equations. The variables of the ball and plate system are shown bellow but in the text some of them are being accompanied by subscript b for the ball and p for the plate.