Mathematical modeling of the deflection of a rod

[COLOR=#333333][FONT=PT Sans]A rod is radially mounted on a motor shaft and provided with a flat end plate. By turning movement, the end plate will touch a pointed object, and the angle turned is measured.By the torque of the motor during acceleration and deceleration, a vibration and deflection happens on the rod. The model shows the deflection depending on temporal torque and angle.[/FONT][/COLOR]

[COLOR=#333333][FONT=PT Sans]This deflection will affect the angle measurement . So the idea is to find the mathematical formulae for the deflection and vibration, account it as the error and minimize it using controller(Simulink model or so). [/FONT][/COLOR]
[COLOR=#333333][FONT=PT Sans]This system is a higher order system(parameters like acceleration, length, torque, angle, etc) and for me it looks a very complicated task but interesting.[/FONT][/COLOR]

[COLOR=#333333][FONT=PT Sans]Can someone guide me to start the modeling. Can an FEM analysis help me with understanding the behaviour of vibration and deflection?[/FONT][/COLOR]
[COLOR=#333333][FONT=PT Sans]Even after FEM how do/ where do I start the modeling task?[/FONT][/COLOR]
[COLOR=#333333][FONT=PT Sans]Can anyone suggest me/ tip me some similar mathematical modeling examples or even a suitable literature so that I can learn more?[/FONT][/COLOR]