Mathematical Model

By determining the equations of motion, we are able to describe the motion of the pendulum bob. The motion of the pendulum bob can be completely described by analyzing q and f. The following is a derivation of these equations. For the purpose of this derivation, the following variables will be used:

m = non-conservative force applied to frame assembly
L = length from the top of the pendulum to the center of mass
m = mass of bob
g = acceleration of gravity
= angle of pendulum with frame assembly
= angle of frame assembly
Ip = moment of inertia for pendulum assembly
If = moment of inertia for frame assembly
T = kinetic energy
V = potential energy
Le = Lagrangian

Newtonian Derivation:

Lagrangian Derivation:

Derivation of Reaction Forces:

Our apologies for the poor looking derivation images. We were having great difficulty convincing Microsoft Equation to work.