I studied the sum of energy of the device for a small angle like 0.001 rd for example. I studied only the horizontal forces here because the vertical force is at 0.

**I supposed the wheel rotates and moves before the study of the sum of the energy****I supposed an external device force the wheel to turn and rotate without an acceleration like that it's easier to calculate the energy in/out.****1) enumerate all axes**The green axis is fixed on the wheel

**2) enumerate all fixed bodies**The ground

The device that gives the force Fq

**3) enumerate all discreet mobile bodies**All the device moves in translation and rotates clockwise like a wheel of a bike

The red wall

The outer circle of the wheel and the blue wall (blue color = one body)

N balls (small like molecules of water, just for simplify the calculations), without mass (simplify)

N springs, without mass (simplify calculations)

Gaskets (I don't drawn them)

**4) enumerate all connections and constraints**The red wall can only turn around the green axis, the red wall is in contact with balls only, the red wall receives the pressure from the balls

Each ball is attracted by a spring from the center C

The device like that is unstable but I give the force Fq from an external device

**fixed on the ground**.

**5) describe all constraints on motion for mobile bodies relative to their point of connection to the root object (most likely a fixed body)**When the wheel moves and rotates, all the device turns and moves, the springs never lost their potential energy because the balls are always in the same relative position

**6) describe significant physical properties of all bodies (are they rigid? flexible?)**All bodies are rigid except the springs

The springs and the balls are without mass

The wheel has a mass.

Each ball is attracted with the law 1/dē with 'd' the distance between the center of the wheel and the ball

The device:

The names of points:

The integrals:

All the device moves and rotates like a wheel of a bike (balls don't escape):

The energy: