can you give me an example of not conservative case ?
the archer quinn S.O.G. device comes to mind.....
--------------------------------------------------------------
Gravity is only conservative when analyzed from the perspective of lift vs fall. (mgh)
an object accelerates with the square of time on the way down, and inversly deccelerates on the way up.
If the object already has a velocity when it is released (i.e. throwing it down), then is allowed to fall, it is the same as dropping it from a higher altitude.
This higher altitude, would be equivalent to the original (mgh) + the kinetic energy of the 'throw'.
However, the momentum of the object, is its mass times its velocity. The time derrivative is not squared.
When you impart this 'throw' energy in the same directional vector as the gravitational force, the momentum force added to it, results in a greater final momentum than when the object is allowed to free-fall from the 'higher' altitude.
for instance, take the Chalkalis device, and move the drive-wheels to the other side of the wheel; Such that they are driving the wheel up and over the top, instead of pushing it on the down side. If the drive-wheels are set so that the wheel just barely completes the full circle when pushed on the down side,
when you move them to the up side, the wheel will not make it around the top, and back into the drive-wheels.
too much momentum is eaten by the gravitational decceleration.
it goes up, over the top, then pendulates to a stop at bottom dead center, never re-entering the drive-wheels for another cycle.
The same ammount of energy was added to the system, yet the wheel retains less momentum.
-------------------------------------------------------
using the rock thrown from a bridge example::
you calculate the gravitational displacement from the top of the bridge (mgh), and add the energy of the "throw", then launch the rock with this set ammount of energy, vertically upwards from the ground.
You will observe the 'conservative' gravitational field. Up / Down.
allow the rock to land on an impact-scale.
the rock arrives back at the ground with the same ammount of force you imparted upon it.
Now, take this rock to the top of the bridge (mgh input), and give it an equal 'throw' downwards.(same total input energy) and allow this rock to strike an impact-scale on the ground. the impact force(momentum) of the rock, moving faster now, is greater than in the first test. This is defined in Newton's second law.
The total Energy in both cases is the same yet the momentum (impact force) is quite different. Momentum is a vector quantity (directional) and does not significantly affect the total energy of the system until you approach relativistic velocities.
It does however affect the kinetic energy of the system in motion.
and in the case of the unbalanced wheel, this becomes more complex. Momentum is increasing and decreasing during different parts of the cycle (up / down).
--------------------------------------------------------------
When the mass is attached to a fixed wheel, and the additional momentum is in the same vector are the gravitational force, this momentum is added to the gravitationally imparted velocity as the wheel turns around. Because the added momentum is conserved all the way around the wheel.
This is why when the drive-wheels are placed on the down-side of the chalkalis wheel, it allows the wheel to complete a full circle and re-enter the drive-wheels.
--------------------------------------------------------------
another example would be if you have a mass, rotating at a set distance around a fixed axis. Then you change this distance.
like a kid on a whirl-a-round, moving inwards or outwards.
The momentum increases or decreases accordingly, and this affects the rotational velocity of the whirl-a-round.
Yet no "energy" is added to or subtracted from the system.
------------------------------------------------------------
The important difference in the Chalkalis device, is that extra energy IS actually added to the system, from the drive-wheels.
When this translates to increased momentum, there is a greater rotational force imparted upon the axis.
To determine the extent of this effect, would require a "load" placed upon the axis, increasing until the wheel no longer makes it over the top. When this maximum output is reached, it should then be compared to the energy input INTO the drive-wheels.
This would be the ONLY definitive test, to determine wether or not the Chalkalis device is "OU".