@Frog ,
From NASA at
https://www.grc.nasa.gov/www/k-12/airpl ... quilibrium.
A very basic concept when dealing with forces is the idea of equilibrium or balance. In general, an object can be acted on by several forces at the same time. A force is a vector quantity which means that it has both a magnitude (size) and a direction associated with it. If the size and direction of the forces acting on an object are exactly balanced, then there is no net force acting on the object and the object is said to be in equilibrium. Because there is no net force acting on an object in equilibrium, then from Newton's first law of motion, an object at rest will stay at rest, and an object in motion will stay in motion.
Equilibrium is balance , yet you stated on page 1 , that 3 of those DP's does not create equilibrium , and that if there are more or less than 3 DP's that there are no equilibrium points which makes a motion impossible .
Yet later (recently) you state the 3 DP's is in complete balance (equilibrium).
Equilibrium means balance , which means you admit that 2 DP's in the same manner of operation does not create balance and that 3 DP's in the same manner of operation does not create balance , but about 10 creates balance .
Three equally distributed pendulums with equal weights do not create equilibrium positions on a flywheel.
If there are more or fewer pendulums, there will be an equal number of equilibrium points, which makes a large circular pendulum movement impossible.
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These are not masses in periodic motion on two sides of a wheel.
- It's not a whole pendulum movement.
- It’s not a wheel that has equilibrium points.
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There are three holders for double pendulums, but they do not change the flywheels equilibrium, so the wheel can stand in any position - the wheel is balanced in any position.
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If a holder with double pendulum is locked into the flywheel, -ONE -equilibrium position occurs.
If the wheel is turned out of this equilibrium position, the wheel will return to this - ONE - equilibrium position with an oscillating movement.
Or a pendulum movement.
Torque is the force measurement that creates a rotation on an object about its axis , if the wheel turns in any direction even for 1 degree due to a force then it had a torque force , a torque force is the rotational equivalent of a linear force .
If there is any Torque on the wheel , then it is not in equilibrium/balance , the only way that a Torque is produced on a wheel to rotate about its axis , is when there are forces not in equilibrium/balance , if all forces are equal and in
equilibrium/balance then there would be no motion about its axis of rotation , and hence that means there is no net force on the object in any direction .
If there are equal weights on a lever and these weights are applying their equal forces at equal distances from the axle and their total calculated Torque forces cancel out - then they are in equilibrium/balance (it does not matter how many) , no torque results.
However when there are equal weights on a lever but some of them are applying their force's at different distances from the axle and their total calculated Torque forces does not cancel out - then they are not in equilibrium/balance , a torque results.
Take a look at this lever , it has a pendulum (B) on the one end hanging on a pivot at a distance of 1 meter from the axle, and a pendulum (A) locked on to the lever facing to the side on the other end at a pivot of 1 meter from the axle , for convenience lets say the pendulum arms are massless.
Lets say pendulum B stays hanging perfectly on its pivot , because pendulum B hangs from its pivot point on the lever , its weight's force is pulling on the pivot point , its force is acting downwards on the pivot point , and if the lever was rotated at a slow speed it would keep hanging and its weight's force would keep pulling on the pivot , so the force acting on the pivot for the lever stays more or less the same and at the same position , 1 meter away from the axle.
Pendulum A however which is locked to its pivot on the lever and pointing to the left , applies its weight's force at a greater distance from the axle than the distance to its pivot point , so the forces on the axle for each is different because the distances to where the forces apply are different , they are not in equilibrium/balance.
Its all relative.