linearity

[gavin]

not sure if this has been covered before, but i'm starting to think about the linearity of the forces at our disposal.

for instance mass is linear with weight, leverage is linear etc. the problem i keep encountering with linear relationships is that whatever i gain on one side of the wheel, i lose the exact same amount on the other.

certain aspects of gravity are non linear such as distance, which is clearly seen with magnets (i don't think he used magnets, but they do ilustrate the point). The nice thing about convexity is that it may be possible to engineer a situation where you gain more than you loose. i guess i'm looking for a situation where a positive increament in some variable reacts with a bigger gain in force than the loss in force from a negative increment in the same variable.

if this hasn't been done already i'd like to pull together a list of all governing equations and identify non-linear processes which may be of use.

i believe pendulums exhibit non-linearity where large oscillations are concenered.

it could be possible that the combination or a linear and non-linear process may yield a net gain.

[LustInBlack]

Take a vertical pendulum, it's rest point at 6 o'clock.

Rotate that pendulum 90 degrees, so that the anchoring pivot is at 9.
You want it's rest point to be at 3, so the pendulum is perfectly horizontal
at REST .

The gravity pull the pendulum down.

So you need a force to pull it back up.

What is nice about gravity, is the fact that it will pull on any object regardless of how much mass it has (hint) .

I don't want to say the way to achieve this, but I'll give you clues.
[Something I am working on] .


I think there is a net gain in a system similar to this .

[Fletcher]

The gravity pull the pendulum down.

So you need a force to pull it back up.

What is nice about gravity, is the fact that it will pull on any object regardless of how much mass it has (hint).

The gravity pull the pendulum down. What is nice about gravity, is the fact that it will pull on any object regardless of how much mass it has (hint).

Gravity pulls everything down with the same acceleration regardless of its mass.

This is a very unusual property. If you apply a shifting force to the same mass to shift it horizontally you must apply greater force for the same rate of acceleration as the mass increases & conversely for less mass which is quite a different proposition from falling vertically. In one orientation the inertia doesn't matter, in the other it does. Galileo proved this as prior scientists thought more mass accelerated more quickly when let fall vertically.

So you need a force to pull it back up.

Gravity causes things to fall to their position of least Gravitational Potential Energy. As it does so the objects inertia changes. That inertia becomes momentum & this is what allows an object such as a pendulum to rise upwards again. Momentum also allows a free weight to bounce if combined with elasticity of the object & the contact medium. The amount of momentum that can be used depends on 'impulse v's impact'.

[LustInBlack]

So basicly you are describing the pendulum as an inertia converter, in that it translates properties of gravity into lateral acceleration .. ??


In my example, pull on the pendulum to bring it to the top.
Put a 5 Lbs weight on it, let it fall .
Do the same thing, with no weight this time, it will fall .

Using that property alone, you can bring down the pendulum without spending energy .

The analogy with a real pendulum is this, bring the vertical pendulum to 9 with a weight or no weight, it will go to less than 3 on the other side .

The horizontal pendulum, will always go to 6 no matter how much weight, or no matter where you started it, of course, you need to start it above ground .


So basicly, you are left with a weight that can be removed or connected to the pendulum system..

You can use that property to lift the pendulum, the weight can be connected to a pulley system that will lift up the pendulum, on release it will let go the pendulum to the bottom .

That's simple and don't need much explanation, but there is a reason for the explanation ....


Basicly, if you bring up the pendulum, loaded, you unload it, let go down the pendulum unloaded, pull back on it to lift it again with the potential of the unloaded weight.

Inversely :
You load the pendulum to the top, it falls, unload, lift back up unloaded.
You just need a counter-weight.

The missing part is bringing those 2 systems together and gaining an advantage, I think this advantage can be found where the pendulum stop it's course.

You'll understand that this is not a standard pendulum, but more of a lever, but seeing it as a pendulum helps.

[LustInBlack]

... Then you will understand that a horizontal pendulum, is in fact a vertical pendulum.

Now you will convert the system from a pendulum to a lever and back to a pendulum.

Maybe it doesn't make much sense yet.