Lagrange Maths 101

[agor95]

The overview landscape of my journey on 'The Quest' with the interactions of moving masses.

Also the design framework seems to fit better to
this mathematical methodology.

I am really at the start of this mathematics. it is cryptic at this time.

[Furcurequs]

Hey Agor95,

Thanks. I've saved that to my "projects" folder.

I have an engineering degree, but I don't remember having covered Lagrangian methods in school. My specialty was in electrical engineering, though.

I think the higher level physics and mechanical engineering courses covered the Lagrange stuff.

I think I have some college lectures that cover it which I' downloaded from youtube. I'll check to see which those are and may post back later. (...if my headache doesn't get the best of me.)

Dwayne

[agor95]

Well some basics

Gottfried Wilhelm Leibniz 1716 died
Bessler 1717 wheel
Newton 1727 died

Euler & Lagrange maths developed 1750

You never know; could Bessler stating mathematicians would not figure out his device trigger this new maths?

Well back to studying - I like the 'Stationary Action' concept.

[agor95]

As you jump off into the abyss of confusion heading to the terminal rocks of despair.

Some people believe you see your life flash before your eyes.

What is actually happening is your subconscious is wanting to look the other way
at your passed as a distraction form the inevitability of the now.

I see my subconscious trying that game and this popped up

A simple use of maths

https://en.wikipedia.org/wiki/Newton%27s_method

No No temptress be gone. Although this is torture
it must be done.

So back into the studying this infernal maths.

https://www.youtube.com/watch?v=zhk9xLjrmi4

about 38 minutes in but I must watch all.

Then more, jump into the maelstrom deep.

https://www.youtube.com/watch?v=4uJaKJASKnY

https://www.youtube.com/watch?v=0Zss63BLZjI spring roller

[agor95]

Here are some more links

Details on the notation forms

https://en.wikipedia.org/wiki/Notation_ ... rentiation

Moments of inertia

https://en.wikipedia.org/wiki/List_of_m ... of_inertia

https://www.youtube.com/watch?v=eoBYvPF5KL0

P.S. I don't want to post much.
There is a dangerous potato gun user about.

Best not to get a roasting.

[Furcurequs]

A real potato gun would be too dangerous for someone like me. The last time I ignited alcohol vapor in an experiment, I roasted my thumb and it hurt for days.

[agor95]

The reason for the 101 in this topic is to show this is for beginners like me.

What I am doing right now is staring at a page with 5 equally spaced dots.
All in a horizontal line.

They pivot around the center mark.

Simple start but one has to start some where.

So inertia, gravity, CF and elastic spring force all need to be defined and set to interact as the point masses move.

[agor95]

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

A nice shallow/simple web site.

http://hyperphysics.phy-astr.gsu.edu/hb ... html#irod3

Or may be not

Just wanting to know the rate of change from the center to the end is steady.
What is the rate of change in I ?

I being inertia

Time to do a graph

[Gregory]

Hey agor95,

The moment of inertia for point masses is simply m*r^2
So the relationship is parabolic, respect to the radius squared.

For not point masses the formula for I is different, depends on the exact geometric shape and the center of rotation.
For example MoI of an ideal disc rotating around its center point is: 1/2*m*r^2
Similarly a rod with axis in the center: 1/12*m*d^2

Here is a list of these:
https://en.wikipedia.org/wiki/List_of_m ... of_inertia

[agor95]

@Gregory

Thank you for your help.

There are some formulas I am looking for that combined could help members.

I = m*r^2 point mass

I = 1/12*m*L^2 rod around the center
I = 1/3*m*L^2 rod around the end

The formula I am looking for is 1/2*L <= y <= L for Function (1/x*m*L^2)

So we start with rotation in the center y = L/2 and x = 12
We finish at the end y = L and x = 3

Given the delta y rate is constant what formula represents delta x?

I am using L = 2 meters and starting with basic maths.
Then getting to the rate of x for dy.

Figure what that looks like in differencial notation.
Then figure that in Latex format and update the web site.

This is odd - I am missing something

Found the odd thing L=2m mass=2kg and L=1m mass=1kg

http://hyperphysics.phy-astr.gsu.edu/hb ... .html#irod

I = 1/3kgm^2 where m=1kg and L=2 meter rotating around the center of mass. [should be 2kg to I = 2/3kgm^2]

However two rods rotating around the ends m=1kg, L=1 meter.

I = 1/3 kgm^2 for rod 1 and I = 1/3 kgm^2 for rod 2. That is I = 2/3 kgm^2 for these two rods.

Yes I have glued them together.

So the first center rotation rod needs a mass of 2kg.

Therefore I = 2/3kgm^2

Strange the formula derivative changes and the I result of the original formula seems secondary.

Regards

[agor95]

Parallel - Axis Theorem

https://www.youtube.com/watch?v=VNInrOTUh-Y

Small steps long journey

[Gregory]

@Gregory

Thank you for your help.

There are some formulas I am looking for that combined could help members.

I = m*r^2 point mass

I = 1/12*m*L^2 rod around the center
I = 1/3*m*L^2 rod around the end

The formula I am looking for is 1/2*L <= y <= L for Function (1/x*m*L^2)

So we start with rotation in the center y = L/2 and x = 12
We finish at the end y = L and x = 3

Given the delta y rate is constant what formula represents delta x?

I am using L = 2 meters and starting with basic maths.
Then getting to the rate of x for dy.

Figure what that looks like in differencial notation.
Then figure that in Latex format and update the web site.

This is odd - I am missing something

Found the odd thing L=2m mass=2kg and L=1m mass=1kg

http://hyperphysics.phy-astr.gsu.edu/hb ... .html#irod

I = 1/3kgm^2 where m=1kg and L=2 meter rotating around the center of mass. [should be 2kg to I = 2/3kgm^2]

However two rods rotating around the ends m=1kg, L=1 meter.

I = 1/3 kgm^2 for rod 1 and I = 1/3 kgm^2 for rod 2. That is I = 2/3 kgm^2 for these two rods.

Yes I have glued them together.

So the first center rotation rod needs a mass of 2kg.

Therefore I = 2/3kgm^2

Strange the formula derivative changes and the I result of the original formula seems secondary.

Regards

Hi agor95,

I am not sure I understand what are you trying to do.

Describe in simple terms and step by step what physical process you want to represent, then me or somebody else can come back with an answer.

[agor95]

@Gregory

Thanks I will try to put the idea into words.
Some of it is to get my mind around maths formula.

I trust you have seen my web site?

I am looking at several formulas that together model the movement of the M. Turbine device.

Some are going to be dumb or I know them or are simple.
But I am looking at this from a really different perspective.

Questions like:

Do electric / magnetic fields stretch?
When a magnetic field collapse does it overshoot its start value?
Is inertia a time delay from transition from the electric to magnetic fields?
Proton's inertia does that create a magnetic super conductive current in space?

Lets ignore those

I am just learning and hopefully others will learn along the way.

I found Lagrange formula when using VPython and am impressed how accurate it is at modelling movement.
Using iterative models are so prone to accuracy errors.

So some parts of the formula will be

1. rotational inertia.
2. linear inertia.
3. displacement of a sliding bar due to gravity.
4. displacement of a sliding bar due to ( ok CF).
5. torque effects.

6. restoring force of a elastic spring.

Then combining these together to find a solution to the behaviour of the spring force with respect to length.

The key is understanding the method/maths and bringing members along in that understanding.

Regards

[agor95]

In my pursuit of more maths some of my little grey cells have ran off.

https://en.wikipedia.org/wiki/Double_pendulum

I am thinking a coupled double pendulum with a little CF in the mix could be a direction to go.

I will explain when I come back from this study.

Just treat a sliding rod with a return spring and the same rod swinging
down and around as two coupled pendulums.

[ME]

MoI Beam vs Center beam in Python:
http://www.besslerwheel.com/forum/viewt ... 214#151214