Geometric Algebra

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agor95
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Geometric Algebra

Post by agor95 »

In searching for a mathematical model that is suitable for our needs.

I have looked at

Revision of 101 mathematics
Matrix Algebra in relation to transformations
Partial Differentials
Complex Numbers for rotation on 2d plans
Quaternions Rotation in a 4d plans
Lagrangian Mechanics

And now this Algebra

https://www.youtube.com/watch?v=2hBWCCAiCzQ
https://www.youtube.com/watch?v=tX4H_ctggYo
https://www.youtube.com/watch?v=60z_hpEAtD8
Last edited by agor95 on Sun Aug 27, 2023 12:28 am, edited 2 times in total.
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[ Examples ]

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GeometricAlgebra.png
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Learn Starts Here

Post by agor95 »

'You get out more from a subject than you put in.'

https://geometricalgebratutorial.com/

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Basic Movement [copy]

Post by agor95 »

I admit this is an example from the Ganja Coffee Shop site.

I wanted to build from the ground up. So there is a HTML file zipped up attached.

Your choice by placing this on your Desktop and viewing it in your internet browser - Terrible things will happen - yes you will learn.

You should see a moving scene and dragging with left mouse down will rotate the whole scene.

I am working on several aspects of the code.

What does it mean?
How do I get it to work for me?
How do I mash-up this scripting language with the others I have learned?

Anyway the first question: What are you looking at?

Before you is a volume of space, a box, with two points on the back wall P1 and P2.
A pendulum R and another point moving from P1 to P2. A little pointless even though it's mainly points.
There are two plains p1 and p2 with another plain moving from one plain position to the other.

Also there are two lines l1 and l2 with an other line doing the same thing on the front left wall.

What has this got to do with Bessler?

What I think is possible is the creation of Rigid Body Dynamics models in our browsers.

So all the lovely things we talk about can be presented https://en.wikipedia.org/wiki/Rigid_body_dynamics.

Now were are my headache pills.

P.S. That is Projected Geometric Algebra 3D not Professional Golfers' Association.
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PGA_3D_movements.zip
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[ Hanging ]

Post by agor95 »

I have completed my first read of the material on 'Rigid Body Dynamics'.

The example zipped below is something for you too play with after it stops moving.

You can drag the two top dots around.
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Re: Geometric Algebra

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I enjoyed that. (-:
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Re: Geometric Algebra

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I trust those who used the last demo tried dragging the background as well as the dots?
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Re: Geometric Algebra

Post by Senax »

agor95 wrote: Tue Sep 26, 2023 7:02 pm I trust those who used the last demo tried dragging the background as well as the dots?
I hadn't tried that but I have now.
Fascinating.
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Conformal Geometric Algebra

Post by agor95 »

Hi All

For years I have been trying to find a maths that represents dynamic behaviour of movement
with something better than the current methods. This maths is just that 'something better'.

https://en.wikipedia.org/wiki/Conformal ... ic_algebra

We are involved in the rotation of weights and their movement restricted to radial distances.
Any pivoted mass is restricted to this reality.

That is why I prefer polar coordinates over cartesian.

This algebra describes lines as large loops.

So a straight lines are paths of infinite loops.
As we see a straight horizon from our perspective and from space we see a sphere like object.
Therefore the horizon is a curved loop like the equator.

This algebra increases my chances at presenting the movement with more easy than matrix algebra
,Lagrangian or Hamiltonian mechanics [formula].

The target is a mathematics that does not use conservation of energy as a short cut to describing motion.

Regards
Last edited by agor95 on Mon Oct 16, 2023 10:19 am, edited 2 times in total.
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Geometric Algebra Update

Post by agor95 »

Hi All

Well I am still staring at this subject and glimmers of understanding appear from time to time.
It is still weird and dives into physics beyond by pay grade.

So what is weird about it?

Well you may know about Complex Numbers where you have Real Number added to a weird Imaginary Number.
An example 10 + 5i and the i is the square root of minus 1; It gets worse.

There are Quaternions Number 10 + 5i + 2j + 3k all these are imaginary except the first Real Number.

These get replaced with a new thing which gets even worse.

Regards
Last edited by agor95 on Thu Jan 25, 2024 6:37 pm, edited 3 times in total.
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