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August 27th, 2017, 07:23 AM   #1
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As you can see, in article of “The Change Depends on the Direction of the Motion: Generating All Directions in 3D Space” posted on link:

Executive Methods for Problem Solution: The Change Depends on the Direction of the Motion: Generating All Directions in 3D Space

Only one particle (or one point) was moving on a circle or a sphere to produce some formulas. But, if we increase the number of the particles (points) by two, three, four, five and more in which these points are symmetrically and simultaneously travelling on a circle or a sphere, we will have a symmetric group action. In fact, the results of the particles ’motions make some matrices n*n as operators and some matrices m*n as transformation matrices where all these matrices as symmetric groups actions have very interesting properties. In real world, we can see the applications of these symmetric groups actions every day. For example, an airscrew, screw propeller, ceiling fan, turbine, rotary machines, rotary heat exchangers, helicopter blade, vibrations of a circular drum and also in quantum physics, Hamiltonian operator for Schrodinger’s equation, in chemistry the methane molecule (CH4) is a symmetric group action by four points (particles), all are the ideas inferred from the great theory in mathematics which is the Group Theory.
Even though these operators and transformations have many properties, my focus in this article is only to generate the fields (orbits) and its magnitude. Thus, the purpose of this article is firstly to make many operators and transformations matrices for two, three, four and five points which are rotating and secondly to find out one the most important properties which is the fields (orbits) and its magnitude.

You can review full article posted on below link:

Executive Methods for Problem Solution: The Change Depends on the Direction of the Motion: The Symmetric Group Action (1)

Last edited by skipjack; August 27th, 2017 at 07:34 AM.
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