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Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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08-07-2005, 03:28 PM
| | rigid vs. nonrigid transformations
There are at least three special kinds of rigid transformations. These are, not in any order of importance, translation (T), rotation (R), and reflection (M). Using Cartesian coordinate geometry of 2D Euclidean spacetime, the following mappings always hold true.    reflection in the space axis.  reflection in the time axis. The distinction of all rigid transformations is that they do not stretch (dilate), shrink (contract), or twist (curve) the transformed events. Two transformed events do not move closer together or farther apart in spacetime. In other words, events always stay the same distance from each other. Furthermore, the Pythagorean Theorem determines this distance. The mechanics is Newtonian and the spacetime is Galilean. Nonrigid transformations give relativistic mechanics and Minkowskian spacetime. For transformed events involving dilation and contraction refer to Einstein’s special theory of relativity and for the ones involving twisting and curvatures refer to Einstein’s general theory of relativity.  | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48  | |
08-08-2005, 06:19 AM
| | Is there any other "non-main" rigid/non-rigid kind of transformation?
What about division (breaking)? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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08-08-2005, 07:53 PM
| Quote: |
Originally Posted by GUILLE What about division (breaking)? | The divisions of vectors are undefined as far as I know. I'm not sure about tensors divisions. | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
08-08-2005, 09:09 PM
| Quote: |
Originally Posted by AntonioLao The divisions of vectors are undefined as far as I know. I'm not sure about tensors divisions. | A division of something mathematical as a vector I think that can only lead to other vectors (depending on the number of parts resulting).
If not, is it possible that, let's say, if a tensor is devided, then the parts are vectors? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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08-10-2005, 09:55 PM
| | GUILLE,
Vectors have two components, the magnitude and the direction. Although magnitude can be divided, direction cannot. | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
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08-11-2005, 05:42 AM
| Quote: |
Originally Posted by AntonioLao GUILLE,
Vectors have two components, the magnitude and the direction. Although magnitude can be divided, direction cannot. | Can the parts of the magnitude re-unify? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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08-12-2005, 04:44 PM
| Quote: |
Originally Posted by GUILLE Can the parts of the magnitude re-unify? | parts re-unified signify continuity and divided signify quantization. | | | | 2nd degree Black Belt
Join Date: Nov 2006 Posts: 332
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02-25-2007, 08:48 PM
|  Re: rigid vs. nonrigid transformations
Quote:
Originally Posted by AntonioLao  parts re-unified signify continuity and divided signify quantization. | Quite right, what about the process of division, I have been thinking about this fine point for awhile, the process it seems is continuous and the result is defined, but if we can agree to a mathematical process of division, then I think we could define this universally for all particles. It is necesarily discrete and immaterial what process we agree on so long as it is scaleable. | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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02-26-2007, 02:56 PM
| | Re: rigid vs. nonrigid transformations
Quote: |
Originally Posted by theunify but if we can agree to a mathematical process of division | Logarithmically, a process of division becomes a process of subtraction where the dividend is replaced by the minuend and the divisor is replaced by the subtrahend.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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