Timeline for Is there any fundamental reason why acceleration is a linear function of external forces?
Current License: CC BY-SA 4.0
11 events
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| Jun 28, 2021 at 7:06 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @MattThompson It is not the linearity of the vector sum. I have edited the first part of my aswer to add clarification on such an issue. | |
| Jun 28, 2021 at 7:04 | history | edited | GiorgioP-DoomsdayClockIsAt-90 | CC BY-SA 4.0 |
Edited the first part of the answer to add clarity and generality.
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| Jun 28, 2021 at 4:54 | comment | added | Matt Thompson | Presumably 'linearity' here refers to the formal mathematical definition of the term, whereby components can be added and subtracted (your pair-wise linearity). It is in this sense that Fourier transforms are 'linear operations', although they're clearly not the linear-as-in-straight-line definition we all heard in high school. | |
| Jun 27, 2021 at 19:09 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @Soleil Every discussion without formulae would be inconclusive. Please, state what you mean by linearity and it will be possible to analyze the situation. | |
| Jun 27, 2021 at 18:42 | comment | added | Soleil | Pair-wise additivity is the consequence of linearity, it's not one {or,instead of} the other. | |
| Jun 27, 2021 at 16:47 | comment | added | RBarryYoung | Pair-wise additivity is one of the features of linear functions/operators/systems. Linearity is the appropriate mathematical term so long as it's clear that it's referring to it's interaction with other instances of the same type (rather than it's polynomial order). | |
| Jun 27, 2021 at 12:03 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @EricDuminil That's the reason I started saying that linearity is not the right name for that property. | |
| Jun 27, 2021 at 12:03 | comment | added | GiorgioP-DoomsdayClockIsAt-90 | @EricDuminil Look at the example in the second paragraph of the original question and at the example with polarizable bodies. In the first case, there are two forces that add and are individually the same in the presence or in the absence of the other. In my example, the final force is again a sum of forces, but it is not the sum of the forces in the two separate situations. That's the reason for using a term different from linear. Forces are vectors and their sum is a bilinear operator. However, in general, it is not true that each force contribution depends only on the state of 2 bodies. | |
| Jun 27, 2021 at 11:02 | comment | added | Eric Duminil | I don't get the difference between pair-wise additivity and linearity. By varying F_ij, you can prove that the effect of 0 force is 0, and the effect of n times the same force is n times the effect of the force. How is that not linearity? | |
| Jun 27, 2021 at 7:45 | history | edited | GiorgioP-DoomsdayClockIsAt-90 | CC BY-SA 4.0 |
added 2 characters in body
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| Jun 27, 2021 at 5:33 | history | answered | GiorgioP-DoomsdayClockIsAt-90 | CC BY-SA 4.0 |