Timeline for Does decomposition of motion rely on Pythagorean theorem?
Current License: CC BY-SA 3.0
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| Sep 11, 2015 at 15:30 | history | edited | JJM Driessen | CC BY-SA 3.0 |
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| Sep 11, 2015 at 14:20 | comment | added | CuriousOne | @YiFei: The appearance is accidental because you are using an orthogonal coordinate system. The same formula, when expressed in non-orthogonal coordinates would not look like the Pythagorean one. | |
| Sep 11, 2015 at 13:12 | comment | added | YiFei | In a word, is the square in velocity in KE expression just coincide with Pythagorean theorem? | |
| Sep 11, 2015 at 11:48 | comment | added | JJM Driessen | I don't understand your question. I just used the Pythagorean theorem as mathematical tool. You could rotate your frame with any angle, compute the new velocity components and use those to calculate the energy. You'll see that the energy is exactly the same. You don't "need" Pythagoras. | |
| Sep 11, 2015 at 11:41 | comment | added | YiFei | So the problem comes when you are saying $\dot{x}_2 = \sqrt{\dot{x}_1^2 + \dot{y}_2^2}$ which tacitly used the Pythagorean theorem and so they're coincidentally consistent | |
| Sep 11, 2015 at 11:33 | history | answered | JJM Driessen | CC BY-SA 3.0 |