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May
1 |
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comment |
Is there a fundamental misunderstanding here or have I made an algebraic slip? @JasonDeVito : Also it is now ${\dot{u}^2\over 1-u^2}=1$ not simply $\dot{u}=1$ |
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May
1 |
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Is there a fundamental misunderstanding here or have I made an algebraic slip? @JasonDeVito : No probs, note that in the original coordinates, that curve is just $a=u, b=0$. ${d\over dt} ({1\over 1-u^2}\dot{u})={1\over 2}({\partial \over \partial u}({1\over 1-u^2})\dot{u}^2)$ |
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May
1 |
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awarded | Teacher |
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May
1 |
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comment |
Is there a fundamental misunderstanding here or have I made an algebraic slip? Ok, apparently I cannot accept the answer within 2 days... |
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Apr
30 |
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comment |
Is there a fundamental misunderstanding here or have I made an algebraic slip? @JasonDeVito: I have added an answer, as per requested. |
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Apr
30 |
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answered | Is there a fundamental misunderstanding here or have I made an algebraic slip? |
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Apr
30 |
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Is there a fundamental misunderstanding here or have I made an algebraic slip? @FernandoMartin: But I have to wait a further 3 hours since it says that I have too few "reputation points" so I can't post an answer within 8 hours of my asking the question... |
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Apr
30 |
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revised |
Is there a fundamental misunderstanding here or have I made an algebraic slip? added 285 characters in body |
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Apr
30 |
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revised |
Is there a fundamental misunderstanding here or have I made an algebraic slip? added 3 characters in body |
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Apr
30 |
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revised |
Is there a fundamental misunderstanding here or have I made an algebraic slip? added 392 characters in body |
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Apr
30 |
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Is there a fundamental misunderstanding here or have I made an algebraic slip? @JasonDeVito: thanks for commenting! en.wikipedia.org/wiki/… offers a bit of info. But generally, for a Riemannian metric of the form $Edu^2+2Fdudv+Gdv^2$ and a geodesic $g(t)=(a(t),b(t))$, the Euler Lagrange equations are ${d\over dt} (E\dot{a}+F\dot{b})={1\over 2} (E_u\dot{a}^2+2F_u\dot{a}\dot{b}+G_u\dot{b}^2)$ and ${d\over dt} (F\dot{a}+G\dot{b})={1\over 2} (E_v\dot{a}^2+2F_v\dot{a}\dot{b}+G_v\dot{b}^2)$ |
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Apr
30 |
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comment |
Is there a fundamental misunderstanding here or have I made an algebraic slip? Anyone, please? |
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Apr
30 |
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awarded | Editor |
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Apr
30 |
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revised |
Is there a fundamental misunderstanding here or have I made an algebraic slip? added 16 characters in body |
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Apr
30 |
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awarded | Student |
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Apr
30 |
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asked | Is there a fundamental misunderstanding here or have I made an algebraic slip? |
