Timeline for Hamiltonian for a free particle in polar coordinates
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2021 at 13:54 | comment | added | Cosmas Zachos | For free motion, all projections of the acceleration vanish, as you illustrated. Liboff's "nvolves accelerations in the r and 𝜃 components of motion" is misleading. You now have the right idea here. You might repeat your exercise, with the same type result. | |
| Jan 25, 2021 at 2:16 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 25, 2021 at 1:36 | vote | accept | Lost | ||
| Jan 25, 2021 at 1:12 | answer | added | Cosmas Zachos | timeline score: 4 | |
| Jan 25, 2021 at 0:49 | history | edited | Lost | CC BY-SA 4.0 |
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| Jan 25, 2021 at 0:47 | comment | added | Lost | @CosmasZachos Sorry. I do not understand. Where did I blow up the sign? $a_r$ comes zero. That I have calculated and it is correct. | |
| Jan 25, 2021 at 0:43 | comment | added | Lost | @Rumplestillskin Please also check the edit I made. Also, do you mean that having a non-zero $\dot p_r$ doesn't imply a $a_r=0$ since $\dot p_r=m\ddot r$ while $a_r$ has a term of $r \dot \theta^2$ as well? I think this was the mistake I was making. But then how does Liboff conclude from non -zero expressions of $p_\theta$ that there is an azimuthal acceleration? | |
| Jan 25, 2021 at 0:34 | history | edited | Lost | CC BY-SA 4.0 |
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| Jan 25, 2021 at 0:19 | comment | added | Lost | @Rumplestillskin Since, $\dot p$ is non-zero, then radial force and acceleration is non-zero. This is what I reasoned. What is wrong with it? | |
| Jan 24, 2021 at 23:53 | comment | added | Cosmas Zachos | Did you blow a sign? $ma_r= \dot{p}_r-\dot{p}_\theta^2/mr^3=0$ by your EOM. | |
| Jan 24, 2021 at 22:25 | comment | added | Rumplestillskin | Can you explain why that implies $a_r \neq 0$? It might help to see things a bit clearer if you integrate your second equation $a_\theta$ wrt time and substitute $\dot{\theta}$ into your radial equation. | |
| Jan 24, 2021 at 19:44 | history | asked | Lost | CC BY-SA 4.0 |