Timeline for Why not a $(q,\dot{q})$ space in Lagrangian Mechanics?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2020 at 5:33 | comment | added | Himanshu | Hamiltonian developed his mechanics in 1833 while Lagrange's mechanics was developed in 1788. So at that time, we don't about canonical transformation and the benefits of using $(q,p)$. So why choose configuration space instead of $(q,\dot{q})$. | |
| Nov 9, 2020 at 5:29 | comment | added | Himanshu | By independent means, I can independently specify the initial conditions. | |
| Nov 9, 2020 at 5:14 | comment | added | ZeroTheHero | I’m not sure I understand what you mean by “both are independent”. Of course Lagrangian mech. is in some sense precursor to Hamilton mech and in LMech you do use $(q,\dot q)$, but the formalism is less powerful because it does not allow for canonical transformations that can mix $q$ and $p$ and all these other things you miss out on. | |
| Nov 9, 2020 at 5:06 | comment | added | Himanshu | For a second , Can you just leave $(q,p)$? Suppose it's not constructed, Lagrange had taken configuration space instead of $(q,\dot{q})$. What's the reason of this? I mean if both are independent then obvious choice should be later. | |
| Nov 9, 2020 at 4:57 | history | answered | ZeroTheHero | CC BY-SA 4.0 |