Timeline for Hamiltonian for multidimensional dissipative system
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2021 at 16:20 | comment | added | Eli | This should be your force law $\begin{align*} &\mathbf{F}_\beta= \left[ \begin {array}{c} {\frac {\beta\, \left( x{\dot{x}}+y{\dot{y}} \right) x}{{x}^{2}+{y}^{2}}}\\\\{\frac {\beta\, \left( x{\dot{x}}+y{\dot{y}} \right) y}{{x}^{2}+{y}^{2}}}\end {array} \right] \end{align*}$ | |
| Feb 26, 2021 at 16:15 | comment | added | Eli | first obtain the equations of motion with $~T=... -x\,f_x+y\,fy~$ put the force law in the equations of motion, not in the kinetic energy | |
| Feb 26, 2021 at 16:08 | comment | added | Eli | you can put inthe equations for $~f_x~,f_y~$ any force law . but I don't think that your radial damper force is correct. the radial damper force is: $~\beta\,\dot{r}\,\hat{\mathbf{e}}_r~$ with $~r=\sqrt{x^2+y^2}~$ and $~\mathbf e_r=x\mathbf e_x+y\,\mathbf e_y~$ | |
| Feb 26, 2021 at 16:05 | comment | added | user281659 | I understand that, if $T=\frac{1}{2}(\dot{x}^2+\dot{y}^2},$ then when I want to get my EOM from E-L eq., $f_x$ and $f_y$ should be $$ x \cdot f_x = x \cdot \beta\dot{x}\sqrt{\dot{x}^2+\dot{y}^2}, \\ y \cdot f_y = y \cdot \beta\dot{y}\sqrt{\dot{x}^2+\dot{y}^2}. $$ But, is it other way to get this or not? | |
| Feb 26, 2021 at 15:03 | comment | added | user281659 | Now I noticed that I wrote wrong EOM... It should be without second square $$ \ddot{x}(t) + \beta \dot{x}(t)\sqrt{\dot{x}^2(t)+\dot{y}^2(t)} = 0, \\ \ddot{y}(t) + \beta \dot{y}(t)\sqrt{\dot{x}^2(t)+\dot{y}^2(t)} = 0. $$ How much does it change formula for $f_x$ and $f_y$? And can you give me some hints how to calculate this Lagrangian. And thank you very much for help! | |
| Feb 25, 2021 at 9:03 | history | edited | Eli | CC BY-SA 4.0 |
added 217 characters in body
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| Feb 25, 2021 at 8:58 | history | answered | Eli | CC BY-SA 4.0 |