Timeline for Deriving the differential equation of simple harmonic motion through energy conservation equation
Current License: CC BY-SA 4.0
10 events
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| Oct 9 at 17:59 | comment | added | User198 | Ok, thanks. Now it is clear. I see it now as a consequence of the Lagrangian and Hamiltonian formalism. | |
| Oct 9 at 17:11 | comment | added | basics | Try to have a look at the edit at the end of the answer, with the relation between Hamilton equations and energy conservation. Let me know if it's clear enough. | |
| Oct 9 at 17:11 | history | edited | basics | CC BY-SA 4.0 |
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| Oct 9 at 17:04 | history | edited | basics | CC BY-SA 4.0 |
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| Oct 9 at 16:55 | comment | added | basics | It's a consequence of the Lagrangian and Hamiltonian formalism. I'm adding an edit to my answer | |
| Oct 9 at 16:55 | history | edited | basics | CC BY-SA 4.0 |
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| Oct 9 at 16:49 | comment | added | User198 | So it seems that for some simple systems (1dof, no dissipation) the equation $\frac{dH}{dt}=0$ is equal to the equation governing the dynamics of that system? Is there a name for that fact or can we just call it a consequence of the Hamilton's formalism? | |
| Oct 9 at 16:48 | comment | added | basics | Sometimes you can get EOMs from conservation principles, when they hold. Usually for 1-dof systems, energy conservation is enough. | |
| Oct 9 at 16:42 | comment | added | User198 | That is all correct. But my question is I used the equation $0 = \frac{dH}{dt}$ and just did the chain rule differentiation and ended up with $( m \ddot q + k q ) =0 $. I did not use the middle portion of your equation $\frac{\partial H}{\partial p} \dot p + \frac{\partial H}{\partial q} \dot q$ i.e. the Hamilton's equations but I rather only did a chain rule for derivative with respect to time. So it seems strange to me that I was able to obtain the same result you did, but without using the Hamilton equations, only by using the chain rule for time derivative. How is that so? | |
| Oct 9 at 16:24 | history | answered | basics | CC BY-SA 4.0 |