Timeline for When produces the double pendulum a strange attractor figure, indicating chaos, and how does it look like in 3d?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2020 at 9:47 | comment | added | Wrzlprmft | Let us continue this discussion in chat. | |
| Aug 21, 2020 at 9:35 | comment | added | Deschele Schilder | What do you mean by an attractor? I think we might have different thoughts about that. | |
| Aug 21, 2020 at 8:48 | comment | added | Wrzlprmft | The dissipation of energy is not required for the dynamics of a system to be chaotic. – Sure, but I did not claim that. What I said was that the dissipation of energy is required for a system to have an attractor. Conservative systems do not have attractors (as per Liouville’s theorem, see here). | |
| Aug 21, 2020 at 7:51 | comment | added | Deschele Schilder | Well, in the first place I'm not talking about a DP where both arms stay aligned, as suggested in the answer (this would indeed be equivalent to a one-armed pendulum. For sure the dynamics of the DP are chaotic. Even when the friction in the total system can be set to zero. The dissipation of energy is not required for the dynamics of a system to be chaotic. So what do you mean? I can't see this in your answer. | |
| Aug 21, 2020 at 7:41 | comment | added | Wrzlprmft | @descheleschilder: I already try to explain this in my answer. Can you be more specific as to what you fail to understand. | |
| Aug 21, 2020 at 7:39 | comment | added | Deschele Schilder | Okay. But why you need friction to make the dynamics happen or to let the system have a strange attractor? | |
| Aug 21, 2020 at 7:27 | comment | added | Wrzlprmft | @descheleschilder: You need friction to make that specific dynamics (full circle with maximum radius) happen. You also need friction (or some other dissipation of energy) to have an attractor. | |
| Aug 21, 2020 at 6:46 | comment | added | Deschele Schilder | To make such a dynamics happen, you would, e.g., have to have some friction within the double pendulum’s joint and nowhere else. Why do have to have friction to make the dynamics of the DP happen? | |
| Apr 13, 2017 at 12:40 | history | edited | CommunityBot |
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| Feb 5, 2016 at 18:07 | comment | added | Wrzlprmft | the path that the end of the pendulum traces out, never ends in the same situation – That’s not entirely correct: There are initial conditions that provide periodic solutions. — But isn´t the end of the pendulum tracing out a figure that after a long time wil start taking a shape […], no matter what the initial conditions are? – Yes, it will describe some shape, but this is not related to an attractor, simply because it does not attract. Also, this shape depends on the initial conditons. For example, it will be fundamentally different for chaotic and periodic dynamics. | |
| Feb 5, 2016 at 17:11 | comment | added | Deschele Schilder | I understand that if you take many different initial situations (all with the same initial potential energy (for simplicity lets say it´s less than the maximum potential energy possible) for the double pendulum), the path that the end of the pendulum traces out, never ends in the same situation (unlike a ball in a sink that always ends up in the sink, no matter the initial conditions of the ball. But isn´t the end of the pendulum tracing out a figure that after a long time wil start taking a shape, like the butterfly figure (order in chaos), no matter what the initial conditions are? | |
| Feb 4, 2016 at 16:50 | history | answered | Wrzlprmft | CC BY-SA 3.0 |