Talk:Double pendulum

message: This article states that "a double pendulum is a pendulum with another pendulum attached to its end", with link to pendulum. Looking at "pendulum", I see that it consists of two masses connected by two massless rods. Here, however, pendulum consists of two massive rods. I think, by double pendulum, people usually think about the case with two massless rods and two masses, see most of the references given at the end of the article. Understanding that this case might also be called double pendulum, not even mentioning the more usual meaning is not satisfactory.
Cumi 13:41, 24 March 2006 (UTC)
replies: text: On WP we are obliged to use standard terminology, and not invent our own. However there are other ways (parenthetical explanations), to avoid forcing the reader to follow links for the definition of the terms. --catslash (talk) 15:39, 9 March 2013 (UTC)
replies: text: Creating knowledge is forbidden on Wikipedia... Maybe there are good reasons for that, but it annoys me a lot :-( . Bete spatio-temporelle 152.77.24.34 (talk) 16:38, 23 March 2013 (UTC)
thread_title:  What is a double pendulum? 

message: wiki readers:
What units are used for angles < θ1, θ2; CHAOTIC MOTION,  Double pendulum >    
in the x-y graph where:
x axis: angle θ1 is plotted for -3 to +3   (left to right)  
y axis: angle θ2 is plotted for -3 to +3   (top  to bottom)
the graph is described as:
< Graph of the time for the pendulum to flip over as a 
< function of initial conditions
thanks for the information!
veritus 16:15, 24 February 2007 (UTC)
thread_title:  chaos  

message: Ok what is the period of a double pendulum with a small angle?
anyone?
hello?  —Preceding unsigned comment added by 128.226.162.108 (talk) 18:57, 20 February 2008 (UTC)
thread_title:  the period of a double pendulum with a small angle 

message: Hello,
As a dance and movement experiment, I am interested in constructing a human double pendulum - that is, with humans as bobs or masses. I want to hang the first person in a climbing harness by a rope suspended from a truss. Then I want to hang the second person from the first person. Any suggestions?
Heather @ Helium Aerial Dance
www.heliummm.com
64.131.241.205 (talk) 17:06, 25 February 2008 (UTC)
thread_title:  Human Double Pendulum? 

message: Could we include an animation of a double pendulum? I am interested in how it moves and how the bottom one swings in relation to the top one.  203.134.124.36 (talk) 04:11, 6 August 2008 (UTC)
thread_title:  Animated Picture 

message: 1) I assume that "to flip over" means to have the bar l2 vercital (θ2 = π).
2) The mentioned quantities 10\sqrt{g/\ell\ }, 100\sqrt{g/\ell\  }, etc. are not times but inverse of times. Maybe 10\sqrt{\ell\ /g  }, 100\sqrt{\ell\ /g  }, etc.?  —Preceding unsigned comment added by 81.208.31.210 (talk) 12:07, 13 September 2008 (UTC)
replies: text: Someone should verify the first assumption and clarify in the article. It is not apparent. LokiClock (talk) 17:24, 22 December 2009 (UTC)
thread_title:  Chaotic motion: time elapsed until the double pendulum "flips over" 

message: Of the two bodies the first pendulum is certainly rotating about its end. The second pendulum is only rotating about its end when the when the first one is stationary. When the first pendulum is moving, then the second is rotating about some point in space which is harder to locate.
The quantity wanted to write the Lagrangian is the total kinetic energy of the two the pendulums. We could write the KE of the first pendulum as
:\mathrm{KE}_{1} = \frac{1}{2} I_{end} \dot{\theta_{1}}^{2}
where (as you stated)
:I_{end} = \frac{1}{3} m l^{2}
Alternatively we could write this energy (and have written it) as the sum of the kinetic energy due to the motion of the centre of mass of the pendulum, plus the kinetic energy due to rotation about this centre of mass (see the kinetic energy article). That is
:\mathrm{KE}_{1} = \frac{1}{2} m v_{1}^{2} + \frac{1}{2} I_{cm} \dot{\theta_{1}}^{2}
where 
:v_{1} = \frac{l}{2} \dot{\theta_{1}}
(the centre of mass being halfway along the rod, and hence at a radius of l/2 from the pivot), and where
:I_{cm} = \frac{1}{12} m l^{2}
Either way we get
:\mathrm{KE}_{1} = \frac{1}{6} m l^{2} \dot{\theta_{1}}^{2}
Both ways are correct. The first way (using the moment of inertia about the end) is simpler, and therefore the preferred way to do it for a single pendulum.
The motion of the second pendulum is more complicated, it's both swinging and moving as whole. To use the first method we'd have to work out the centre of rotation for the combined motion, and then the moment of inertia about that point. This seems difficult, so we use the second method.
Of course we could use one method for the first pendulum and another method for the second, and write
:\mathrm{KE}_\mathrm{total} = \frac{1}{2} I_{end} \dot{\theta_{1}}^{2} + \frac{1}{2} m v_{2}^{2} + \frac{1}{2} I_{cm} \dot{\theta_{2}}^{2}
but somebody has decided that it's neater to write
:\mathrm{KE}_\mathrm{total} = \frac{1}{2} m v_{1}^{2} + \frac{1}{2} I_{cm} \dot{\theta_{1}}^{2} + \frac{1}{2} m v_{2}^{2} + \frac{1}{2} I_{cm} \dot{\theta_{2}}^{2}
which comes to the same thing.
Sorry that was a bit long - hope it made sense! --catslash (talk) 00:21, 20 September 2008 (UTC)
replies: text: Thank you for this clarification, it was really helpful. User:Nillerdk (talk) 14:12, 22 January 2009 (UTC)
thread_title:  Why we use the inertia about the centre of mass, not about the end 

message: It seemed to be talking about a clock with two pendulums hanging down, that are swinging precisely in anti-phase. That's not what this article is about, the pendulums are hung end-to-end in this article. The maths and everything else would be completely different. Because it was unreferenced and clearly distinct, I removed it.- Wolfkeeper 17:08, 1 April 2010 (UTC)
thread_title:  removed horology definition 

message: Why do you include the "rotational energy" in the Lagrangian? Kinetic energy in terms of x1,y1 and y1,y2 is enough to specify the Lagrangian => transform to theta1 and theta2. Seems to be an error, unless I'm missing something. Someone should look into that and fix it. Danski14(talk) 20:10, 12 September 2010 (UTC)
replies: text: I see the description above, but that is a very confusing way to  do it. I would recommend changing to the normal way of solving this problem.Danski14(talk) 20:12, 12 September 2010 (UTC)
replies: text: You may have overlooked the fact that the analysis and description relate to compound pendulums of equal length, while the first diagram shows simple pendulums of unequal length. For simple pendulums there need be no rotational energy terms since they are point masses. The article history shows that the diagram was removed in April for this reason - but it was then replaced. There is probably less work in replacing the first diagram, rather than rest of the article. --catslash (talk) 21:02, 12 September 2010 (UTC)

text: If you are not in a hurry, I could make an appropriate SVG diagram. --catslash (talk) 21:12, 12 September 2010 (UTC)

text: Done: the diagram now exactly matches the text of the analysis. It should make more sense now. --catslash (talk) 01:25, 22 September 2010 (UTC)
thread_title: Error in Lagrangian

message: Most of the content of this article appear to be copied directly from this paper:
http://tabitha.phas.ubc.ca/wiki/images/archive/3/37/20080811183757!Double.pdf  — Preceding unsigned comment added by 24.56.46.24 (talk) 17:16, 4 January 2014 (UTC)
replies: text: The paper is dated 11 Aug 2008, so if anything the article includes material copied from this article (check the Jun 2008 version of this article).  Another possibility is that the author of the paper and the relevant contributor to this article is the one and the same person. --catslash (talk) 21:59, 4 January 2014 (UTC)

text: In fact a contributor to this article gives on his user-page a real name and affiliation identical to that of the author of the paper (caution: read WP:OUTING before mentioning real names).  --catslash (talk) 22:29, 4 January 2014 (UTC)

text: That makes sense then. I don't think the author would have copied from here, since the fractal image's origin isn't really explained here, but it is in the paper.  — Preceding unsigned comment added by 24.56.46.24 (talk) 02:41, 5 January 2014 (UTC)
thread_title:  Article citation 

message: In a practical, real life example, the double pendulum can be seen inthe very dangerous design of  the double trailer trucks in highways.  Frequently, their chaotic behaviour has produced large accidents.  If Highway authorities could understand some mathematics and physics, their use would be banned immediately! Their dynamic behaviour is called "Jackknifing" (there is a Wikipedia page on this).  Recently, a double tank trailer went out of control near Mexico City, the tanks were carrying Liquified Petroleum Gas or LPG, causing a huge series of explosions and fire, killing several families that lived at the side of the highway.  — Preceding unsigned comment added by 192.100.180.21 (talk) 17:08, 23 July 2014 (UTC)
thread_title:  Practical example of Double-Pendulum in real life 

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thread_title:  External links modified 

message: I am working on a course for robotics, and I am copying material to the following:
https://en.wikiversity.org/wiki/Robotic_Mechanics_and_Modeling/Dynamics
Admazzeo (talk) 14:18, 3 March 2020 (UTC)
thread_title:  Copying Material to Wikiversity 

message: One can also have more than two pendulums. In some way this counts also for strings and elsatic levers.  — Preceding unsigned comment added by 92.209.199.111 (talk) 07:39, 26 March 2021 (UTC)
thread_title:  There are also multipendula! 

message: Swinging Stick redirects here, but it is not a double pendulum, nor does it function on a similar idea as a pendulum as it is actually electrically driven with an electromagnet and a pair of sensors to prevent it from being over-driven. — al-Shimoni (talk) 02:17, 27 July 2023 (UTC)
thread_title:  Swinging Stick redirects here incorrectly 

message: Currently the proposed solution mixes Lagrangian and Hamiltonian methods.  Since the title of the section is Lagrangian I think the Lagrange equations should be used, not the Hamiltonian ones.  Thus, there should be no use of the generalized momentum.  The dynamic variables should only be (\theta_i, \dot{\theta_i},\ddot{\theta_i})_{i\in\{1,2\}}.--Grondilu (talk) 03:36, 4 November 2023 (UTC)
thread_title:  Mixing Lagrangian and Hamiltonian methods 

message: The redirect Swinging sticks has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  Utopes (talk / cont) 05:17, 25 April 2024 (UTC)
thread_title:  "[[:Swinging sticks]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The redirect Swinging stick has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  Utopes (talk / cont) 05:18, 25 April 2024 (UTC)
thread_title:  "[[:Swinging stick]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]