How to model a fishing rod (or a rope)?

I wish to model a fishing rod (or a rope) by joining short segments. (The segments may have equal (short) length but each segment should be assigned its own individual mass.) One segment will influence the next by the torque between the segments. For the time being the joints can be regarded as plate springs (torque proportional to bending angle (a or alfa), individual k for each joint).

When I apply torque to the first segment (the "handle"), the torque will spread to the rest of the segments.

The problem is that I do not understand how to compute the movements that will occur at segment one (with mass m1) and the following segments, when I apply torque T1 to segment one (during time dt).

https://www.dropbox.com/s/ze7g6dzrzzd6757/DSC_0113.JPG

I am a (retired) medical doctor with interest in biomechanics, so please use only basic physical terminology. (I wish to migrate the model to biomechanical use. I have written computer programs for models before, so hopefully I can manage that part if I just get the motion equations straight.)

• Thank you John Rennie. As you can see I am new here, so I must please ask: Should I repeat the question in the other forum or will it be moved "automatically"?
– cvr
Jun 5, 2014 at 9:23
• If you're in a hurry for an answer I would delete this question and ask a new question in CompSciSE. I would guess a moderator will be along in a while to move the question, but I'm not sure how long it will take.
– John Rennie
Jun 5, 2014 at 9:38
• I leave it here for a while first, to see if any one replies. Thanks for your suggestion.
– cvr
Jun 5, 2014 at 9:42
• Are you sure you want torque (springs) rather than a simpler "chain-link" model? A fishing rod has a lot of elasticity, so it may make sense there, but ropes/lines in general do not. Jun 5, 2014 at 11:59
• may be this will help if you want to do the pendulum approach derivation: 12000.org/my_notes/double_pendulum/main.html Jun 20, 2014 at 5:10

To solve this problem as you have described it, you need to set up a simple system of ordinary differential equations. For each segment in your "fishing rod" you just need to use conservation of linear and angular momentum ($F=ma$ and $\tau = \frac{dL}{dt}$). Each segment will experience forces and torques from its neighbors. There are many ways to formulate this. And many techniques to solve the resulting system of ODEs.

As a starting point, I would suggest attacking a simpler problem that will give you an idea of what's required: a double pendulum. There are many online demonstrations that solve the double pendulum problem including a detailed discussion of the math here, a Flash implementation here, a javascript version here, and a MATLAB version here. Also, some implementations place masses only at the joints while others have the mass distributed evenly along the segments so you might focus on the one you prefer.

Once you understand the double pendulum problem, it can be very easily extended to any number of segments. Adding a force at a given segment just means adding an additional force term to the acceleration equation for that segment and is very easy to achieve. The last step for your problem would be to include torques via conservation of angular momentum. I suggest implementing everything you need up to that point and then come back and ask more specific questions about implementing the torques if you need help once you're there.

• Thank you DougLipinski for a very clear reply. I understand the reply and I can follow the mathematics of the Wikipedia article on the double pendulum. Studying the double pendulum seems to be a good approach for me to get a grasp on how to compute what is moving "between the time frames" of the simulation (the ODEs). --- For me it is still a complex problem and I may have to come back soon for more advice. Any kind of further comments appreciated. Thanks.
– cvr
Jun 5, 2014 at 15:47
• Hmmm... this now reminds me of a partly unsolved problem: why do dry stalks of spaghetti break into 3 pieces when bent? Turns out there are travelling shock waves. Should be some good articles via Google on that. Jun 5, 2014 at 15:50
• To add to CarlWitthoft. I have also heard (but not verified) that pole vaulters can suffer fractures in carpal bones (wrist) if the pole breaks during a jump. Presumably also due to shock waves.
– cvr
Jun 5, 2014 at 16:07
• @ycc_swe Glad to help. If you get stuck, come back and ask more questions. People here are very eager to help, especially if you show equal effort and eagerness on your side. Jun 5, 2014 at 20:11
• Thanks. I appreciate. Also good fun for me to look into. I assume the Hooke's spring constants will go into a new term forming the potential energy in the Lagrange (comparing to the double pendulum). The gravity potential energy term will have to go at first, the fishing rod will be for outer space. Much new interesting stuff for me to try to grasp. (But how the derivation should be generalized to n segments looks a little rough on me now. Will probably start with just two spring loaded segments.)
– cvr
Jun 6, 2014 at 4:52

Just to point out to a great free Open Source software used exactly for the purpose of modeling of a multibody system, just like your fishing rod. It's called MBDyn, and I've used it to model the dynamics of multicomponent airfoils. There is ample documentation available, and also slides that describe the physics. See for instance slide 25 of this presentation, the mutually connected deformable elements correspond exactly to the fishing rod.

I would suggest that you go through the tutorials and join the mailing list for questions. I've seen a presentation of prof. Masarati where he showed how a large part of the dynamical system of an entire helicopter (blades, rotor transmission, the whole deal) was modeled and analyzed using MBDyn, so I am fairly sure that the people on the list will be able to guide you with your model. This way, you won't have to build a framework just for yourself, that is later maybe stiff when it comes to modifications and extensions.

• Thanks, very useful. I signed up for the mailing list now. I might get further using ready made software. I must just learn more about it. Is it possible to input variable forces etc? -- There is also the Finite Elements Method. I don't know yet if Multi body system or Finite Elements would be the best software for me to use?
– cvr
Jun 19, 2014 at 4:07
• Glad to be of help. I have only used rigid bodies, but elastic bodies can be used and they are modeled with FEM in MBDyn. Jun 19, 2014 at 8:22