# Trigonometric equation (Lagrange) for the double pendulum [closed]

I want to model a fishing rod and received a suggestion. I therefore try to follow the mathematics (Lagrange) of the double pendulum. I do not understand how to proceed in the step that Wikipedia calls "Substituting the coordinates above and rearranging the equation gives ...". What I get is totally wrong. Thanks

17/6 EDIT: This question has been marked as "on hold". I therefore rephrase it like this:

In the computations of the Lagrange for the double pendulum, I do not understand how to obtain this equation from the preceeding equations.

(The question has been solved by the answer below.)

• I just edited and rephrased the question. While I did that, it got closed! Well, anyway it is solved. – ycc_swe Jun 17 '14 at 15:39

## 1 Answer

It finally worked out. I had to construct the derivatives in a sketch. (They were wrong in my previous attempt.) I am sure there is a mathematical way of finding them, but I don't know that one. (OK. the derivative of sine is cosine, but it is more to it than that.)

Anyway. If you add several more segments to the pendulum (and then add plate springs), the equations will become very complex, in my opinion.

Any further suggestions how to model a fishing rod (in 2D) using a series of rod segments connected by plate springs are appreciated, either using this approach (Lagrange, suggesting ideas how to realize the computations) or other approach. Here is the simulation of the pendulum.

• I think in your first attempted you have not been using the chain rule of differentiation, i.e. $\mathrm{d}/\mathrm{d}t\, \sin(\theta(t)) = \dot{\theta}\cos(\theta(t))$, not $\cos(\theta(t))$. – AlexE Jun 11 '14 at 11:15
• Chain rule. Spot on! Thanks AlexE for helping me brush up on the basics. But just connecting a few more segments to the model gives equations that are highly time consuming (but I believe straight forward?) to set up and solve. I must see if there are any methods for constructing and solving them by computer. -- I see that you typed the theta-dot character. Must learn about typing math symbols. (In my computer now I only know of Word 2003 and Windows character map. I am not sure they are the easiest.) – ycc_swe Jun 12 '14 at 3:23