Wrote

Have you seen this plot
https://en.wikipedia.org/wiki/Pendulum_(mechanics)

Wrote

Another notable thing about this example is that I would like someone to please explain to me how the hell the Viacheslav plugin manages to handle l'(t) within the equations, because I honestly didn't expect it.

Wrote

Wrote

Another notable thing about this example is that I would like someone to please explain to me how the hell the Viacheslav plugin manages to handle l'(t) within the equations, because I honestly didn't expect it.

I can add that I did not expect the solver to work adequately. The numerical solver in Mathcad is much more complex. It allows solving mixed systems. Valery poses problems that can't be solved in the same way, since current tools have significant limitations.

Wrote

Wrote

In this version you can specify the initial force in the spring. The initial conditions for x and y are adjusted appropriately. ...

A comparison between Martin's solution and that given by the equations of motion obtained from the Lagrangian. Spoiler: both give the same result.

I'd like to point out how incredibly complicated this problem actually is, and what a series of brilliant implementations Martin makes. For example, where the hell does he get the time derivative of the force on an elastic bar when he is given only the length of the bar as a function of the force? Obviously, it is not enough to apply the theorem of the derivative of the inverse function, but you also have to have a deep knowledge of the mechanics of the system to remember something called tangential stiffness, and although it uses k to represent it, we forgive it because It's German and they are well known to use their own abbreviations. Well, actually I don't know what letter to use, because I don't remember ever using that magnitude for any practical purpose, but in Spanish literature it is quite common to use k for its inverse, which is the constant that appears in Hooke's law. Or at least I think so, because the existence of elastic bodies is actually a complication, they should all be rigid better.

Another notable thing about this example is that I would like someone to please explain to me how the hell the Viacheslav plugin manages to handle l'(t) within the equations, because I honestly didn't expect it.

Federpendel-NL - Lagrangian.sm (257 KiB) downloaded 78 time(s).

Best regards.
Alvaro.

Wrote

Hi Martin. I guess that your issue is that the end angle is 460 degrees, not 100. You can also see this post.

Best regards.
Alvaro.