/sci/ - Science & Math

[Anonymous No.4306509]

So, does anyone here think they've got what it takes to derive a general formula for an n-pendulum?

Pic related, it's a 3-pendulum

[Anonymous No.4306519]

The Lagrangian for it? I guess you could

[Anonymous No.4306520]

Isn't a two-pendulum only numerically soluble?

[Anonymous No.4306528]

It can be done one of two ways.

1. Approximate the pendulums as harmonic oscilators and solve the system using a lagrangian

2. Define pend(t) to be the solution to the 1 pendulum case, construct a lagranian for the unapproximated system and express your solution in terms of pend(t)

otherwise no closed form solution exists

[Anonymous No.4306531]

>>4306509
>>4306519
It is pretty trivial to produce the lagrangian, any sophmore physics major should be able to do that shit.

[Anonymous No.4306533]

oh God... this is even worse than an n spring...

[Anonymous No.4306536]

>>4306519
from the general lagrangian you could get the general equations of motion
>>4306520
yes, you can use some techniques to get an approximate analytic solution as well
I don't think you can get an analytic solution that is anywhere near accurate for the triple pendulum though

The reason im interested is that I want to see what happens as we take the limit as the length of each rod goes to zero and as n goes to infinity

[Anonymous No.4306539]

>>4306531

I'm a sophomore physics major and I don't know what a Lagrangian is. Also I'm a pretty high performing student at a solid school.

[Anonymous No.4306543]

What the fuck is a lagrangian?

I read the wikipedia, but I didn't understand.

[Anonymous No.4306548]

>>4306536

I imagine you're thinking about the equation of motion of a chain. You're action principle now looks like the integral of the action over all the infinitessimal points in the system.

This one can be solved exactly I believe.

[Anonymous No.4306551]

>>4306539
>>4306543

[Anonymous No.4306554]

>>4306543

A formula that stores all information about a mechanical system. In classical mechanics its kinetic-potential energy

[Anonymous No.4306562]

>>4306539
What the fuck is a sophomore?

It better mean babby's first physics, otherwise it's unexcusable.

[Anonymous No.4306566]

>>4306548
that's what im thinking, yes

>>4306543
the lagrangian is the thing whos integral is minimised by the equations of motion
from the lagrangian you derive momentum conservation from parallel transporting the whole system, angular momentum by rotating it and energy by chaging the time

the lagrangian is more fundamental than f=ma

imo it should be taught before f=ma, people shouldn't even touch physics before they have the mathematical sophistocation to handle variational calculus

[Anonymous No.4306568]

>>4306562
I believe the principle of stationary action doesn't crop up until 3rd year at uni in most places
Incorporating classical field theory into an action principle could very well be masters degree level material

[Anonymous No.4306571]

>>4306539
>>4306543
The Lagrangian is a way to represent a physical system. Every fucking thing in the universe can be written as a lagrangian.

Once you have a lagrangian for your system, there are known rules to generate the "equations of motion" and all the basic physics information. The rules to generate the equations of motion, and physics, from a lagrangian are pretty fucking general. So it is very very easy to go from a lagrangian to equations of motion (and often visa verse).

1) generate a lagrangian for your system
2) getting the equations of motion, and physical constants from your lagrangian
3) PROFFIT!

[Anonymous No.4306575]

>>4306543
there's also a hamiltonian with it's own set of equations
the hamiltonian equations of motion are two first order differential equations, the lagrangian equations of motion are single second order differential equations
they are entirely equivelant though

[Anonymous No.4306577]

>>4306539
>I'm a sophomore physics major and I don't know what a Lagrangian is.
>Also I'm a pretty high performing student at a solid school.

[Anonymous No.4306579]

I felt like I was reborn when I learned analytical mechanics and realised I wouldnt have to deal with forces almost anymore

[None !SteveAnJ7c No.4306580]

>>4306568
>oh god my brain

[Anonymous No.4306582]

>>4306554
>>4306566
>>4306571
>>4306575
Alright, thanks guys.
Where can I learn more?

[None !SteveAnJ7c No.4306584]

>>4306580
>>4306539
that was for you, not the person i linked ... my bad, your idiocy actually blinded my temporarily, causing me to misslink.

[Anonymous No.4306587]

>>4306582
Leonard Susskind's lecture series on classical mechanics on youtube is a decent introduction to what it is
Once you've watched them you can go on to Landau and Lifshitz - A Course of Theoretical Physics - Volume 1 - Classical Mechanics

[Anonymous No.4306590]

>>4306587
Thanks again.

[Anonymous No.4306591]

>>4306579
fucking this
fuck newtons 2nd law shit
fuck systems with friction as well

[Anonymous No.4306594]

>>4306582
http://en.wikipedia.org/wiki/Double_pendulum#Lagrangian

The Lagrangian for the triple pendulum is very easy figure out from that of the double pendulum. You just add the extra coordinate _3, to every term. The center of mass term will have to be modified as well.

Maybe you should start off with the double pendlum, since they already give you the lagragin, and derive the equations of motion for it. This will give you a feel for the power of the lagragin formalism has over the shitty newton method (rarely used by actual physicists).

[Anonymous No.4306601]

how do you derive equations of motion from a Lagrangian?

[Anonymous No.4306605]

>>4306594
I need something in a form where I can take the limit as n goes to infinity though
I can manually do whatever n I want but I can't seem to find a general formula where you can just plug an n in

[Anonymous No.4306608]

>>4306601
you minimise it's integral over time

[Anonymous No.4306615]

>>4306605
Wat? why?
The pendlum, double pendlum, and triple pendulm are all typically done using lagragian mechanics. It is the simplest way to do that shit.

[Anonymous No.4306620]

>>4306615
yeah, nvm, I thought you were replying to someone you weren't replying to
I thought you were replying to me, the OP
Also, I intend on using a lagrangian, but one with a form that contains an n so I can take it up to infinity

[Anonymous No.4306623]

>>4306601
>>4306601
It depends on the type of lagraian (classical mech, quantum mech, etc)

Classical mech is the simplest case.
http://en.wikipedia.org/wiki/Lagrangian_mechanics

Goto the section part that says: Euler-Lagrange equations.

[Anonymous No.4306628]

>>4306620
It is very easy to generate an "n" pendlum Lagragian analogously to how you derive a three pendulum from a two pendulum >>4306594.

I can't do everything fucking thing for you kid. Start thinking!

[Anonymous No.4306630]

Web resource: Calculus of variations


http://www.math.vt.edu/people/jaburns/class_home/Lecture_notes.pdf

[Anonymous No.4306635]

>>4306620
>>4306620
>mfw I generated an n-pendulum lagrangian in my head by just looking at the form of the 2-pendulum lagrangian

This shit is super-trivial kid. If it is not evident to you, them maybe you are just over your head.

[Anonymous No.4306651]

>>4306571
>The Lagrangian is a way to represent a physical system. Every fucking thing in the universe can be written as a lagrangian.
Well that assumption is a meta statement. It only works as long as it works.

[Anonymous No.4306657]

>>4306651
>It only works as long as it works.

[Anonymous No.4306660]

>>4306651

Can you contrive a statement which is not, by this definition, a meta-statement?

No assertion can be true unless it is true. Even this one.

[Anonymous No.4306663]

>>4306651
Any system can be represented as a Lagrangian, just like every word can be written down. It is tautology as fuck, deal with it.

[Anonymous No.4306667]

>>4306657
>>4306660
Oh jesus, my point is that one shouldn't under- but also not overestimate the Lagrangian formalism. Its a good tool and people force their theories into it or extend it, but it's not true that you can use it for alle systems.

[Anonymous No.4306668]

>>4306651

[Anonymous No.4306678]

>>4306667
But it is true that you can use it for all systems.

[Anonymous No.4306684]

>>4306667

[Lion !FvAwVR8cv6 No.4306698]

Just because you can write out the Lagrangian doesn't make it easy to solve the equations of motion.

In fact, for an n-pendulum it becomes nearly impossible unless you make the assumption that the angle of oscillations are small and you can take the taylor series expansion for sin and cos of the angles. Of course this approximation becomes less true with more pendulums because the angles increase. So good luck.

[Anonymous No.4306709]

>>4306698
>Just because you can write out the Lagrangian doesn't make it easy to solve the equations of motion

Implying anyone said anything like that. They said it was easy to "find the equations of motion", WHICH IT FUCKING IS. No one here mentioned anything about solving that shit.

[Anonymous No.4306710]

>>4306668
>>4306678
>>4306684
Retard mind.

And no, there are systems, like some dissipative systems, for which you can't write down a lagrangian.

[Anonymous No.4306711]

>>4306698
>implying anyone said anything like that

[Anonymous No.4306721]

>>4306711
>>4306709

One post is einough to express your despair dude.

[Anonymous No.4306725]

>>4306710
You can write down lagragians for dissipative systems dipshit.

[Anonymous No.4306728]

>>4306710
>mfw I add a time dependancy

[Lion !FvAwVR8cv6 No.4306731]

>>4306709
>>4306711
From the OP
>So, does anyone here think they've got what it takes to derive a general formula for an n-pendulum?
>implying the Lagrangian is of any interest or has any meaning on it's own.

[Anonymous No.4306732]

>>4306710
Why are there so many dumb people on /sci/ right now?

[Anonymous No.4306734]

mfw any engineer who has taken a dynamics class can solve these easily.
You just find the equations of motion about each point relative to the last point.

[Anonymous No.4306738]

>>4306731
Yes, but no one wants to do all the work for you. Do your own fucking homework kid.

\thread

[Anonymous No.4306743]

>>4306734
>engineer
>do maths or physics

Nope

[Lion !FvAwVR8cv6 No.4306744]

>>4306738

[Anonymous No.4306745]

>>4306732
why do you feel the need to insult people in a discussion?

[Anonymous No.4306751]

How do you find a lagrangian for a disipative system? say a particle acted upon by air friction

[Anonymous No.4306758]

>>4306751
It isn't that hard to incorperate "friction" into a lagrangian. Here is an easy example.

http://www.wepapers.com/Papers/3729/10-_Friction_in_Lagrange%27s_Equations

You should really learn how to look up shit for yourself on google.

[Anonymous No.4306767]

>>4306745
Calling someone dumb, when they are acting dumb IS NOT A FUCKING INSULT. Now stop being fucking retarded!

[Anonymous No.4306777]

>>4306767
yes it is?

If someone comes into your house and kills your family, and you call him asshole, that's still an insult.