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Too early to learn Lagrangians as a first year?

by -Dragoon-
Tags: early, lagrangians, learn
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-Dragoon-
#1
Feb1-12, 09:35 PM
P: 292
I've heard that using Lagrangians to solve mechanics problems is much more efficient and easier than using Newton's laws. In your opinion, is it too early for a student to learn lagrangians for a first year due to a lack of exposure of the mathematics required?
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AlephZero
#2
Feb2-12, 09:23 AM
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Well, if you pick up a science book at random with the title "Introduction to XYZ", there's no way of telling from the title whether it's meant for a bright 12 year old kid, or a final-year grad student just starting an advanced topic. So what you can understand "in the first year" depends very much on what you know already.

But I would qualify your statement by saying
1. Lagrangians are more efficient and easier than Newton's laws for some types of problem, and
2. Unless you have a good understanding of how to use Newton's laws, Lagrangian mechanics will probably seem more like magic than science - and magic that is done wrong usually has bad consequences!
Rap
#3
Feb2-12, 09:31 AM
P: 789
I agree with AlephZero and I would add that some knowledge of calculus is needed

-Dragoon-
#4
Feb2-12, 07:55 PM
P: 292
Too early to learn Lagrangians as a first year?

Quote Quote by AlephZero View Post
Well, if you pick up a science book at random with the title "Introduction to XYZ", there's no way of telling from the title whether it's meant for a bright 12 year old kid, or a final-year grad student just starting an advanced topic. So what you can understand "in the first year" depends very much on what you know already.
I know, that is why I've been looking for text that introduce Lagrangians but only assume that the reader is strong in single variable calculus and is only beginning calculus of several variables. A professor I talked to who is teaching third year classical mechanics at my school recommended I use Introduction to classical mechanis with problems and solutions by D. Morin and its chapter on Lagrangians as an introduction, as it is a first year Harvard text. Any text you would suggest that are similar to it?

Quote Quote by AlephZero View Post
But I would qualify your statement by saying
1. Lagrangians are more efficient and easier than Newton's laws for some types of problem, and
2. Unless you have a good understanding of how to use Newton's laws, Lagrangian mechanics will probably seem more like magic than science - and magic that is done wrong usually has bad consequences!
The main reason I am interested in learning Lagrangians is to have another useful tool to solving mechanics problems. I do feel I understand Newton's laws at an elementary level, but there were some very complex problems that took 2 pages to work out that I feel could have been done much quicker if I knew how to use Lagrangians.
-Dragoon-
#5
Feb2-12, 07:59 PM
P: 292
Quote Quote by Rap View Post
I agree with AlephZero and I would add that some knowledge of calculus is needed
Single variable or many variables? In my few attempts at trying to read advanced analytical mechanics texts, I have seen mostly partial derivatives when introducing the concept of the Lagrangian.
Rap
#6
Feb2-12, 08:47 PM
P: 789
Quote Quote by -Dragoon- View Post
Single variable or many variables? In my few attempts at trying to read advanced analytical mechanics texts, I have seen mostly partial derivatives when introducing the concept of the Lagrangian.
Yes, you need to understand partial derivatives, but if you understand simple derivatives, its not a big jump. Lagrangian dynamics (and its close relative, Hamiltonian dynamics) is very deep physics, but the math is not terribly difficult. What is difficult is understanding the meaning and significance of the terms in the equation, and finding the Lagrangian (or Hamiltonian) of a system. The way I learned it was to take simple problems and solve them both ways. The more problems you solve this way, the better you will understand Lagrangian (and Hamiltonian) dynamics.

Check out the Wikipedia page at http://en.wikipedia.org/wiki/Lagrangian

If you feel like you are ready to tackle the whole idea, check out http://en.wikipedia.org/wiki/Hamiltonian_mechanics


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