Too early to learn Lagrangians as a first year?

In summary, Lagrangians are more efficient and easier to use for some types of mechanics problems, and a lack of exposure to calculus will make it difficult to understand Lagrangian mechanics. A student would need to be strong in single variable calculus and begin calculus of several variables in order to use Lagrangian mechanics effectively.
  • #1
-Dragoon-
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7
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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  • #2
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!
 
  • #3
I agree with AlephZero and I would add that some knowledge of calculus is needed
 
  • #4
AlephZero said:
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?

AlephZero said:
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.
 
  • #5
Rap said:
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.
 
  • #6
-Dragoon- said:
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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1. What is a Lagrangian?

A Lagrangian is a mathematical function used in physics to describe the dynamics of a system. It takes into account the positions and velocities of all the particles in the system and helps us understand how they change over time.

2. Why is it considered too early to learn Lagrangians as a first year?

Lagrangians involve advanced mathematical concepts such as calculus, which are typically not introduced until later in a physics curriculum. It is important to have a strong foundation in basic physics principles before attempting to learn about Lagrangians.

3. What are some examples of systems that can be described using Lagrangians?

Some examples include pendulums, simple harmonic oscillators, and celestial bodies such as planets orbiting around a star. Lagrangians can also be used to describe more complex systems like fluid dynamics or quantum mechanics.

4. Are there any benefits to learning Lagrangians as a first year?

While it may be challenging for first-year students, learning Lagrangians can provide a deeper understanding of classical mechanics and pave the way for more advanced topics in physics. It also allows for a more elegant and efficient approach to solving problems compared to traditional methods.

5. What resources are available for students who want to learn Lagrangians as a first year?

There are many online resources, textbooks, and lecture notes available for students to learn about Lagrangians. It is important to consult with a professor or mentor for guidance and clarification on any difficult concepts. Additionally, practicing problems and attending study groups can also help solidify understanding of Lagrangians.

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