Lagrangian and Hamiltonian mechanics

In summary: I didn't like "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics) because it is written at a level for theoretical physicists and not for mathematicians. It's a good book, but it's not for me. I like the book by Fowles and Cassiday, or the book by Taylor.Spivak's Mechanics for Mathematicians book is not a book for beginners. It's more oriented towards experts in mathematics.
  • #1
Ahmad Kishki
159
13
Recommend an easy going introduction to lagrangian and hamiltonian mechanics (for self study)
 
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  • #2
Ahmad Kishki said:
Recommend an easy going introduction to lagrangian and hamiltonian mechanics (for self study)
I liked "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics)
 
  • #3
Landau/Lifshits vol. 1 is great to. I'd not call it "easy going" however, but it's very worth to struggle through!
 
  • #4
If you're just looking for an intro, nearly any senior-levle UG text will have what you want. The Marion/Thornton book is good. Fowles/Cassiday is also good. There are MANY to choose from. Go to your local university library (if there is one obviously) and just look through the books collected under "classical mechanics" or "analytical mechanics".
 
  • #6
The first bits of Goldstein's book would probably be very beneficial.
 
  • #8
I liked "Classical Dynamics of Particles and Systems" by Marion and Thornton (advanced undergraduate classical mechanics)

Anything but that, unless you like meaningless formulas and calculations. If you don't like meaningless formulas and calculations, maybe Arnold if you can handle it.
 
  • #9
I second David Tong's notes. They are free after all. homeomorphic's recommendation of Arnold may be premature since you are asking for an "easy-going" introduction (the entire book is written from the perspective of differential geometry).

The book by Marion and Thornton is an established undergraduate classic. So is the book by Fowles and Cassiday, or the book by Taylor. They are suitable for senior-level classical mechanics courses.
 
  • #10
I was recommending Arnold in the long term. For now, I'm just unrecommending Marion and Thornton. Unless, of course, ugly calculations and very little physical insight is your thing.
 
  • #11
According to someone, every textbook is full of ugly calculations and very little physical insight lol. But yes, I understand. Arnold is a scary book. Have you run through it? I just finished the whole of Fowles/Cassiday and will be moving onto Goldstein soonish.
 
  • #12
I think it's reasonably obvious to anyone who has read it that Marion and Thornton are not exactly Feynman when it comes to their physical insight. I have read most of Arnold, but the Appendixes get pretty wild, even for me (there's some good stuff in there if you ever want to understand differential geometry, though). But I have a PhD in math, so Arnold is kind of right up my alley. But I did start reading it in my first year of grad school, so it's not THAT bad. And I could have probably read it a bit earlier than that--as he says in the intro it's closer to a course for theoretical physicists than mathematicians.

One book I'd like to read when I get the chance that might possibly (can't say, since I haven't read it) fit the bill here is Spivak's Mechanics for Mathematicians book.

There's a free preview online.
http://www.math.uga.edu/~shifrin/Spivak_physics.pdf [Broken]

As you can see from the preview, it's not really that math-oriented, although maybe in the later chapters, it is. I haven't read the finished product. Anyway, it looks like Spivak wrote a book that is somewhat similar to one I was thinking about writing. So, I'll have to read it, and if I like it enough, maybe I won't have to write my own, but just refer people to Spivak and Arnold.

Lanczos also has a Classical Mechanics book that's somewhat interesting and a bit lower level.
 
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  • #13
I understand better now what you mean about M/T. Thank you.
 

1. What is the difference between Lagrangian and Hamiltonian mechanics?

Lagrangian and Hamiltonian mechanics are two different approaches to studying the motion of particles and systems. Lagrangian mechanics uses the concept of generalized coordinates and the principle of least action to describe the dynamics of a system, while Hamiltonian mechanics uses generalized coordinates and momenta to describe the system's evolution over time. In other words, Lagrangian mechanics focuses on energy conservation, while Hamiltonian mechanics focuses on momentum conservation.

2. What is the significance of the Lagrangian and Hamiltonian functions in these theories?

The Lagrangian and Hamiltonian functions are central to the equations of motion in their respective theories. They are both derived from the system's potential and kinetic energy and represent the system's total energy. The Lagrangian function is used to derive the equations of motion in Lagrangian mechanics, while the Hamiltonian function is used to derive the equations of motion in Hamiltonian mechanics.

3. Can Lagrangian and Hamiltonian mechanics be applied to all physical systems?

Yes, Lagrangian and Hamiltonian mechanics are general theories that can be applied to any physical system, as long as the system has a well-defined potential energy function. These theories have been successfully applied to a wide range of systems, from simple particles to complex systems like planets and molecules.

4. What is the advantage of using the Lagrangian or Hamiltonian approach over Newtonian mechanics?

One advantage of using Lagrangian or Hamiltonian mechanics is that they provide a more elegant and concise way of describing the motion of a system. They also offer a deeper understanding of the underlying physical principles governing the system's behavior. Additionally, these theories can handle more complex systems that may be difficult to analyze using Newtonian mechanics.

5. Are there any real-life applications of Lagrangian and Hamiltonian mechanics?

Yes, there are many real-life applications of Lagrangian and Hamiltonian mechanics. For example, they are used in the analysis of mechanical systems like pendulums, springs, and rigid bodies. They are also used in the study of celestial mechanics, such as the motion of planets and satellites. Additionally, these theories have applications in quantum mechanics, fluid dynamics, and many other areas of physics and engineering.

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