• SaintRodriguez
In summary: I'm thinking more like an intro to strings or quantum mechanics class.I don't believe this is beyond Classical Mechanics. A chain of balls falling freely from a height would be a good example.
SaintRodriguez
I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.

The most magical part of Classical Mechanics has to be the Lagrangian formulation. In Susskind's book on Classical Mechanics, he derives Newton's third law, F=ma from the Lagrangian formulation.

https://en.wikipedia.org/wiki/Lagrangian_mechanics

It's magical because by simply describing the potential and kinetic energies of a system, just scalar quantities, one can then determine the motion of the system.

Another topic would be the Hamiltonian formulation which became really useful in Quantum Mechanics.

https://en.wikipedia.org/wiki/Hamiltonian_mechanics

Lastly, an interesting problem would be cool:
- like the three-body problem as there are several exact solutions now. (https://en.wikipedia.org/wiki/Three-body_problem)

- the brachistochrone problem (https://en.wikipedia.org/wiki/Brachistochrone_curve)

- the problem of an object falling from a great height takes 9/11 of the time to fall the first half the distance. (Marion Chapter 5 problem #5 pg 205)

I'm sure there are youtube videos on these topics for further research.

PhDeezNutz and SaintRodriguez
SaintRodriguez said:
I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.
First, welcome to PF!

Classical Mechanics is a large subject. Is this an essay for school? If so, what level of school? Have you had much mechanics and physics in school? What are you interested in?

malawi_glenn
I am in Classical mechanics course at university. I have seen Lagrangian and Hamiltonian formalism, Routh formalism, Legendre transfomation, etc.

bob012345
jedishrfu said:
The most magical part of Classical Mechanics has to be the Lagrangian formulation. In Susskind's book on Classical Mechanics, he derives Newton's third law, F=ma from the Lagrangian formulation.

https://en.wikipedia.org/wiki/Lagrangian_mechanics

It's magical because by simply describing the potential and kinetic energies of a system, just scalar quantities, one can then determine the motion of the system.

Another topic would be the Hamiltonian formulation which became really useful in Quantum Mechanics.

https://en.wikipedia.org/wiki/Hamiltonian_mechanics

Lastly, an interesting problem would be cool:
- like the three-body problem as there are several exact solutions now. (https://en.wikipedia.org/wiki/Three-body_problem)

- the brachistochrone problem (https://en.wikipedia.org/wiki/Brachistochrone_curve)

- the problem of an object falling from a great height takes 9/11 of the time to fall the first half the distance. (Marion Chapter 5 problem #5 pg 205)

I'm sure there are youtube videos on these topics for further research.
Thank you very much!

jedishrfu said:
It's magical because by simply describing the potential and kinetic energies of a system, just scalar quantities, one can then determine the motion of the system.

Another topic would be the Hamiltonian formulation which became really useful in Quantum Mechanics.
… and I would argue it is at least as beautiful as Lagrangian mechanics. Just symplectic geometry and a single energy function.

PhDeezNutz, vanhees71 and jedishrfu
As mentioned, would be very helpful to know the scope of the essay.
Is it supposed to be 4 pages or 20 pages for instances?
Who is the intended audience, the teacher or fellow students?

Here is a suggestion for a topic, useage of lagrangians in special relativity and then discuss the nambo-goto action (the action for a bosonic string on a world sheet)

malawi_glenn said:
Here is a suggestion for a topic, useage of lagrangians in special relativity and then discuss the nambo-goto action (the action for a bosonic string on a world sheet)

Is this beyond Classical Mechanics ie bosonic strings? It looks really cool though. I found this writeup on wikipedia:

https://en.wikipedia.org/wiki/Nambu–Goto_action

and this Khan Academy video on Lagrangians:

jedishrfu said:
Is this beyond Classical Mechanics ie bosonic strings? It looks really cool though. I found this writeup on wikipedia
As long as it is not quantum it is classical imo.

More suggestions for OP:
- from particles to fields, scalar field theory
- explain the euler disc
- surfaces of soap bubbles

jedishrfu and vanhees71
More ideas

Self falling chain fountain

Explaining two balls attached via rubber band rotation

vanhees71
malawi_glenn said:
jedishrfu said:
Is this beyond Classical Mechanics ie bosonic strings? It looks really cool though. I found this writeup on wikipedia:

https://en.wikipedia.org/wiki/Nambu–Goto_action
Of course I may just be out of date since Strings weren't things when I was studying classical mechanics (in the Dark Ages before we even knew the universe was accelerating) but this seems way beyond what one would typically cover in a such a course.

bob012345 said:
this seems way beyond what one would typically cover in a such a course.
Well depends on the scope of the essay. Is it to apply concepts from the course to a own choosen topic or something else? We still don't know? It would be very helpful to know the scope and the instructions for this project.

You can write down the action of and study the behaviour of non-quantum mechanical relativistic strings with just basic analytical mechanics. I had a friend who did his entire bachelor thesis on this. Did not touch quantization at all.

It is when you start to quantize it that you open the pandoras box with virasoro algebras, extra compactified dimensions, string charges,... and so on.

Another nice topic for essey work is of course Noethers Theorem.

jedishrfu

vanhees71

## 1. What is classical mechanics?

Classical mechanics is a branch of physics that deals with the motion and behavior of macroscopic objects, such as planets, cars, and baseballs. It is based on the laws of motion and gravitation developed by Sir Isaac Newton in the 17th century.

## 2. Why is classical mechanics important?

Classical mechanics is important because it provides the foundation for understanding the motion of objects in our everyday lives. It also serves as the basis for more advanced fields such as quantum mechanics and relativity.

## 3. What are some potential topics for an essay about classical mechanics?

Some potential topics for an essay about classical mechanics could include the history of classical mechanics, the laws of motion and how they apply to real-world situations, the role of classical mechanics in modern physics, or the impact of classical mechanics on technology and engineering.

## 4. How can I choose a specific topic for my essay about classical mechanics?

To choose a specific topic for your essay about classical mechanics, you can start by brainstorming ideas that interest you and relate to the subject. You can also research current developments and controversies in the field to find a topic that is both relevant and engaging.

## 5. What resources can I use to research my essay on classical mechanics?

There are many resources available for researching an essay on classical mechanics, including books, academic journals, websites, and scientific databases. You can also consult with a physics professor or visit your local library for additional resources and guidance.

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