Please help me pick a topic for an essay about classical mechanics

[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.

 

[jedishrfu]

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.

 

[bob012345]

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?

 

[SaintRodriguez]

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

 

[SaintRodriguez]

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!

 

[Orodruin]

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.

 

[malawi_glenn]

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)

 

[jedishrfu]

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:

 

[malawi_glenn]

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]

Also the Feynman pie plate or the motion of tops or the collest one the motion of the frisbee

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

There's a thesis by Sarah Hummel on the motion and biomechanics of the frisbee that is quite cool

https://morleyfielddgc.files.wordpress.com/2009/04/hummelthesis.pdf

 

[malawi_glenn]

More ideas

Self falling chain fountain

Explaining two balls attached via rubber band rotation

 

[bob012345]

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.

 

[malawi_glenn]

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]

The movement of a slinky.