Can't get Hamilton and Lagrangian stuff

[finchie_88]

I'm really confused when using Hamilton and lagrangian equations, and have read loads of documents on it, but its not getting any clearer, I was hoping someone might be able to help me.
Thanks in advance...

 

[nbo10]

What don't you get? Try to explain to us what you understand. And we'll intercede when you veer off course.

 

[finchie_88]

I understand the principle of what is happening, its just that I can't come up with the equations myself unless the situation is really simple (like a object falling), anything more complex than that and I get confused. Also, I can't see the point, all it is is another way of writing Newtonian mechanics, what is the benefit of it?

 

[ZapperZ]

I understand the principle of what is happening, its just that I can't come up with the equations myself unless the situation is really simple (like a object falling), anything more complex than that and I get confused. Also, I can't see the point, all it is is another way of writing Newtonian mechanics, what is the benefit of it?

1. Newtonian mechanics deal with VECTORS, as in forces. Lagrangian/Hamiltonian deal with scalars, as in energy. You have ONE less thing to worry about using the latter approach.

2. Because of #1, there are more instances where it is easier to write the Lagrangian/Hamiltonian than to write the Newtonian differential equation of motion. The fact that you are only seeing the introduction to both types of mechanics using simple examples doesn't tell you how well the Lagrangian/Hamiltonian approach is more useful. Wait till you have to deal with more complicated situations.

Zz.

 

[robphy]

Also, I can't see the point, all it is is another way of writing Newtonian mechanics, what is the benefit of it?

more benefits

• much easier to solve the "roller coaster on a frictionless track" problem... with Newton, you'll have to start by drawing a different Free-Body diagram at each point along the track;
• "conserved quantities" and "symmetries" are more easily handled.. and exploited;
• freedom in choosing "[generalized] coordinates" to simplify the mathematics;
• associated with the "Principle of Stationary Action" (a.k.a. Least Action), which can be used to formulate many theories [optics, electromagnetism, gravitation, other classical field theories]
• used as a route to Schrödinger and Heisenberg quantum mechanics

When dealing with problems, a good first step is really trying to identify the "degrees of freedom" (i.e., the configuration space) of the system. This suggests a possible set of "generalized coordinates".
Get a hold of the Schaum's outlines on Lagrangian Mechanics.
Flip through http://alamos.math.arizona.edu/~rychlik/557-dir/mechanics/ and http://mitpress.mit.edu/SICM/