Deriving the Hamiltonian of a system

In summary, the task was to derive the Hamiltonian equation in terms of momentum and position (p and r) for a given system with a Lagrangian of L=ř^2/(2w) - wr^2/2. The equation for the Hamiltonian is H=př-L. The solution was attempted by exchanging r with q, however, it was not the correct approach as the Hamiltonian equation was needed, not the Hamiltonian itself. Therefore, the solution needed to start from the Lagrangian equation of motion.
  • #1
middleearthss
13
1

Homework Statement


Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2

Homework Equations


L=ř^2/(2w) - wr^2/2 and H=př-L

The Attempt at a Solution


Notice here ř means first derivative of r. As i haven't learned how to write equations i derives a solution whoch looks correct and took a picture. I am hoping you can see if it is correct and point at mistakes. In the work i exchanged r with q.
Here are the links to 2 photos i took[/B]
http://www.photobox.co.uk/my/photo?album_id=3508111407&photo_id=8712540967#8712540967

http://www.photobox.co.uk/my/photo?album_id=3508111407&photo_id=8712541232#8712541232

 

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  • #2
It says You cannot access this album
 
  • #3
You need hamiltonian equation, not the Hamiltonian. So start from lagrangian equation of motion.
 

What is the Hamiltonian of a system?

The Hamiltonian of a system is a mathematical function that determines the total energy of the system. It takes into account both the kinetic and potential energies of the system.

How is the Hamiltonian derived?

The Hamiltonian is derived from the Lagrangian, which is a function that describes the dynamics of a system. The Hamiltonian is obtained by performing a Legendre transformation on the Lagrangian.

What is the purpose of deriving the Hamiltonian?

Deriving the Hamiltonian allows us to describe the dynamics of a system in terms of its energy, instead of its position and velocity like in the Lagrangian. This can make solving and analyzing the system easier in certain cases.

What are the important properties of the Hamiltonian?

Some important properties of the Hamiltonian include conservation of energy, symplecticity, and invariance under time translations. These properties can provide insight into the behavior of the system.

Are there any limitations to using the Hamiltonian?

While the Hamiltonian is a useful tool for analyzing systems, it does have limitations. It can only be used for systems with conservative forces and it does not take into account dissipative forces. Additionally, it is not applicable to systems with constraints.

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