Deriving the Hamiltonian of a system

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SUMMARY

The discussion focuses on deriving the Hamiltonian equation for a system with a given Lagrangian, L = ř²/(2w) - wr²/2. The relationship between the Hamiltonian (H) and the Lagrangian (L) is established through the equation H = př - L. Participants emphasize the importance of starting from the Lagrangian equation of motion to correctly formulate the Hamiltonian, clarifying that the Hamiltonian equation itself is needed rather than the Hamiltonian function.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with Hamiltonian formalism
  • Knowledge of calculus, particularly derivatives
  • Ability to interpret physical equations and symbols
NEXT STEPS
  • Study the derivation of Hamiltonian mechanics from Lagrangian mechanics
  • Learn about the role of momentum (p) and position (r) in Hamiltonian equations
  • Explore examples of Hamiltonian systems in classical mechanics
  • Review the mathematical techniques for manipulating derivatives in physics equations
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Physics students, educators, and researchers interested in classical mechanics, particularly those focusing on Lagrangian and Hamiltonian formulations.

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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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You need hamiltonian equation, not the Hamiltonian. So start from lagrangian equation of motion.
 

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