Classical Mechanics- something bothering me

AI Thread Summary
A Hamiltonian can be constructed from a given Lagrangian under specific conditions, primarily when the Lagrangian is in the standard form of kinetic and potential energy. The relationship does not depend on the potential as long as it is coordinate-dependent and excludes generalized velocities. Degenerate systems may also influence the ability to build a Hamiltonian. The discussion highlights the importance of having the appropriate form of the Lagrangian to facilitate this process. Understanding these conditions is crucial for effectively transitioning between Lagrangian and Hamiltonian mechanics.
Palindrom
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Under what conditions can I "build" a Hamiltonian from a given Lagrangian?
I'm thinking it might have something to do with the potential, but it's not really clear to me what it is the question is.
 
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Palindrom said:
Under what conditions can I "build" a Hamiltonian from a given Lagrangian?
I'm thinking it might have something to do with the potential, but it's not really clear to me what it is the question is.

Any conditions,provided the Lagrangian has the "familiar" form:Kinetic-Potential energy.
It has no connection with the potential,as long it is coordinate dependent only and does not contain "generalized velocities".
Daniel

PS.In the first statement i included the degenerate systems.
 
dextercioby said:
Any conditions,provided the Lagrangian has the "familiar" form:Kinetic-Potential energy.
It has no connection with the potential,as long it is coordinate dependent only and does not contain "generalized velocities".
Daniel

PS.In the first statement i included the degenerate systems.
I think that might be it. Besides, they gave me the kinetical energy, but not the potential, so it's probably it.
Thanks!
 

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