The discussion centers on the conditions necessary to construct a Hamiltonian from a given Lagrangian in classical mechanics. It is established that a Hamiltonian can be built from a Lagrangian as long as the Lagrangian is in the familiar form of kinetic and potential energy. The key requirement is that the Lagrangian must be coordinate-dependent and should not include generalized velocities. This principle applies even in the context of degenerate systems.
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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.
I think that might be it. Besides, they gave me the kinetical energy, but not the potential, so it's probably it.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.