Relationship between Lagrangian and Energy

Thread starter theneedtoknow
Start date Feb 10, 2011
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Energy Lagrangian Relationship

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For time-independent potentials, the energy relationship is expressed as E = sum(Vi * partial dL/dVi) - L. When dealing with time-dependent potentials, the relationship modifies to total dE/dt = - partial dL/dt. This adjustment reflects the dynamics introduced by the time dependence of the potentials. A request for textbooks that derive this relationship was made, noting that "Mechanics" by Landau and Lifgarbagez does not cover it. The discussion emphasizes the need for resources that address energy and Lagrangian dynamics in the context of time-dependent systems.

Feb 10, 2011

theneedtoknow

I know that, for time-independent potentials, we have E=sum (Vi*partial dL/dVi) - L
What if one or more of the potentials are time-dependent?
Is the relationship between energy and the lagrangian then "total dE/dt = - partial dL/dt "?

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Feb 11, 2011

dextercioby

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Yes.

Feb 11, 2011

theneedtoknow

Thank you! Would you happen to know of any textbooks where this is derived? I have the Landau and Lifgarbagez "Mechanics" one and they do not do so.

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