Motion in a non-inertial frame

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The discussion focuses on the treatment of total derivatives in Lagrangian mechanics, specifically in a non-inertial frame as noted in Landau's extract. It highlights that total derivatives can be neglected in the equations of motion since they contribute only as boundary terms. The concept of boundary terms is explained through the divergence theorem, which relates volume integrals of total derivatives to surface integrals over boundaries. The conversation emphasizes the mathematical implications of these terms in the context of motion equations. Understanding these principles is crucial for analyzing dynamics in non-inertial frames.
Andrea Vironda
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Hi,
in this Landau's extract i note that the total derivative is neglected in 2 places.
in the first case i think because it's raised twice, but in the second case?
 

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A total derivative in the Lagrangian does not affect the equations of motion as it only contributes with a boundary term.
 
Orodruin said:
a boundary term.
sorry for my english, but what is that?
 
A contribution from the boundary that remains after integration. Think divergence theorem where the integral total derivative ##\nabla\cdot \vec v## is rewritten as a surface integral over the boundary of the original integration volume.
 

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