Motion in a non-inertial frame

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Discussion Overview

The discussion revolves around the treatment of total derivatives in the context of Lagrangian mechanics, specifically in non-inertial frames. Participants explore the implications of neglecting total derivatives in equations of motion and seek clarification on the concept of boundary terms.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes that total derivatives are neglected in two instances in a Landau extract, questioning the reasoning behind the second case.
  • Another participant asserts that a total derivative in the Lagrangian does not impact the equations of motion, as it contributes only a boundary term.
  • A participant expresses confusion about the term "boundary term," prompting a request for clarification.
  • A later reply explains that a boundary term is a contribution that remains after integration, referencing the divergence theorem and the relationship between total derivatives and surface integrals.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasoning for neglecting the total derivative in the second case, and there is ongoing clarification regarding the concept of boundary terms.

Contextual Notes

The discussion includes assumptions about the treatment of total derivatives and boundary terms without fully resolving the implications or providing definitive definitions.

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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