- #1

Robin04

- 260

- 16

## Homework Statement

There's the following problem (the task is to construct the Lagrangian) in the first Landau (part a):

My problem is that I don't understand what did we omit exactly and why.

## Homework Equations

## The Attempt at a Solution

I did the calculation myself (even checked with Mathematica) and got the following result:

##L= \frac{1}{2}ml^2\dot{\phi^2} + mla\gamma sin(\phi - \gamma t)\dot{\phi} +mgl cos(\phi) + \frac{1}{2}ma^2\gamma^2##

The solution says that we omit the terms that depend explicitly only on time, but there's no such term here. They omitted the last term for sure, but that's a constant, it has no time-dependence.

Also, the time derivative of that cosine term:

##\frac{d}{dt}[mla\gamma cos(\phi - \gamma t)]=...=-mla\gamma sin(\phi - \gamma t)\dot{\phi}+mla\gamma^2 sin(\phi-\gamma t)##

Landau seems to only leave the first term here, but why? The 'total derivative' (as he mentions) should mean both terms together, what makes the first one negligable?