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# Motivation

Attempting a mechanics problem from Landau I get a different answer. I wrote up my solution to see if I can spot either where I went wrong, or demonstrate the error, and then posted it to physicsforums. I wasn’t wrong, but the text wasn’t either. Here’s the complete result.

# Guts

## Question: Pendulum with support moving in circle

section 1 problem 3a of [1] is to calculate the Lagrangian of a

pendulum where the point of support is moving in a circle (figure and full text for problem in this google books reference)

## Answer

The coordinates of the mass are

or in coordinates

The velocity is

and in the square

For the potential our height above the minimum is

In the potential the total derivative can be dropped, as can all the constant terms, leaving

so by the above the Lagrangian should be (after also dropping the constant term

This is almost the stated value in the text

We have what appears to be an innocent looking typo (text putting in a instead of a ), but the subsequent text also didn’t make sense. That referred to the omission of the total derivative , which isn’t even a term that I have in my result.

In the physicsforum response it was cleverly pointed out by Dickfore that 1.7 can be recast into a total derivative

which resolves the connundrum!

# References

[1] LD Landau and EM Lifshitz. *Mechanics, vol. 1*. 1976.