# Lagrangian dynamics

## Homework Equations

The last part of this question is an example of this result:

## The Attempt at a Solution

Here is the solution

I think L' is missing a term: If we take the Earth as your frame of reference.(i.e. You are stationary, watching the movement of the railway carriage).Then there should be an extra term for the KE of pendulum,due to horizontal movement of the carriage. (see below, the y dot term corresponds to v of the carriage)

Why is it not involved in L' ?

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Orodruin
Staff Emeritus
Homework Helper
Gold Member
Your constraint equation is ##\dot y = v(t)##. This implies that the term you are referring to only depends on t and therefore is a total derivative (and hence irrelevant for the equations of motion).

Your constraint equation is ##\dot y = v(t)##. This implies that the term you are referring to only depends on t and therefore is a total derivative (and hence irrelevant for the equations of motion).
Sorry, could you explain it in more detail? I couldn't get it

Orodruin
Staff Emeritus
$$\frac{\mu v(t)^2}{2}.$$