- #1

tissuejkl

- 8

- 0

## Homework Statement

## L (v^2 + 2 \pmb{v} \cdot \pmb{ \epsilon } ~ + \pmb{ \epsilon} ^2)##, where ## \pmb{\epsilon}## is infinitesimal and ##\pmb{v}## is a constant vector (## v^2 ## here means ## \pmb{v} \cdot \pmb{v} ## ), must be expanded in terms of powers of ## \pmb{\epsilon} ## to give $$ L(v^2)+\frac{\partial L}{\partial v^2}\ 2 \ \pmb{v} \cdot \pmb{\epsilon} $$

where terms above the first order have been neglected.

## Homework Equations

## The Attempt at a Solution

I thought about using the Taylor expansion to expand L in terms of ## \pmb{\epsilon} ##, but that seems to work only if ##\epsilon ## were a scalar, so I'm not quite sure what to use to expand L.