- #1

Saladsamurai

- 3,019

- 6

## Homework Statement

## Homework Equations

Chain Rule

## The Attempt at a Solution

So we have that [itex]f = f(x,t)[/itex] as well as the transformations [itex]x = x' + Vt'[/itex] and [itex] t = t'[/itex]

By the chain rule:

[tex]\frac{\partial{f}}{\partial{t'}} =

\frac{\partial{f}}{\partial{x}}\frac{\partial{x}}{\partial{t'}} +

\frac{\partial{f}}{\partial{t}}\frac{\partial{t}}{\partial{t'}}

[/tex]

[tex]\Rightarrow

\frac{\partial{f}}{\partial{t'}} =

\frac{\partial{f}}{\partial{x}} *

\left [ \frac{\partial{x}}{\partial{t'}}+V+t'\frac{\partial{V}}{\partial{t'}}\right ]

+ \frac{\partial{f}}{\partial{t}}\frac{\partial{t'}}{\partial{t'}}

[/tex]

[tex]\Rightarrow

\frac{\partial{f}}{\partial{t'}} =

\frac{\partial{f}}{\partial{x}} *

\left [ \frac{\partial{x}}{\partial{t'}}+V+t'\frac{\partial{V}}{\partial{t'}}\right ]

+ \frac{\partial{f}}{\partial{t}}

[/tex]

Not really sure what the next move is? Is the above equation in its simplest form? Or can I do something more with it?

Also, I don't really see how I go about transforming [itex]\rho'[/itex] and [itex]v'[/itex] into the

*x-t*coordinates?

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