MEDAL ~ Another way to represent (u_x)' = u_x - v

Question

zzr0ck3r · Answer

what?

adamaero · Answer

$$u'_{x} = u _{x} - v$$
Where v is constant.

adamaero · Answer

How to represent that the other way. With dt (as a function of time or something).

zzr0ck3r · Answer

I have no idea what you are asking

adamaero · Answer

Is it du'/dt = du/dt - v ?

zzr0ck3r · Answer

So the derivative of a function is equal to the function minus some constant?

adamaero · Answer

This is just part of a reading. I'm assuming the notation was switched from using prime to the other way...

adamaero · Answer

I think the prime has nothing to do with derivatives and such

legomyego180 · Answer

The derivative of a constant is 0 so technically the anti-derivative could have a constant C or in this case "v" of any value. Thats why whebn integrating you always tack on a +C

legomyego180 · Answer

For example the derivative of 2x is 2

But the derivative of 2x+3 is also 2.

so the antiderivative of 2 is 2x+C with the C accounting for all constants that can be attached.

adamaero · Answer

@legomyego180 I suppose I really didn't know what I was asking, but it wasn't about integrals. Thanks tho

legomyego180 · Answer

Yea on second glance, it looks like this isnt about what I mentioned. Good luck though

phi · Answer

apparently, they are using "u" to represent velocity
and specifically,
$ u_x $ is the velocity in the x-direction.

phi · Answer

the primes are used to distinguish between two different "reference systems"

phi · Answer

the symbols
$$ \frac{dx}{dt}$$
is from calculus, and represents the change in x (i.e. position in the x direction) divided by the change in time.

phi · Answer

usually we think of dx/dt as one "thing", in particular, as velocity.
similarly,  if we let u= dx/dt  (just renaming)
then du/dt represents acceleration.

irishboy123 · Answer

$\dfrac{du'}{dt} = \dfrac{du}{dt} - v $       ??

yes

evoker · Answer

I believe you are looking at the galilean velocity in a reference frame,  probably leading to the relativistic velocity in a reference frame.  Saying that for instance if you are moving at 40mph  and another car is moving towards you at 30mph then in your reference frame it appears to be moving at 70mph towards you.