- #1
MostlyHarmless
- 345
- 15
Homework Statement
Starting with the Lorentz transformation for the components of the velocity, derive the transformation for the components of acceleration.
Homework Equations
Lorentz Transformation for position and time :
##x'={\gamma}(x - vt)##
##t'={\gamma}(t - {\frac{vx}{c^2}})##
Resulting transformation by taking ##{\frac{dx'}{dt'}}##
##u'_x={\frac{u_x-v}{1-{\frac{vu_x}{c^2}}}}##
The Attempt at a Solution
Before I go through the trouble of typing out my attempt in LaTex (I'm on my phone), let me make sure I'm going at this right because I think I'm over thinking this and now its all twisted in my head.
Based on what they did to get the velocity transformation, I should be able to just take ##du'_x## and divide by the same ##dt'## used in the velocity transformation? Because it should be CHANGE of velocity over change in time. So ##{\frac{du'_x}{dt'}}## should give me what I want right?EDIT: I've refined my confusion.
Its about how they are getting dx' and dt'.
They are given as:
##dx'= {\gamma}(dx - vdt)##
##dt'={\gamma}(dt - {\frac{vdx}{c^2}})##
I'm not sure what they are differentiating with respect to so I don't know how to treat ##u'_x## as far as differentiation goes. I'm assuming(hoping) that my confusion is a result of the my notions of classical mechanics not being consistent here and not a result of losing my grip on Cal 1 stuff.
Last edited: