(adsbygoogle = window.adsbygoogle || []).push({}); 4-velocity --> 4-acceleration?

Hey all, my first post here.

Now, Im trying to derive the 4-acceleration from the 4-velocity by explicitly calculating du/d(tau). So from Hartle we have

u=( gamma, gamma*v)

where gamma=1/Sqrt(1-v^2)

and v is the 3 velocity, taking c=1

So then,

du/d(tau)=( d(gamma)/d(tau), d(gamma*v)/d(tau) )

from the book we have

du/d(tau)=(gamma*(a dot v), gamma*a)

so then we should have

d(gamma)/d(tau)=gamma*(a dot v)

but when i calculate d(gamma)/d(tau) i get....ok im going to show all my steps so people can know what ive done....

d(gamma)/d(tau)=[d(gamma)/dv)]*[dv/dt]*[dt/d(tau)]

=[d(1/(1-v^2)^(1/2))/dv]*[a][gamma]

=[(-1/2)(-2*(v)/(1-v^2)^(3/2)]*[a]*[gamma]

=[ va/(1-v^2)^(3/2)*[1/gamma]

=v*a*gamma^4 != v*a*gamma

does anyone know whats going wrong or what im doing wrong??

Any help would be appreciated, Thanks in advance.

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# 4-velocity -> 4-acceleration?

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