Understanding Geodesic Deviation: Solving for Equations (7) to (8)

[Arcon]

Can someone take a look at

http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf

and tell me how they go from Eq. (7) to Eq. (8)? I've tried this and keep getting additional terms.

 

[lethe]

Originally posted by Arcon
Can someone take a look at

http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf

and tell me how they go from Eq. (7) to Eq. (8)? I've tried this and keep getting additional terms.

i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.

 

[Arcon]

Originally posted by lethe
i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.

I fingered it out

One has to drop not only the term &chi*&chi but the term which is the product of &chi and a derivative of &chi. That was what I was missing.

 

[Arcon]

Thank you

I believe that I've fingered it out

One has to drop not only the term χ*χ but the term which is the product of χ and a derivative of χ. That was what I was missing.

Again - thanks for the response

Arcon

 

[Arcon]

Originally posted by lethe
i took a look at it, and did the calculation. i thought it was pretty straightforward. where did you get stuck? what extra terms do you have?

remember that x is a geodesic. so there is a geodesic equation in x, and it therefore vanishes. and remember that χ is very small; drop any term with more than one χ in it.

Seems that this small detail (drop term with χdχdT) has always tripped me up in that derivation. I guess I was just blind to it. But now that I know it then the derivation is simple.

Just to make sure I understood the approximation can you check this for me?

http://www.geocities.com/physics_world/gr/geodesic_deviation.htm

I commented on the terms to drop right after Eq. (14) and right after Eq. (15)

Thanks

I don't know how I missed this before but the equation of geodesic deviation clearly shows that tidal forces are velocity dependant!

Arcon