# Contravariant components and spherical component of acceleration

1. Jan 1, 2012

### world line

Hello
i know how to derive the components of acceleration in other coordinates like spherical
start here :
http://up.iranblog.com/images/0mbwuclckbu51bxt8jfa.jpg
and at last we have :
http://up.iranblog.com/images/geotowiaxdya2s6ewxk.jpg

also , i know that acceleration is a contravariant vector :
http://up.iranblog.com/images/fl7eosq4cieeoc1kroy.gif
but when i use that definition i don't derive the above result for acceleration !?
and reach to a different results
so what is my mistake ?

2. Jan 1, 2012

### George Jones

Staff Emeritus
It is very difficult to find your mistake without seeing what you have done.

3. Jan 1, 2012

### world line

for example :
http://up.iranblog.com/images/90cm6lacnzsoxcju1v9.png
that it is different with the corresponding spherical component

if we use the covaraint unit vector the problem will be solved !
and both solution will have unique result
is it correct ?

4. Jan 1, 2012

### George Jones

Staff Emeritus
This expression relates the components of a vector with respect to one coordinate basis to the components of the same vector with respect to a different coordinate basis. In general, coordinate basis vectors are not unit vectors. Standard Cartesian coordinate vectors are unit vectors, but spherical coordinate vectors are unit vectors.

http://up.iranblog.com/images/geotowiaxdya2s6ewxk.jpg

is with respect to contravariant unit vectors.

5. Jan 1, 2012

Thank you