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Contravariant components and spherical component of acceleration

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world line
#1
Jan1-12, 06:20 AM
P: 8
Hello
i know how to derive the components of acceleration in other coordinates like spherical
start here :

and at last we have :


also , i know that acceleration is a contravariant vector :

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 ?
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George Jones
#2
Jan1-12, 07:34 AM
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so what is my mistake ?
It is very difficult to find your mistake without seeing what you have done.
world line
#3
Jan1-12, 09:52 AM
P: 8
for example :

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 ?

George Jones
#4
Jan1-12, 10:18 AM
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Contravariant components and spherical component of acceleration

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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.

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


is with respect to contravariant unit vectors.
world line
#5
Jan1-12, 09:16 PM
P: 8
Thank you


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