Contravariant components and spherical component of acceleration

  1. Hello
    i know how to derive the components of acceleration in other coordinates like spherical
    start here :
    [​IMG]
    and at last we have :
    [​IMG]

    also , i know that acceleration is a contravariant vector :
    [​IMG]
    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. jcsd
  3. George Jones

    George Jones 6,364
    Staff Emeritus
    Science Advisor
    Gold Member

    It is very difficult to find your mistake without seeing what you have done.
     
  4. for example :
    [​IMG]
    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 ?
     
  5. George Jones

    George Jones 6,364
    Staff Emeritus
    Science Advisor
    Gold Member

    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.

    [​IMG]

    is with respect to contravariant unit vectors.
     
  6. Thank you
     
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