My question comes after some introductory background because I do not know how to construct a simpler form of the question. Suppose I have some equations such as x = xFunction(time) y = yFunction(Time) z= zFunction(Time) From the above, I can compute the following via taking derivatives Vx = VxFunction(Time) . . . Ax = AxFunction(Time) . . . The above is (I think) very elementary for an introductory calculus course. Now suppose I want to express the Positions, Velocities, and Accelerations in Spherical coordinates. Positions are as follows. R = SquareRoot(x^2 + y^2 + z^2) Longitude = InverseTangent( y / x) Latitude = InverseTangent[ z / SquareRoot(x^2 + y^2) ] Now what formulae do I use for Velocites & Accelerations in Spherical coordinates? Method one: Apply the above formulae for (R, Longitude, & Latitude) to the Cartesian Velocity & Accelerations Vectors. Method two: Differentiate the (R, Longitude, Latitude) Position Vector once to get Spherical Velocities and again to get Spherical Accelerations. The second method is a formidable task. Are the two methods equivalent? Is the first method valid? If you answer, please tell me if you really know or are making a SWAG. BTW: At another Forum, there is VB code for subscripts & exponents (or superscripts). It that possible here?