Dinosaur

10-19-02, 08:13 PM

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?

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?