I am attempting to define the rotation angle of an ellipse about the cartesian coord frame @ (0,0).  I am pretty sure the slope of the tangency vector @ both the major & semi-major axis is orthogonal to the vector originating from the origin from (0,0) with a length of a or b depending on which axis I am using.

My thought was in the case of the major axis that x = a*cos(theta) & the slope of the vector emanating from the origin is tan(theta).  So if I set dy/dx = -1/tan...

I input into MAPLE the following differential eq & it returned that it is classified as an Emden-Fowler Differential Equation:

r^2*F"+1/r*F'-k^2*F=0   where F is a function of r

MAPLE was able to generate a solution.  I am attempting to figure out how this eq is actually solved & I typed in Emden-Fowler into the SEARCH window on this website & got ZERO results.

See the post link below which gives the ability to find the gradient of a vector, not a scalar field.

http://www.mapleprimes.com/forum/gradientvectornotgradientscalarfunction

The solution was to use the Jacobian command.  Now I need to take the time derivative of that expression because now the velocity is a function in time.  Unfortunately, MAPLE wants an algebraic expression for d/dt operations.  What command to I need to use for this operation??

Operations on matrices that presumably contain information on a physical field such as stress, voltage potential, or temperatures should essentially be the same between tensor vs vector operations is my understanding.  The only difference is conventions in how the expressions are conveyed on paper, ie- indicial vs vector notation?

If I am correct is the gradient of a the 3X3 tensor each element on the same row differentiated with each coordinate variable x, y ,z or is that a different operation?  I am unable to find the correct operation or I am not using the MAPLE command correctly to get an output.  I did load the Vector Calculus package.

What is my problem??