I am not following.
I should have said: assuming that the Levi Civita 3x3x3 matrix would have to remain the same for orthogonal curvilinear coordinates. That's my own thought as I knew I had to somehow generate the same velocity vector. And I think the article confirms my thinking; I quoted it...
If given a position vector defined for a orthogonal curvilinear coordinate system HOW would the matrices that make up the Levi Civita 3x3x3 matrix remain the same?
"Levi Civita 3x3x3 is said to be independent of any coordinate system or metric...
I am interested in the Frenet-Serret Formulas (theory of curves?) relationship to theory of surfaces.
1) Can one arrive to the Frenet-Serret Formulas starting from the theory of surfaces? Any advice on where to begin?
2) For a surface that contain a space curve: if the unit tangent...
1) What are some alternatives to iterative design in control theory?
2) I have a certain plant transfer function PTF(s) that is higher order than two and non-unity numerator.
I want certain characteristics such as a certain damping ratio (zeta).
So I want approximate it as...
1) Why are Time Response Characteristic's Expressions derived from only from Zero State Equations?
NOTE: Nise Control Systems Engineering 6ed uses step inputs to derive Time Response Characteristics for 1st
and 2nd order ordinary differential equations...
NOTE: zero here does not mean the roots of the denominator in a transfer function
TRUE/FALSE -Please provide feedback- some answers are based on ODE example listed below
1/True) The Homogenous Solution is either zero or transient.; i.e. it can never be steady...
So, I was beginning to build a new and deeper understanding when I noticed that Particular Solutions can also be transient:
Thus in that scenario, I believe, the Particular Solutions can, jointly, represent the Transient Response. And as expected there isn't a Steady State Response because the...
-Does the Homogenous Solution represent the Transient Response?
Let me specify. For a N-DOF spring, mass, and damper mechanical system:
-Does the Homogenous Solution represent the Transient Response for given mechanical system?
http://www.dartmouth.edu/~sullivan/22files/New Laplace Transform Table.pdf
(see item 26a)
homogenous solution to underdamped in amplitude phase form: (see attached image)
2. Relevant info
- non zero initial conditions: x(t=0) = xo AND dx/dt(t=0) = vo