# Recent content by ltkach2015

Ltkach2015
2. ### A Cross Product Matrix

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...
3. ### A Cross Product Matrix

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...
4. ### A Theory of Surfaces and Theory of Curves Relationship

Oh ok! So the sphere's gradient vector would point in the same direction as the circle's negative normal vector?
5. ### A Theory of Surfaces and Theory of Curves Relationship

Ok Why doesn't the normal to space curve contained on a surface not point in the same direction as that surfaces normal vector (gradient)?
6. ### A Theory of Surfaces and Theory of Curves Relationship

Hello 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...
7. ### Alternative Methods vs Iterative Design — Control Theory

QUESTION (2/2) 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...
8. ### Why Time Response Characteristics Derived from Zero State Equation

QUESTION: 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...
9. ### Zero Homogenous Solutions with transient Particular Solutions- Physically Possible? & More Questions

That is an error on my part. Correction: dy/dt + y = exp(-t) Zero-Initial Condition: y(0) = 0
10. ### Zero Homogenous Solutions with transient Particular Solutions- Physically Possible? & More Questions

ASSUMPTIONS: BIBO/stable systems 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...
11. ### Homogenous Solution Represents the Transient Response Right?

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...
12. ### Homogenous Solution Represents the Transient Response Right?

Ok. Yes it is interesting. Thank you for the reply.
13. ### Homogenous Solution Represents the Transient Response Right?

CONCEPTUAL QUESTIONS: -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? MY ANSWER: Yes. ASSUMPTIONS: -only...
14. ### Dartmouth Extended Laplace Tables -- Not general enough? item26.a

Yes I agree the dimensions do look off
15. ### Dartmouth Extended Laplace Tables -- Not general enough? item26.a

Homework Statement [/B] 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 - unforced...