# Search results

1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### Steady Flow-Does That Mean ALL Properties of Flow are Steady?

QUESTION: In general: when a flow is considered steady does that mean all properties of the flow are steady? Or: can a flow have steady and unsteady properties?
9. ### Dynamics Problem: Not Understanding the Acceleration Term

Homework Statement [/B] If particles at B and C of equal mass m are connected by strings to each and to points A and D as shown, all points remaining in the same horizontal plane. If points A and D move with the same acceleration a along parallel paths, solve for the tensile force in each of...
10. ### Projectile Motion on Inclined Surface Question

Homework Statement Water is sprayed at an angle of 90° from the slope at 20m/s. Determine the range R. PLEASE SEE ATTACHMENT Homework Equations [/B] Kinematic Equations: acceleration: A = 0i +g(-j) + 0k; velocity: dV/dt = A; position: dR/dt = V; Origin set at the point...
11. ### Resolved Shear Stress VS General Shear Stress -Contradiction?

TERMS: Slip Plane: is the plane that has the densest atomic packing—that is, has the greatest planar density. Slip Direction: corresponds to the direction in this plane that is most closely packed with atoms—that is, has the highest linear density. NOMENCLATURE: θ = angle of the slip plane as...
12. ### Resolved Shear Stress Compared w/ Shear Stress-Contradictioni

TERMS: Slip Plane: is the plane that has the densest atomic packing—that is, has the greatest planar density. Slip Direction: corresponds to the direction in this plane that is most closely packed with atoms—that is, has the highest linear density. TEXTBOOK: Materials Science and Engineering...
13. ### Thermal Ckt Parallel Configuration & 1-D HeatFlow Contradictory?

1. My Conceptual Questions (5) is at 3. CONSIDER: Case 1: two dissimilar slabs of material (say slab 1 and slab 2) connected in series (bonded at their interface). There is a temperature difference: T1 @ slab1 and T2 @ slab2. Case 2: two dissimilar slabs of material bonded together, i.e...
14. ### Alternative Vector Method to Finding Angles of Vertices of Triangle?

NOTE: I know the solution, but I challenge it. Specifically, I feel that the generally accepted solution to this problem is not intuitive. I have shown the accepted solution, and below that I have shown what I feel seems more intuitive (from a geometric standpoint)...