Orientation Definition and 201 Threads

Hello all, I'm having a bit of a difficult time following a specific conversation that I had with one of my professors. Occasionally, we would be given a 3-phase load (balanced or unbalanced), with merely the wires shown (the formation of the sources was not revealed. See the image below. I...

Say we have a disconnected manifold with components C1, C2, C3. (I know in the threat title I said just topological space, but I'm actually thinking of manifolds here, sorry! Not sure how to change the title) It makes intuitive sense that if we're looking at just one of the components, then...

I was thinking about something that really confused me... Say you have a vector in R^2 that is defined by (0,2) so that it is pointing upward on the y-axis. What would the coordinates of the vector with the opposite orientation be (so that the tail of the vector is at the point (0,2) and...

Homework Statement During the warm-up for the 1990 Olympics free skating competition, Debi Thomas, mass 60kg, moving at 5 m/s and looking intently at her coach, collides with Katerina Witt, mass 65 kg,who is smiling at a photographer. The two skaters were moving at right angles to each...

Does a Lorentz boost change the "direction" of an electron's spin orientation? For example, if an electron is in a state "spin-up" along x, and this electron is subjected to a large boost along another direction, say z, will the electron's spin remain "spin-up" along x? What if the...

If I parameterized a surface by the vector function r(a,b) I would then proceed to find the normal to the surface by crossing ra and rb. But how would I determine which normal raXrb or rbXra has the positive orientation? Im assuming you would first need to know if the concave side of the...

Given the following statement: "A plane wave is incident (from the free space) upon a semi-infinite medium made of N=100 different lossless dielectric slabs." Visually/spatially, what does this look like? I can see two possibilities 1) the slabs are stacked on top of each other...

Hi, All: There is a standard method to construct a nowhere-zero form to show embedded (in R^n ) manifolds are orientable ( well, actually, we know they're orientable and we then construct the form). Say M is embedded in R^n, with codimension -1. Then we can construct a nowhere-...

Homework Statement a hockey player of mass 80 kg was skating at a velocity of 7.5 m/s [E 20 S] when he accidentally hit a linesman who was just standing on the ice. The mass of the linesman is 90 kg and his velocity after the collision was 3 m/s [ N 30 E]. Find the velocity of the hockey...

Hi Folks, I'm building an ellipsometer-like system similar to the one shown in attached picture, but with much longer and thinner rotation bars carrying viewing optics assembly (VOA) and incident optics assembly (IOA), respectively; the system would require that the sample holder plane can...

Hi, Everyone: A way of defining an orientation form when given a codimension-1 , orientable n-manifold N embedded in R^{n+1} , in which the gradient ( of the parametrized image ) is non-zero (I think n(x) being nonzero is equivalent to N being orientable), is to consider the nowhere-zero...

I got these people trying to say that you can orientate a solid oblong so that it looks half the length and width with the only residule effect that it looks like it is slanted sideways a bit. Does anyone know what it is or are they crazy. I think they might be crazy. How do you explain this to...

Hi, I'm currently reading Manfredo do Carmo's "Differential Geometry of curves and surfaces" and I'm stocked with problem 2 of section 2-6 which is "Let S_2 be an orientable regular surface and \varphi:S_1 \rightarrow S_2 be a differentiable map which is a local diffeomorphism at every p \in...

As I know, electrical conductivity is a second rank tensor. So in a cubic structure, there is no orientation dependence of electrical conductivity (isotropic). But how come Si has higher electron conducitivity along [001] and hole conductivity along [110]?

Homework Statement I have a long EM question in which there is a Hertzian dipole at a point (0,0,-100), (unknown orientation) and I am told the equation of the physical magnetic field detected 100m away at the origin of Cartesian coordinates. $$(B_0 \sin (2 \pi f t)\mathbf{e}_x$$, and $$B_0 =...

First, I am not an electrical engineer - I am a hobbyist building a prototype linear-stlye generator based on an idea I had which, for various reasons, cannot be built with magnets that pass completely inside of coil(s) like most of the ones I have seen described for wave energy capture and...

Say I have a coil that is stationary and I have magnets that move past it in a fashion similar to the example in this video: . What is the optimum orientation of the magnet and coil to induce the most current? I know I will want to optimize the rate of change of magnetic flux through the coil as...

LaTeX Help! Currently I writing my Thesis report using LaTeX. I have been noticing the following problem. I need the figures and text to be aligned in a page in the following orientation text figure text figure However, what I obtain is figure text text figure At times, this gets...

Homework Statement Not technically a homework problem, has arisen as a point on my A-Level specification and I'm a little unsure as to how they are seeing this situation. "Relate qualitatively the instantaneous e.m.f. induced in a coil rotating at right angles to a magnetic field to the...

Homework Statement I'm a bit confused as to how to determine which component must be positive or negative if the question gives you a surface and says the normal vector is pointing outward or inward. Some surfaces have it so that the z component is positive if n is pointing outward and...

Hi, sorry if this is a bad question - I'm not very good at physics. We polarize sunglasses vertically because of glare reflecting off of a horizontal surface orients the waves in a horizontal pattern. Is it possible to experience vertical glare in a natural environment? Like off of a glass...

In solving a flux integral over a flat surface, inclined above the xy-plane, does the boundary of the surface influence the flux only through the integral limits? (and not through its normal vector) Let's say that there is an elliptic surface inclined above the xy-plane. The orientation is...

Homework Statement An electric dipole antenna used to transmit radio waves is oriented vertically. At a point due north of the transmitter, how should a second electric dipole antenna be oriented to serve as a reciever? Homework Equations Im not sure if my answer below makes sense, is...

Homework Statement I have a graph, with 4 vertices and 4 edges, i.e. a square. I need to find all non-isomorphic orientations of this graph. Homework Equations "Orientation of a graph arises by replacing each edge {x,y} by one of the arcs (x,y) or (y,x)." The Attempt at a Solution...

Homework Statement Plane shange a satellite's orientation from an inclination of 28.5 degrees to 0 degree Magnitude velocity is in both orbits is 7.726 km/sec Determine magnitude and direction needed for velocity change Homework Equations The Attempt at a Solution

I am wondering about the following issue; on a 3 dimensional scale, how is space oriented? For example, if I took a spaceship and traveled straight down from Earth (down referring straight down from the south pole), what would I see? Furthermore, if the center of the universe if defined as one...

How would one go about calculating the size of a tidal bulge created by the moon? I know how to calculate the gravity between two points and to calculate the attractive force of matter to the center of the Earth in the bulge you would subtract its opposite direction attraction to the matter...

Consider a function Q, from some set D in R2 to some set in R3. Suppose Q parametrizes a surface S. Orientation of the edge of the surface must be compatible with orientation of the surface. I read that if the parametrization of the Boundary of the domain D give it anticlockwise direction...

Hello, I apologise if this has been asked before. I did a search, but quite frankly, I'm not even sure what to search for. My gut feeling is that this problem has already been well defined and solved, so if someone could point me in the proper direction, that would be great. Consider...

Hi, If I have a magnetic field orientated in the x-direction, a dipole positioned on the z-axis how do I find which direction the dipole is orientated? Is it just as simple as using the right hand grip rule? In which case the dipole is orientated along the y-axis? Or is it more complicated...

A non-zero alternating tensor w splits the bases of V into two disjoint groups, those with \omega(v_1,\cdots,v_n)>0 and those for which \omega(v_1,\cdots,v_n)<0. So when we speak of the orientation of a vector space, we need to say the orientation with respect to a certain tensor, correct?

I am writing some code in which I am working with ellipsoids. The ellipsoids can be rotated in its body frame with three angles (First rotation is about the z-axis in the body frame, second is about the y-axis in the body frame, and finally another rotation about the z-axis in the body frame)...

How to prove that two reciprocal basis are either both right ended or both left-handed? If (e_1,e_2,e_3) and (e^1,e^2,e^3) are two such basis, since the scalar triple products depend on orientation, it would be enough to show that VV'=1 (where V and V' are the volumes, taken with their sign, of...

Hi, having trouble determining the convention for determining the orientation of the principal axes. (Please refer to the attached file for a diagram of my question) So in Q1, theta = -19 degrees and the principal axes is rotated one of the following the conventions (from what I can tell)...

some telecomunication satellites in orbits are made to be kept oriented in a certain way where their reception and broadcasting antenna or whatever is called should awalys face the Earth so while orbiting the satellite has to be interlocked with the surface of the earth. My question is: can the...

Hello! I was hoping someone on this board might be able to point me in the right direction to solve my problem. I am trying to determine how the tilt angle (from the horizontal) and azimuth of a solar array changes as the array rotates around a fixed axis running from north to south. The...

Hello All, Quick question regarding a testing procedure. I am currently tasked with determining if a test can be performed in a vertical orientation. This is in opposition to the current horizontal set up of the test. Currently, we test needle sharpness horizontally by attaching a device...

I have the result that any 1 dim topological manifold is either R or S1. And I have the fact that every 1-dim topological manifold is orientable in the sense of orientation on simplices. i want to get that any 1-dim manifold (smooth) is orientable, where orientability is given by the...

Homework Statement Suppose a fixed distance separates the centers of two circular loops. What relative orientation of the loops will give the maximum mutual inductance? What orientation will give the minimum mutual inductance? Homework Equations none The Attempt at a Solution...

calculating magnitude and orientation of a resutanr force? • A mass of 10 kg has 3 forces exerted against it, as shown in the diagram below. Given the information below, calculate the magnitude and orientation of the resultant force. F1 has a magnitude of 10.5 N, with θ = 15° to the horizontal...

Hello everybody. I am currently in a French engineering school, one of the best. The hard part was getting into it; now I am pretty assured to graduate and I just have to follow some very basic courses. I could be perfectly happy, except...I'm not really sure I want to be an engineer...

I keep reading about right-handed and left-handed spin. But if the spinning object is featureless, then there should only be one spin. It is just a matter of orientation of the spinning object. For example, if we look on the Earth from above the north pole, it spins counter-clockwise. But if...

Dear all, i want to draw the Mhor's circles for various orientation agles on a same axes

My text says, "Note that in an arbitrary n-dimensional vector space, there is no well-defined notion of "right-handed", although there is a well defined notion of orientation." I don't see why. An n frame (a1,a2,...,an) is called right handed in R^n if det[a1 a2 ... an] > 0, but I guess we'd...

my book defines an orientation preserving parametrization of a manifold as one such that: Ω(D1γ(u), ..., Dkγ(u)) = +1 for all u in the domain of γ, where D1,...Dk are the derivatives of the parametrization γ. my book also defines the orientation of a surface in R^3 by Ω(v1,v2) = sgn...

I am trying to get a different orientation on this triangle; specifically I want this output: ********** ********* ******** ******* ****** ***** **** *** ** * Here is the code that I have #include <iostream> using namespace std; int main () { int lines=10; int start =...

Hello, here is my exercise: Let M be a orientable manifold of dimension m and let N be a submanifold of M of codimension 1. Show that N is orientable <=> it exists a X \in \tau_1 (M), s.t. span<X(p)> \oplus T_p N= T_p M \; \forall p\in N The X is a vector field, i.e. X(p) is an...

Homework Statement A particle with charge Q is located on the Y axis a distance a from the origin. A second particle with a charge q is played on the X axis a distance d from the origin. The value of d for which the x component of the force on the second particle is the greatest is: a)0...

Homework Statement I was given a question to transform the LA system to the CI system. (Local astronomic and Conventional Inertial) Homework Equations r^LA=P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P*r^CL The Attempt at a Solution I attempted this on MATLAB but I used the...

There's a problem here from past years qualifiers exam that says "Show that if M is an oriented manifold,F:M-->N is smooth, and c is a regular values of F, then S:=F-1(c) is an orientable submanifold of M." I know that in the case where N=R, then there is a canonical transverse vector...