Orientation Definition and 201 Threads

An orientation of a real n dimensional vector space V is an equivalence class of an ordered basis. Equivalently, this corresponds to a choice of a generator of H_n(V,V-0)=Z. The correspondence between the two is this: given an ordered basis (v_1,...,v_n) of V, the convex hull of...

Very amusing. Left wingers have thicker anterior cingulate while right wingers have more pronounced right amygdalas. The mischievous could argue this is about brains tuned for handling task complexity and brains sensitised to fearful threat. http://www.bbc.co.uk/blogs/today/tomfielden/

Hello, i need help to chose my specialization in electrical engineering. My options are: energetics, automatics, electronics and IT engineering. Can you please tell me more specs about any option. Till now, my favorite is energetic engineering, but I'm ready to listen any comment. I still...

Homework Statement From Calculus:Concepts and Contexts 4th Edition by James Stewart. Pg.965 #13 Verify that Stokes' Theorem is true for the given vector field F and surface S F(x,y,z)= -yi+xj-2k S is the cone z^2= x^2+y^2, o<=z<=4, oriented downwards Homework Equations The Attempt at a...

Is every orientation form w on a compact smooth manifold closed?(i.e. dw=0)

This is actually a problem from Lee's Introduction to smooth manifolds 14-21: Let M and N be compact, connected, oriented, smooth manifolds. and suppose F, G:M->N are diffeomorphisms. If F and G are homotopic, show that they are either both orientation-preserving or both...

This is from O'Neil's differential geometry. I'm having trouble parsing through the problem/hint. Given any curve a that does not pass through the origin has an orientation-preserving reparameterization in the polar form: a(t) = (r(t)*Cos(V(t)),r(r)*Sin(V(t))) where r(t)= ||a(t)||...

Hi everyone. I have been around a problem that I cannot figure out a solution (if there is one) which is related with sphere orientations and rotations. I already searched in many places, including here in this forum but without success. Let me introduce my problem. Given a black sphere...

Hello, I'm new here and have joined to ask the following two questions: 1 - The distance to the CMB has been measured at approximately 14 billion light years. How was this achieved, what is the error and is it the same in all directions? 2 - WMAP data clearly shows that the CMB has a plane...

How are artificitial satellites made to point to the surface of the Earth as they orbit? Is it due their spin angular momentum?

Hi everyone, I have a question that seems simple, but I cannot come up with the right answer. Suppose you have a square with sides 2 (xrange[-1:1], yrange[-1:1]) Further suppose that there are equal number of vertical, horizontal and diagonal (exactly 45 degrees) lines of various...

Dear all, I'm trying to implement an Extended Kalman Filter based SLAM for orientation and angular rates. To ease up things I discarded the estimation of position and linear velocities. I'm using a quaternion based approach with translation vectors of 3D-points/landmarks as measurements...

How do we show that, given a matrix $A$, the sign of the determinant is positive or negative depending on the orientation of the rows of A, with respect to the standard orientation of $R^n$?

Find an isomorphism from the subgroup of GL2(C) of the form \begin{pmatrix} a & b\\ 0 & 1 \end{pmatrix} ,\left | a \right |=1 to the group of orientation preserving rigid motions. *The problem is from Artin's Algebra Chapter5

Could you teach me about spin orientation by optical technique. Thanks a lot!

Hi, I'm working with my granddad on a project to build a (simple!) electricity generating windmill. We're not trying to make the most efficient design possible, just a reasonably efficient design given the simple tools and materials we're using. It's mostly just a project for fun! :) So, we...

Homework Statement There are 2 problems a and b. I've solved for both already. I just need to know how to describe them by type and orientation. In other words, what does what I got tell me in regards to type and orientation and how do I know this for future problems? (e.g. hyperbola or...

Hi, I'm trying to compute the equations of motion for a car as shown in the attached image. α = steering angle θ = orientation of the car relative to the world coordinate system Say you're given the linear velocity v and the steering angle α. How do you compute the position and angle...

O.K, please let me see if I got it right: Let M be an orientable m-manifold with non-empty boundary B. Let p be a point in B , and let {del/delX^1,...,del/delX^(m-1) }_p be a basis for T_pB for every p in a boundary component . Let N be a unit normal field on B . Now, this is the...

A spinning object such as a gyroscope is known to maintain its orientation. I am wondering *what* it maintains its orientation with respect *to*. One answer is itself. Something else I have read is "with respect to the distant stars". If it is not with itself but with "distant stars", one can...

Homework Statement The final answer should be \begin{equation} + g^{2} \int_{-\infty}^{\infty} d \Delta'\; {\cal \rho}(\Delta')\, \frac{1}{s+\gamma+i\Delta'} = + g^{2} \frac{1}{s+\gamma+\gamma_{n}} \end{equation} but I get a - in front of g \begin{subequations} \begin{eqnarray}...

strain of material w. (111) orientation is asymmetric about center point? Why?? My calculation shows an asymmetric strain distribution in InAs/GaAs(111) heterostructure while it is symmetric in InAs/GaAs(001). Someone could give explanation on it??

I have just seen a photograph known as a Laue photograph. I am reading about the Laue method of X-ray Diffraction. This method is supposed to be useful for determining the orientation of a crystal, according to Ashcroft. My question is how? Orientation with regards to what? It seems to me...

Hello again everyone, I'm in the process of winding/sourcing out coils to produce induced flux of one or the other pole orientation. I understand that when a coil is induced by a permanent magnet the resulting force will be opposite and equal to the force that caused it. So if one induces...

Hello every, I have a question I've never found a good explanation for. Referring to the picture, imagine a coil that is horizontally situated. A magnet is placed below it with the poles perpendicular to the center of the coil. The magnet can be rotated as shown. Now my question is, why does...

Hello! I have an 8-pin IC that does NOT have a notch in it, and I'm a bit confused on the orientation. The schematic I'm using specifies the orientation using a notch, as does the datasheet from the manufacturer. So, as you can see, I'm in a bit of a pickle. The chip does have a dot on the...

Hello, How can you reverse the orientation (handedness) of elliptically polarised light? Thanks! Graham.

I've been building an electromagnetic wheel (a bike wheel which rotates by electromagnetic interaction between electromagnets on the hub and permanent magnets on the rim) and I've come across an interesting problem. Currently, I've got the electromagnets mounted on the hub with the coils pointed...

Electromagnetic radiation has a magnetic aspect at 90 degrees to the electro aspect of the radiation. We see light, experience heat, use radio, x-rays, microwaves, etc. Can someone please help me with this question about the above: - Which way is the magnetic aspect orientated to the...

i have got 3 questions... What is material property orientation in orthotropic materials...in what way it differs from material distribution with respect to two or three planes?..and how does it affect the material behaviour?

When a burial grounds of Germanic and/or Nordic/Germanic people is discovered, archaeologist seem to know that it is heathen or pre-christian by the south-west to north-east orientation of the graves. I can not determine which way the head points though. Does anyone know or have a guess why this...

Hi All, i am a new bee. if an object is release from certain height with some initial orientation. how do i know, what will be its orientation after collision with the ground. Thanks and Regards, K.Prabhakar

Homework Statement A 150MHz sinusoidal plane wave propagates in air at 30 degrees with respect to the +x-axis in the x-y plane. The E-Field is polarized parallel to the plane of incidence and has a magnitude of 2 V/m.The Attempt at a Solution My only question is about the orientation. I...

in kleppner's textbook he expalins quite well why we can't have angular orientation vector (because then we wouldn't have commutavity of vectors), but we can have angular velcoity as a vector, my question is how does this work when we integrate from an angular velocity vector to get an angular...

hello all... A part of my final year project involves the determination of frictional power of an I.C.Engine(for this we used a 4cyl isuzu si engine) using a typical motoring test(using a 3ph ind motor and the engine was stripped of all its accessories liek alternator water pump), and finding...

I know when spinning a gyroscope will resist change in orientation so that the rotor is still pointing in the same direction. But, is that direction with respect to Earth's center of gravity or is it an "absolute direction". So, if I point a gyroscope upwards and spin the rotor and I go...

Hi , I am currently using quaternions in my dynamics simulation library for the orientation of rigid bodies . The bodies are very simple spacecraft orbiting around Earth and what I need is the relative yaw pitch and roll of one spacecraft against an other one (let's call them chaser...

"paradox" regarding energy of dipole orientation I've ran into a "paradox" concerning deriving the energy of a dipole's orientation in an external field. For example, the energy of a magnetic dipole m in an external field B is known to be: U= - \mathbf{m} \cdot \mathbf{B} In Griffiths...

The energy of a magnetic dipole in an external magnetic field is U = - \mathbf{m} \cdot \mathbf{B} Yet if I try to show this by calculating the energy in the fields, I get the wrong answer. I believe the problem is that I am making some arguements which neglect strange behavior at r=0, and...

I need to find an isomorphism between the group of orientation preserving rigid motions of the plane (translations, rotations) and complex valued matrices of the form a b 0 1 where |a|=1. I defined an isomorphism where the rotation part goes to e^it with angle t and the translation...

Why is the parallel orientation slightly lower in energy than the anitiparallel orientiation?

I've been thinking about the probability interpretation of quantum states. In the density matrix formalism, or in measurement algebra like Schwinger's measurement algebra, one makes the assumption that pure states can be factored into bras and kets, and that bras and kets can be multiplied...

if someone ask about optimum orientation of a molecule what exactly are they asking for?

what exactly is that?

I was looking at some web sites about the Gravity Probe B. Some show the spin axes of the gyroscopes oriented perpendicular to the Earth or else in the direction of movement of the satelite. Wouldn't these orientations cause lots of precession? I'd expect the gyroscopes' axes of rotation to...

Can someone help me prove two theorems? I know they both are true, but can't come up with proofs. 1) Prove that a 3x3 matrix A is orientation preserving iff det(A)>0. 2) Prove that for A, B (both 3x3 matrices) that det(AB)=detA*detB. (A, B may or may not be invertible). THANK YOU!

Hi there, (I hope this post is in the right forum) I'm trying to integrate a 3x3 orientation matrix using a vector representing rotational velocity (in 3d) This is the formula I'm using: newOrientation = orientation + (dt)(~w)(orientation) where w is the vector rotational velocity...

1. Is it true that when the orbital plane of planets about a star is perpendicular to our line of sight, that we will not detect the star wobble they may cause? 2. How many degrees from perpendicular is star wobble is detectible? For this question, I will accept an answer based on currently...

From New Scientist: More of the article is here: http://www.newscientist.com/article.ns?id=dn7069

The three UK A level examination boards do not appear to examine to the same level of theoretical and speculative physics. Reading through the syllabi I suspect that OCR Syllabus A requires more theory than most, and less disgorging of learned information. I'd be grateful for advice on this...