Coordinate Definition and 868 Threads

Homework Statement Please see the rotation formula in the attachment. Homework Equations The Attempt at a Solution I understand this formula rotates x,y into x',y' by some angle theta. Problem is, how is this formula derived? I cannot for the life of me visualize the cosine and...

How do you define a right handed coordinate system for a basis which is not orthonormal?

find the equation of a circle whose center falls ont he line y=6-2x and which passes through the points A(-2,0) and B(4,0). poor in circles. how to even start?

Find the equation of the circle whose centre is (-3,4) and which touches the y-axis. how do i even begin?

Homework Statement http://img811.imageshack.us/img811/9092/captureykj.png The Attempt at a Solution The answer is also in the image above. I have no clue how to start this question. Could anyone be so kind to give me a hint on how I should approach this question? Thanks!

Homework Statement http://img15.imageshack.us/img15/1671/capturetwy.png The Attempt at a Solution Could someone please explain what is meant by "if v is constrained to 0"? Also how do you find a relationship between two axis of different coordinate systems? I really have no clue where...

The question I have is a bit strange. I do not have ANY formulas or equations given. I was only given bunch of points with r, theta, and z. Z being the depth. R being radius and Theta being the angle. I was wondering if there is a way to find a rough estimate volume of the following. R...

Homework Statement https://dl.dropbox.com/u/64325990/velocity%20of%20ball.PNG The Attempt at a Solution I was thinking I could just convert from metres to feet but turns out that's not the right answer. Am I suppose to change the coordinate systems so I get a distance vs time graph? I...

We may solve a function or check a theorem but sometimes the mathematics is easier when we switch from different coordinate systems. What can we look for that tells us changing is a good idea?

Homework Statement Consider a very thin conducting ring of radius R which contains a total positive charge of +Q coulombs. (a) Derive a formula for the z coordinate which gives the maximum value for the magnitude of E ring (Z)? (b) Suppose that the charged ring is oriented horizontally, as...

How would you graph a square of any dimension on the cartesian coordinate system?

Dear all, I'm wondering, how one could justify mathematically the equality \int O(E(\vec{x}_1,...\vec{x}_N)) exp(-\beta E(\vec{x}_1,...,\vec{x}_N)) d\vec{x}_1...d\vec{x}_N = \int g(E) O(E) exp(-\beta E) dE where O(E(x)) is an observable and g(E) the density of states. Is there a...

Given two points in 3D, is there a way to find the slope of that line.

Homework Statement http://www.brookscole.com/math_d/special_features/stewart_shared/mathematica_labs/14-multipleintegrals/p05a.pdf Homework Equations The Attempt at a Solution My question concerns the (1) and (2) next to the figure of the rotating coordinate system...

Homework Statement Find the volume enclosed by the spherical coordinate surface ρ = 2sin∅ Homework Equations dV = ∫∫∫(ρ^2)sin∅dρd∅dθ The Attempt at a Solution (Sorry about my notation!) Alright, here's what I've done so far... Since the region is a torus, centered...

I have been studying gradience; divergence and curl. I think i understand them in cartesian coordinate system; But i don't understand how do they get such complex stuffs out of nowhere in calculating divergence in spherical and cylindrical coordinate system. Any helps; links or suggestion...

I know the orientations of the x-, y- and z- axes for a right-handed and a left-handed system. But that's for the cartesian coordinate system. How are the orientations of the coordinate axes for other coordinate systems defined? Also, i X j = k, j X k = i and k X i = j. How does this apply...

I have read over and over in various places about coordinate transformations, and understand the theory (really!), but can't find any worked examples of actual use of the transformation equations. Does anyone know of any web references or tutorials on the subject? To make things a little more...

In a uniformly rotating coordinate system the trajectories of freely moving objects are influenced by an apparent centrifugal and Coriolis force. Is there a coordinate system or metric (or both) in which these trajectories are geodesics instead?

The position operator in coordinate representation is: Xab=aδ(a-b) this is diagonal as expected The momentum operator turns out to look like Pab=-ih∂aδ(a-b) Now, this is not supposed to be diagonal because it does not commute with X. However it looks pretty diagonal to me. What am I...

In general relativity, we have a gravitational time dilation of: \frac{d\tau}{dt} = \frac{1}{\sqrt{1 - \frac{2GM}{rc^2}}} The term - \frac{2GM}{rc^2} appears to be based on the fact that gravity is attractive. If I understand correctly, if the curvature of space-time leads to attraction, then...

Homework Statement Given a symmetric tensor T_{\mu\nu} on the flat Euclidean plane (g_{\mu\nu}=\delta_{\mu\nu}), we want to change to complex coordinates z=x+iy, \,\overline{z}=x-iy. Show, that the components of the tensor in this basis are given by...

If we have any two orthonormal vectors A and B in R^2 and we wish to describe the circle they create under rigid rotation (i.e. they rotate at a fixed point and their length is preserved), how can we describe any point along this (unit) circle using a linear combination of A and B? I was...

Homework Statement Two particles are fixed to an x axis, particle 1 of charge q1 = 2.1x10^-7 C at x = 20cm and particle 2 of charge q2 = -4.00q1 at x = 70cm. At what coordinates on the axis is the net electric field produced equal to 0? Homework Equations The Attempt at a Solution...

I have looked at the definition of the metric tensor, and my sources state that to calculate it, one must first calculate the components of the position vector and compute it's Jacobian. The metric tensor is then the transpose of the Jacobian multiplied by the Jacobian. My problem with this...

Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of a particular bone and describe its motion. My maths knowledge is a bit lacking. However using logic I felt that I would need to track 3 constant markers on the particular bone...

How can Eddington-Finkelstein coordinate be transformed into Lemaitre coordinate? I know the transformation between the Lemaitre and Schwarzschild coordinate, and also between Eddington-Finkelstein and Schwarzschild coordinate. So I tried to find the connection between Lemaitre and E-F...

I am trying to make a game in Chipmunk Basic using the arrow keys but I can't because I cannot figure out how. I have programmed in other Basic Softwares but I cannot figure out how to use the arrow keys and spacebar in my programs. An example (much simplified) of a game I am making is snake (if...

Spacetime curvature observer and/or coordinate dependent? In another topic several people suggested that spacetime curvature is not absolute, it apparently depends on the observer and/or coordinate system. Apparently if someone goes fast (whatever that might mean in relativity) curvature is...

Hi there, I am confused about the relationship between coordinate systems and reference frame in GR. I understand the coordinate systems can be used to describe reference frames, for example, Local inertial frames in GR can be defined by Riemann Normal Coordinates. However, take the...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...

Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...

Homework Statement Here is a picture of the problem with the free body diagram: http://dl.dropbox.com/u/64325990/HW%20Pictures/problem101.PNG I am confused about why the free body diagram has the force vector in the direction of the aθ. When I did it I thought the force that the rod...

Homework Statement Given the tensor F_{\mu \nu }= \left[ \begin{array}{cccc} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} &-B_{y} \\E_{y} & -B_{z} & 0 & B_{x} \\E_{z} & B_{y} & -B_{x} & 0 \end{array} \right] F^{\mu \nu }F_{\mu \nu }=2(B^2-\frac{E^2}{c^2}) and metric tensor n_{\mu \nu...

1. Homework Statement Prove that there is an additive identity 0∈R^n: For all v∈R^n, v+0=v2. Homework Equations Axiom of Real Numbers: There is an additive identity 0∈R : For all a∈R, a+0=a and o+a=a 3. The Attempt at a Solution Solution 1 (My own attempt) : Let v=(v1, v2, v3... vn). Then...

Let say I have a triangle(polygon). I know all the co-ordinates of all points(x1,x2,x3,y1,y2,y3). Let say the polygon is inclined(at x3,y3) and it's angle is 30 degree. How to get the point x4, y4?

Hey guys, I am having some problems with the concept of inertial/non-inertial frames of reference and their applications in engineering dynamics. So I've learned that a given frame of reference is defined to be non-inertial when something in the studied system can only be explained through...

I had a tutorial today and my tutor said these questions are very trivial so we can simply look at it at home. But after going home, I found that I don't know how to do Q 35. I know that p<3 is responsible for the big sphere with r=3. But I don't know why the other part is responsible for...

If you already have one of the two coordinates?

Someone posted this animation in a previous discussion and I just 'rediscovered' it in my notes: http://www.adamtoons.de/physics/gravitation.swf Do you experts think it accurate, and if so, wouldn't this be a nice tool to display coordinate time versus proper time?? [Is it worth...

According to Peterdonis in an old thread According to Matterwave in https://www.physicsforums.com/showthread.php?t=573589 msg #11: Peterdonis said Time is a parameter in non-relativistic QM while as a coordinate in relativistic QM/QFT. But Matterwave said parameter and coordinate has...

Hello, So, I have just started studying relativity, and I am confused about some basic concepts in relativity. So, the book we use says that that time has three different kinds, proper or path time, coordinate time and spacetime intervals. I understand that coordinate time is the same as...

Hello Everyone, I am just wondering what the difference in these is. Could someone please give a brief example of non-coordinate based differential geometry vs the equivalent in coordinate based, or explain the difference (whichever is easier)? Also, what advantages does one have over the...

Homework Statement 17. xy = 2 The Attempt at a Solution Do you see that step where they do the following: √2/2 - √2/2 = my answer is 0 and they multiply that to √2/2 + √2/2 = my answer is √2 So to me the answer is 0 * √2 = 0, but the book shows that that calculation = 2, then they...

In lorentz transformation, why has t -sign

Hi, (attachment with visuals is included) I have a 3-D vector dataset that is measured in a reference frame (measurement reference frame) that is oriented relative to a horizontal coordinate system. In this dataset I have x-y- and z-component data for the vectors relative to a coordinate...

Hi, I hope this is the right forum to post. My question is, which is the math implied for transforming an objectA local space, to anothers objects local space, and then transforming it to world space? For example, Lets say we want to know if objectA is infront of objectB, So the...

Homework Statement (a) In cylindrical coordinates , show that \hat{r} points along the x-axis is \phi = 0 . (b) In what direction is \hat{\phi} if \phi = 90° Homework Equations The Attempt at a Solution here is my solution. for a. \vec{r} = \rho cos \phi \hat{i} + \rho...

I've been told that for upper level physics classes it's imperative to know how to switch between coordinate systems, however I'm unsure of what is exactly necessary to know. For example, today I was reading up on divergence and I noticed that there are formulas for divergence in spherical and...

Hello PF, I have just been given an introduction to special relativity and its postulates. One of the consequences of special relativity of course is that space and time are entangled and that in order to assign a coordinate to an event, you must give it spatial (x, y ,z) and temporal...