Coordinate Definition and 868 Threads

1. Calculate the coordinate of a triangle's 3rd corner when 2 corner coordinates and area is given (in Surveying). Given: Area of triangle ABC = 14994sqm Corner B coordinate = +3541.620 (Y); -5467.650 (X) Corner C coordinate = +3300.580 (Y); -5503.150 (X) Calculate corner A's coordinates? I...

Hi everyone I have a little problem in understanding the trasformation of vectors component when passing to a different coordinate system (abbreviated CS). Theory says that the components of a vector in the first CS x with component (V^0,V^1,...,V^n) will transform changing CS according to...

I was wondering, if a metric known to be a solution of Eintein field equation can be a static or expanding spacetime depending on a change of coordinates, what does this tells us about that metric? Can it be physical? I mean in the sense that it is usually said that to check if something is...

Find the change of coordinate matrix from\gamma coordinates to \beta coordinate where \beta is the standard basis for P2(R) and \gamma={ 1+t^2, t-t^2, 1-2t +t^2} Since i can't figure out how to type matrices i will explain what I did. I made a 3 by 3 matrix and put the \beta basis on the...

what does this mean please: bisectrix of the rectangular coordinate system

Homework Statement Find the area enclosed by the curves: r=\sqrt(3)cos(\theta) and r=sin(\theta) Homework Equations The area between two polar curves is given by: A=(1/2)\int{R^2 - r^2dr} where R is the larger function and r is the smaller function over an interval. The Attempt at a...

Homework Statement An ant walks from the inside to the outside of a rotating turntable. Write down it's velocity vector. Use polar the cartesian coordinates. Homework Equations I have already derived the velocity vector in polar coordinates which is: \hat{v} = \dot{r}\hat{r} +...

The title pretty much says it. According to my book, Classical Dynamics by Thornton and Marion, generalized coordinates can be quantities other than position such as energy or length squared, but what about time?

Hello, I am trying to understand this partially rotated coordinate systems. I do not understand how does x'=xcos(theta)+ysin(theta) and y'=ycos(theta)-xsin(theta) I am probably stuck at silly answer but i need this to understand deriving of formulas for special relativity. Thanks

Hi, I am trying to simulate a freely jointed chain polymer to do that I want to put several rods (length a) on top of each other but with different angles. My problem is like this I have a vector(1) and at the end of this vector(1) I put another vector(2), the z-axis of this vector(2)'s...

Hello, I have a question related to coordinate transform. If this is not the right section please feel free to move this thread. My problem is the following: I have a positioning system to move an antenna, that allows me to perform scans according to a great circle coordinate system. Check...

Given a surface of positive curvature embedded in R^3 choose coordinate charts around each non-umbilic point so that the cross terms in both the first and second fundamental forms are zero. These are coordinates where the tangents to the coordinate axes point in the direction of the...

Hello! When using the Schwarzschild exterior metric in the klein-gordon equation one can perform the standard tortoise(E-F) coordinate transform to yield a wave equation which has a well defined potential that is independent of the energy term. My understanding is that the motivation for this...

Hi there, Physics lovers. I'm studying "The Classical Theory of Fields" from the "Course of Theoretical Physics" book series by Lev D. Landau, and I'm stuck with simultaneity in General Relativity. In page 251 of the Fourth "revised" english edition, by Butterworth Heinemann, There begins the...

Hi everyone, Given two different reference frames in a vector space; say left and right. v is a vector defined in the left frame and u is a vector defined in the right frame. What is the nature of a matrix A that can satisfy the equality u= A.v? Thank you

Homework Statement What are the signs of the forces (positive + or negative -) acting on both situations? Situation 1: Situation 2: Homework Equations Not really necessary The Attempt at a Solution I'm not sure about Situation 1 at all, but I think I got Situation 2: If I have this...

Calculus: Coordinate Changes, Jacobian, Double Integrals?? Homework Statement Show that T(u,v) = (u2 - v2, 2uv) maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D, bounded by x=0, y=0, and y2 = 324 - 36x. Use T to calculate ∬sqrt(x2+y2) dxdy on the region D...

hey, I know this might be abit silly, but u know the cauchy-reimann formula for a complex function to be diffrentiatable? here is a link to what I am talking about: http://en.wikipedia.org/wiki/Cauchy-Riemann_equations my question is: how do I write it in polar coordinates?:redface:

Hi, My question is the following. In special relativity, the Lorentz transformations correspond to a physical situation in which two frames of reference move with uniform rectilinear motion one with respect to the other. In general relativity, given the physical situation in which one frame...

For a defect in a semiconductor. We plot the energy against some "configuration coordinate", noted in general as "Q". What is this coordinate ? In my understanding it is some position related to the defect in question. Also, is the energy plotted in the diagram the energy of the...

Given a set of 2D coordinates (real numbers, involves positives and negatives), I could calculate the (weighted) barycenter by simply using the logic with plain numbers. For the barycenter calculations, I sum all the values with respect to x-axis and y-axis separately, and then divide with the...

Homework Statement Please help me graph this on xyz coordinate plane A golfer strikes the ball of the tee at x=0;y=0;z=0. The hole center is located at a distance of 150m north(+x) and 75m west(+y) of the tee. The upper edge of the hole is 10m below(-z) the height of the tee. If the the...

Homework Statement A regular tetrahedron has the vertices of its base A(1,1,0) B(3,1,0) C(2,1+(3^(1/2),0). Find coordinate of vertex S? Homework Equations The Attempt at a Solution If this is a tetrahedron Then we know the length by caclulating the distance formula, which gives...

Hi, I am reviewing some vector calculus and have a problem on the derivation of the divergence in the spherical coordinate. Assume there is a small volume located at r_0, \theta_0, \phi_0 with a volume of r_0^2\sin\theta_0 \Delta r \Delta \theta \Delta \phi. My question is that why...

I feel I may have improperly posted this thread https://www.physicsforums.com/showthread.php?t=469331" but am just not as knowledgeable in my matrix math as I need to be. One (me) would think that somehow you should be able to get a rotation matrix from these two systems. Homework Statement So...

Hey everyone, I'm working on my degree and have started getting into some deeper lin alg than I took previously regarding coordinate system transformations. I was hoping someone might be able to shed some light on it for me. I'll do my best to explain the problem .. I have a global...

In an earlier thread, I asserted that a rod has one true length, its rest length. If so, then the shorter coordinate length which is measured in some other frame must be somehow untrue. In this thread I argue that the coordinate length is a distorted view of the true length. In the graphic...

How will you graph θ=π/4? In polar coordinates you can graph an equation like, r=a(1-sinθ) which gives a cardioid graph. But when my teacher giving me a class of sketching in polar coordinates then he ask to sketch θ=π/4. But as we know that in polar coordinates (r,θ). so in θ=π/4, there is...

Dear Friends, I have below query Available data: Point1 (r1,theta1,phi1) Point2 (r2,theta2,phi2) where in spherical coordinate system r(i)=radius theta(i)=angle phi(i)=azimuth Required output: Line of intersection by individual planes generated by each point i.e. from point1 we...

if the 3 spatial dimensions are represented on a 3 axis graph. would time be a straight line through the origin? if not could your direct me to some reading that i may find answers? I'm uncertain whether space-time can be represented using euclidean geometry.

The wikipedia article on connection forms refers to a local frame. What is the relationship between local frames and coordinate bases? Are they the same thing? Is one a subset of the other? The connection form article uses general notation e_\alpha for the basis elements instead of the...

Problem is here http://engineeringhomework.net/statics/FG02_32-03UNP62.JPG Determine the magnitude and coordinate direction angles of the resultant force. I don't know where to start on this one.

How can you express the del operator after a change of variables? For example, if I want to use cylindrical coordinates for a fluids problem, what is the del operator in terms of the new coordinates? And how do you derive it for any other arbitrary coordinate transforms?

Homework Statement A block of mass m slides down a plane inclined at an angle theta with initial velocity v down the slope and with friction coefficient mu. Find T, the time in which the block comes to a rest due to friction. Use coordinates with y vertical and x horizontal. Homework Equations...

I don't understand what's wrong with it:

I am confused with the spherical coordinate. Say, in 2D, the polar coordinate (r, \theta) The mathworld website says that http://mathworld.wolfram.com/SphericalCoordinates.html D_k A_j = \frac{1}{g_{kk}} \frac{\partial A_j}{\partial x_k} - \Gamma^i_{ij}A_i I don't know why we...

Homework Statement Given the equation r²=25sin2Θ Asked to find symmetry with respect to line Θ = pi/2 Homework Equations w.r.t. Θ = pi/2: (r,Θ) - (r, pi-Θ) and (r, Θ) - (-r,-Θ) The Attempt at a Solution For the first case, I plugged in (pi-Θ) for Θ, but I'm confused about what to do...

I just want to ask a simple question: Is it true that Newtonian/Classical Mechanics does not hold true for all coordinate systems, while General Relativity does?

General four-dimensional (symmetric) metric tensor has 10 algebraic independent components. But transformation of coordinates allows choose four components of metric tensor almost arbitrarily. My question is how much freedom is in choose this components? Do exist for most general metric...

Hello, I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates). Griffiths gives the definition of the maxwell stress tensor...

Hi Homework Statement Two points X(a,b) and Y(b,a) Prove that the distance = sqrt2 (a-b) Homework Equations d = sqrt(x2-x1)^2 + (y2-y1)^2) The Attempt at a Solution I have drilled it down to (sqrt 2b^2+2a^2-4ba) but unable to drill it down to sqrt2 (a-b) Help...

Lets say I have Coordinate Frame's A and B. and... I have the coordinates of the 3 principle axes of B in terms of Frame A, So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A: XA -> -YB YA -> XB ZA ->...

hello, am confuse with this problem. I have B = {U1,U2} and B' = {u'1,u'2} u1 = [2,2], u2 =[4,-1] u'1 = [1,3], u'2 = [1,1] Now I have found the transition matrix from B' to B which is 13/10 -1/2 -2/5 0 Now, the question that am having trouble with is: Compute the coordinate...

Homework Statement [PLAIN]http://img25.imageshack.us/img25/3409/linearf.jpg Homework Equations The Attempt at a Solution Is this the right method to do this type of question (as I haven't seen an example of finding a coordinate vector before)? Do I solve the following system of...

Homework Statement Write down the transformation laws under general coordinate transformations for a tensor of type (0,1) and a tensor of type (2,1) respectively The Attempt at a Solution I seem to have two transformation formulas but they could in fact just be the same thing. I'll just do...

Does anyone know of a good book for relearning and working with different cooridinate systems like polar cylindricaly spherical the typicall engineering stuff...

I have a metric of the form ds^2 = (1-r^2)dt^2 -\frac{1}{1-r^2}dr^2-r^2 d\theta^2 - r^2 sin^2\theta d\phi^2 A singularity exists at r=\pm 1 . By calculating R^{abcd}R_{abcd} i found out that this singularity is a coordinate singularity. I found the geodesic equations for radial photons...

The thread bcrowell had on time reversal in GR got me thinking about this. Some limitations are obvious: mapping two events onto one, discontinuity,... I will use x*, t*, etc. to refere to tansformed coordinates (primes always confuse me with derivatives). Similarly, the transform x* = t, t*...

Homework Statement \Delta f = \frac{1}{{r^2 }}\frac{\partial }{{\partial r}}\left( {r^2 \frac{{\partial f}}{{\partial r}}} \right) + \frac{1}{{r^2 \sin \phi }}\frac{\partial }{{\partial \phi }}\left( {\sin \phi \frac{{\partial f}}{{\partial \phi }}} \right) + \frac{1}{{r^2 \sin ^2 \phi...

Homework Statement The points A and B are located on the line 5x-12y=6.The perpendicular distances of A and B respectively from the line 3x-4y=-2 are both 4 units. A lies on the same side of 3x-4y=-2 as the origin ,and B lies on the other side. Find the coordinates of A and B. Homework...