Coordinate Definition and 868 Threads

Homework Statement How does \delta_{b}C^{d} transform? Also compute \delta^{'}_{b} C^{'d}The Attempt at a Solution \delta_{b} C^{d} = \frac{dC^{d}}{dX^{b}} ?I think I am supposed to prove that its a scalar, but I really have no starting point. Any extensive help would be really great.

In "Gravitation" - Misner, Thorne, Wheeler, the second part of formula 25.38 (first part describes the proper time left till the singularity) seems to suggest it describes some kind of coordinate time left. But the question is what exactly? Here is the formula: t={\it 2M}\, \left( -2/3\...

Homework Statement The graph below represents the time versus velocity of a particle. The x coordinate of the particle at 30 seconds is 20 feet. What is the x coordinate of the particle at 50 seconds?Homework Equations These are the equations I think could be used to solve this problem; the...

Hi, I'm looking for an efficient way of achieving the following, but having trouble thinking it through: Let's say I have a triangle in three dimensions with vertices A, B and C. Let's say I also have a three dimensional coordinate D. I know the x and z component values for D and I am...

Homework Statement Prove that the coordinates of the point (x',y') where the counter-clockwise rotation through the angle @ around (0,0) brings the given point (x,y) are x' = xcos@ - ysin@ y' = xsin@ + ycos@ Hint: show that for the points (x,y) = (1,0) and (x,y) = (0,1) directly, and...

1. Find the derivatives of the spherical coordinates in terms of df/dx, df/dy, and df/dz. 2. f(x,y,z) x=rcos\thetasin\varphi y=rsin\varthetacos\varphi z=rcos\varphi 3. The Attempt at a Solution [/b] I took the derivatives of the three equations and I got...

Having trouble with this "Moments about the coordinate axes" problem! When a force F is applied to the handle of the valve shown, its moments about the x and z axes are, respectively, M_x= -77 lb ft and M_z= -81 lb ft. For d=27 in., determine the moment M_y of F about the y axis...

Homework Statement Starting from one oasis, a camel walks 82.021 ft in a direction 30 degrees south of west and then walks 30 km toward the north to a second oasis. Without using a coordinate system, calculate the magnitude and the direction of the displacement from the first oasis to the...

I want to make sure of my understanding of coordinate transformations. First of all, is it true that if \[{x_i}\] is a coordinate system on a manifold, then \[{q_j} = {q_j}({x_i})\] is a coordinate transform from "x" space to "q" space? If so can "x" be a flat space and "q" a curved...

A charged particle in a magnetic field is spiralling along a path defined in cylindrical coordinates by r = 1 m and θ = 2z rad (where z is in meters). The speed along the path is constant at 3.87 km/s. What is the z-component of the velocity, vz, in cylindrical coordinates? My attempt...

Homework Statement The distance of point X (k,2) from the line y=x+4 is four. Find the values of k. Homework Equations The Attempt at a Solution (y-2)/(x-k)=-1 y=-x+k+2 I think this gives me the equation of the line from the point to the line y=x+4, but not sure what to do next...

How does one determine when a coordinate covalent bond will occur?

Hi, I have some doubts about the precise meaning of Euclidean space. I understand Euclidean space as the metric space (\mathbb{R}^n,d) where d is the usual distance d(x,y)=\sqrt{\sum_i(x_i-y_i)^2}. Now let's supose that we have our euclidean space (in 3D for simplicity) (\mathbb{R}^3,d)...

Let's take a system, for simplicity with only one degree of freedom, described by a certain lagrangian L[x,\dot x] I define the momentum p=\frac{\partial L}{\partial\dot x} Now, if I make a change of coordinates x\longmapsto y\qquad\qquad\qquad(1) I obtain a second lagrangian M[y,\dot...

Hi! I see there are three 3D coordinate systems based on either 3 number (cartesian), 2 numbers and 1 angle (cylindrical) and 1 number and 2 angles (spherical). So can't there be a system based on 3 angles? Thank you.

Homework Statement This question is on my physics homework, I guess it could be posted elsewhere, but I'm not sure where. Here is the problem: Which of the following are the same as 18 degrees below the -x-axis? Choose all that apply: !The choices I selected are in red! A) 72 degrees left...

Say we have a vector field defined in R^3. That is, at every point p in R^3, we have the corresponding set (p, v(p)). In representing this field, as far as I can tell, we have a certain list of very general requirements. That seems to be a.) an origin, b.) three everywhere non-coplanar curves...

Homework Statement I will to explain this without a diagram. Consider a coordinate system(1st quadrant) where the x and y-axis both stop at 7 units (i mean the boundary), there are two points P(3,3) and Q(4,4). How many points can R be positioned such that PQR is an isosceles triangle...

Homework Statement With a > 0, b > 0, and D the area defined by D: \frac{x^2}{a^2} + \frac{y^2}{b^2} \leq 1 Change the integral expression below: \iint\limits_D (x^2+y^2) dx\,dy by using x = a r cos θ, y = b r sin θ. After that evaluate the integral. The Attempt at a Solution...

I'm working on a problem that involves two Earth stations that scan the skies. I'm writing a simulation program (no physics involved) that simply finds the az/alt of an event observed simultaneously by each station. At this point, I'm warming up to the mathematics, spherical geo, etc. to pull...

I am having trouble understanding how (2x - x2)1/2 becomes 2 cos θ. Thanks

Currently I am using a graphying application called "Autograph" and modeling a building with a dome shaped roof on top. I need to define parabolic shapes in 3d system. But i can't do it ( my math knowledge is pretty elementary) What would be the basic parabolic function in 3d that i can base...

Homework Statement Use polar coordinates to find the volume of the given solid. Inside the sphere x²+y²+z²=16 and outside the cylinder x²+y²=4. Homework Equations x=rcosΘ,y=rsinΘ, x²+y²=r² The Attempt at a Solution 2∫∫ (√(16-r²)r)drdΘ R{(r,Θ)l 0<Θ<2∏, 2<r<4} I was...

Homework Statement Could some mathematically minded person please check my calculation as I am a bit suspicious of it (I'm a physicist myself). This isn't homework so feel free to reveal anything you have in mind. Suppose I have two functions \phi(t) and \chi(t) and the potential V which...

Homework Statement cylindrical coordinates: r=2cscƟ, give both rectangular and spherical cordinates Homework Equations I know this: From rectangular to cylinder z=z r2=x2+y2 tanƟ=y/x From Cyl to rectangle x=cosƟ y=sinƟ z=z From cyl to spherical Ɵ=Ɵ...

Hi all, I've been struggling with this for a couple of days now and am positing a question in the hope that someone can help me out. I have a global cartesian coordinate system X, Y, Z and a cube with it's centre at (0,0,0) and dimension 1. Hence it's corners are: (0.5, -0.5, 0.5), (-0.5...

I am new to this subject of topology. I want to know if bending and stretching of a manifold is same as a general transformation of a coordinate system drawn on the manifold. Or the mathematical definition of bending and stretching shall equally help.

hi, i am doing a simulation of 3D problem.i want to draw it cylindrical coordinate sysyem(r,z, o).but gambit shows X , Y , Z Coordinate . how to do in cylindrical co ordinate , will it show r, z and o axis ? i opened the Tools command button then i changed the co ordinated system to...

Sorry i wasnt able to get help in the homework department. figured id try here. Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) =...

Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) = \frac{ds}{dt} = \sum g_{ij} \frac {d\alpha^{i}}{dt} \frac {d\alpha^{j}}{dt} (well that's actually...

Hello Forum, since my GR tutor can't help me with some issues arising I thought it is time to register here. I am very confused about the phrase "coordinate independence". Especially regarding the Lie Derivative and the Commutator of two vector fields. 1) The Lie Derivative is said...

Homework Statement When you have a point in \Re3, like for example let J(3, 7, 3) and Q(1, 2, 3). What is the distance in terms of coordinate between them? Like can you just subtract the corresponding components? Homework Equations I am not sure if it only works for the formula...

Here I am doing a spherical pendulum problem, and i was asked to represent the unit vectors of spherical coor in terms of Cartesian coor, which i have already solved: r=sinθcosφ i + sinθsinφ j + cosθ k θ=cosθcosφ i + cosθsinφ j - sinθ k φ= -sinφ i + cosφ j where φ is the angle on the X-Y...

Hello to all, I am currently studying computer graphics and I have came up with the following problem. Consider that we have three coordinate systems, let's say CSA1, CSA2 and CSA3 that have the same origin and differ by a rotation. That is to CSA2 connects to CSA1 by R12 and CSA3 to CSA1 by...

In the coordinate representation of a quantum mechanical system, is it always true that the Hamiltonian of the system is diagonal? If so, can someone explain to me why this is true?

Hello, Is there a formula for calculating a range of latitude-longitude coordinates within a certain radius of a given point? Using ellipsoidal geometry, preferably.

if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is B=(r2,\theta2,z2) (if ar,a\theta,az are unit vectors) then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az> and the position vector of B is = r2<ar>+\theta2<a\theta>+z2<az> so vector BA=...

Now I'm study the Schwarzschild geometry from "General Relativity (M.P. Hobson)". Since the Schwarzschild metric has coordinate singularity at r=2M so to remove this singularity they use the Eddington-Finkelstein coordinate, first they begin with introduces new time parameter "p" p=ct+r+2M...

can someone explain to me why my teacher divided the area into two? I=\int1,0\int(2x-x^2)^.5,0 1/(x^2+y^2)^.5dydx ugggggh i tried to use the latex... anyway... he used the polar coordinate to do this. once he turned it into polar coordinate, he divided the area into 2 bounded by (pi/4 - o...

Sorry, I do realize that this is probably a really stupid question, but can someone please help me understand the following statement: My understanding of a timelike path, is one which always stays inside a light cone, defined by lines with gradients c and -c that cross at the origin...

Homework Statement The following vectors form an ordered basis E = [v1, v2] of the subspace V = span(v1,v2): v1 = (1,2,1)^T , v2 = (3,2,1)^T. The vector v = (24,-8,-4)^T belongs to the subspace V. Find its coordinates (c1,c2)^T = [v]E relative to the ordered basis E = [v1,v2]. Homework...

Hey If you have the Minkowski line equation of -ds^2 = c^2 d tau^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 I don't understand how you can assume from this ^ that each observer in different reference frames will experience time changing at the same rate 'dt'. I thought that tau was the relative...

Homework Statement Let B be a basis of R^2 consisting of the vectors <5,2> and <1,5> and let R be the basis consisting of <2,3> and <1,2> Find a matrix P such that [x]_r=P[x]_b for all x in R^2 Homework Equations Ax=B? The Attempt at a SolutionI attempted by using Ax=B as a format to solve...

I have a sphere, with center x0,y0,z0 and a radius r. Furthermore I have a point 1 outside the sphere x1,y1,z1. But now I want to calculate the coordinates of Point 2, which is on the surface of the sphere, and the CenterP2P1 is 90 degrees there. With these two points known points (Center...

I'm having trouble finding information online regarding figuring out vector components when you set up your own axes. All examples just show a basic x-y coordinate system where the cos and sin components of the vector are obvious. However, suppose you have a problem where, for example you have...

How do i randomize a position on a sphere? Using a random number between 0 and 360 for longitude and a number between -90 to 90 for latitude would make it more probable to get closer to the poles right?

I'm working with a cartestian system that has certain periodic properties I'd like to exploit with a new coordinate system, but I don't know one that would work. The trajectory of the state of the system is symmetric across non-adjacent squares (ie a checkerboard of sorts), so that (x,y) can...

Homework Statement Using the concept of equal slopes, state whether the following sets of points are collinear or not A(5, -6) B(0, -1) C(-4, 3)Homework Equations Slope = vertical rise/horizontal runThe Attempt at a Solution I only got as far as... 5-0/-6+1 = 5/-5 I think what I just did...

I'm confused by the relation of coordinate transformation and conformal transformation. I found a nice note about conformal field theory written by David Tong. It does contain the demonstration related to my question, but I still don't understand. Here it goes, The definition of conformal...

Hello, I've been searching all over for the epoch time of the WGS84 coord system. A GPS I'm using says its 06/01/1980, but I don't know if starts from 12:00:00 ET. Is there an epoch by definition or is it arbitrary?