Coordinate Definition and 868 Threads

I'm looking to establish a simple explanation of coordinate acceleration- Basically, as GR established, gravity is the curvature of space. If we use the ball on a trampoline analogy (which is a 2 dimensional representation of what is happening in 3 dimensions), we have a sphere creating a...

Homework Statement Suppose I define a linear coordinate transformation that I can describe with a matrix U. If U is unitary. i.e. U^{-1}U = UU^{-1}=1 does that necessarily imply that the transformation corresponds to a pure rotation (plus maybe a translation), so that I may assume that...

I'm stuck on a problem on vector calculus. Given a surface S defined as the end point of the vector: \mathbf{r}(u,v) = u\mathbf{i} + v\mathbf{j} + f(u,v)\mathbf{k} and any curve on the surface represented by \mathbf{r}(\lambda) = \mathbf{r}(u(\lambda),v(\lambda)) and it mentions the...

Homework Statement I have a bit of a general question, and I don't know whether or not the problem has a solution, but here's the idea behind it. I have two coordinate systems, let's call them CS A, and CS B. I have an infinite set of corresponding points for each system (both are 3D, so I...

I have been trying to derive a set of equations for a new Cartesian coordinate system after a rotation of an original coordinate system. This is what I did: 1) I transformed the Cartesian coordinates (x,y,z) into spherical coordinates (r,p,q): x= r cos(q) cos(p) y= r cos(q) sin(p)...

Guys, Any ideas on how to calculate distance between two points in Polar coordinate system without converting their coordinates to Cartesian? Ps. I know that if I converted from Polar (r, t) to Cartesian (x, y) by x = r.cos(t), y = r.sin(t), then the distance between two points would be d =...

I wonder if there are coordinate systems that gobally curve and twist and turn and curl, that do NOT admit local orthonormal basis. I know that the Gram-Schmidt procedure converts ANY set of linear independent vectors into an orthnormal set that can be used as local basis vectors. And I assume...

What are the r and θ limits for the triple integral of y where there's a parabloid cylinder x=y^2 and planes x+z=1 and z=0? I rearranged x+z=1 to get z=1-x => so 1-rcosθ; 0 ≤ z ≤ 1-rcosθ but I don't know how to get the limits for θ or r. How do I do this?

Coordinates are sometimes described as "null coordinates". An example in SR is the coordinate u = x - ct. Another example is one of the coordinates in the Eddington-Finkelstein metric. But I've never seen an explicit rigorous definition of a null coordinate. The defining property seems to be...

Homework Statement Evaluate the integral below, where H is the solid hemisphere x^2 + y^2 + z^2 ≤ 9, z ≤ 0 \iiint 8-x^2-y^2\,dx\,dy\,dz. Homework Equations none The Attempt at a Solution \int_{0}^{2\pi} \int_{\frac{\pi}{2}}^{\pi} \int_{0}^{3} (8-2p^2 \sin^2{\phi}) p^2...

Greetings, Regarding a mass on a spring – I know the classic differential equation is m \frac {dx^2(t)}{dt^2} + B \frac {dx(t)}{dt} + kx = f(t) F(t) = outside force applied B = damping coefficient “X” is in the vertical direction and +x direction is down. In reading I have...

Sorry to bring up again a question that I asked before but I am still confused about this. In SR we have Lorentz invariance. Now we go to GR and one says that the theory is invariant under general coordinate transformations (GCTs). But, as far as I understand, this is simply stating that...

Homework Statement which of the following is a coordinate system for specifying the precise location of objects in space? a. frame of reference b. diagram c. x-axis d. y-axis Homework Equations The Attempt at a Solution I thought it would be a diagram since it would use vectors...

GR is invariant under general coordinate transformations. If I understand correctly, this is basically devoid of any physical content. It just means that relabelling points does not change anything physical. So it's devoid fo physical content, right? On the other hand, in special...

Coordinate acceleration without a Force ! Hi GR had presented two types of motion , the geodesic motion and the non-geodesic motion . We know that the geodesic motion equation is : \[ \frac{{d^2 x^\alpha }}{{d\tau ^2 }} + \Gamma _{\beta \mu }^\alpha \frac{{dx^\beta }}{{d\tau...

Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Homework Equations...

Homework Statement Everyone tells me that I should use right-handed coordinate systems. But no one tells me what happens if I don't. What is the danger of not using right-handed coordinate systems?Homework Equations The Attempt at a Solution

Hi, I am using the book "Advanced Engineering Mathematics" by Erwin Kreyszig where I am reading on the transformation of coordinates - when changing from \int f(x,y) to \int f(v(x,y),v(x,y) it is necessary to multiply with the size of the jacobian, |J| - I cannot find the proof in the book...

Homework Statement Transform the following vector into cylindrical coordinates and then evaluate them at the indicated points: \vec A = (x + y)\hat x at P_1 (1, 2, 3) Homework Equations r = \sqrt{x^2 + y^2} \phi = \tan^{-1}(\frac{y}{x}) z = z The Attempt at a...

Homework Statement Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet. Is this true: A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat ? Homework Equations The Attempt at a...

Homework Statement Describe in words the region of R^3 represented by the equation or inequality. Homework Equations xyz=0 The Attempt at a Solution I'm not really sure how to look at the equation. I would think its just the point (0,0,0). Can someone explain if this is wrong.

is one -one correspondence must for a theory like coordinate geometry , polar coordinate ,vector analysis etc to work , i.e theories which work by representing a quantity by a different set of quantities behaving alike

I have problem with getting normal coordinates offset. I have cube1 and cube2. cube1 position is 10,10,10 and cube2 position is 10,9,10. Cube 2 offset refers to local coordinate system of cube1. If rotation of cube1 is 0,0,0 i get position offset 0,-1,0. But if cube1 rotation is 45,0,0 i get...

Help neede in coordinate geometry! Homework Statement here is the question : If the pairs of lines x^2-2pxy-y^2 and x^2-2qxy-y^2 are such that each pair bisects the angle between the other pair , then pq equals ...??the answer somehow is -1. i think it uses the concept of homogenisation (if u...

Homework Statement I want to show that the homomorphism phi:A(X)->k+k given by taking f(x_1,...,x_n)-> (f(P_1),f(P_2)) is surjective. That is, given any (a,b) in k^2 (with addition and multiplication componentwise) I want to find a polynomial that has the property that f(P_1)=a and f(P_2)=b...

Homework Statement Frame S' has an x component of velocity u relative to the frame S and at t=t'=0 the two frames coincide. A light pulse with a spherical wave front at the origin of S' at t'=0. Its distance x' from the origin after a time t' is given by x'^2=(c^2)(t'^2). Transform this...

(a) A point is observed to have velocity v_A relative to coordinate system A . What is its velocity to coordinate system B which is displaced from system A by distance R ? ( R can change in time) I think its v_B = v_A - \frac{dR}{dt} . But I am not completely sure why this is the...

http://p14.freep.cn/p.aspx?u=v20_p14_p_0711201047589252_0.jpg Formula: http://freep.cn/p.aspx?u=v20__p_0711201059233972_0.jpg 1)I need to find out V(\theta). But I remember that r\theta<dot> = \omega = V(\theta) Something seems like contradict Where my concept wrong? How should I...

Identify the curve by finding a Cartesian equation for the curve. r=2 My attempt: r=2 makes a circle with a radius of 2, so: \begin{array}{l} x^2 + y^2 = r^2 \\ y^2 = r^2 - x^2 \\ \\ y = \pm \sqrt {r^2 - x^2 } \\ \\ y = \pm \sqrt {2^2 - x^2 } \\ \\ y...

Homework Statement Three odd-shaped blocks of chocolate have the following masses and center-of-mass coordinates: (1) 0.310 kg, ( 0.200 m, 0.310 m); (2) 0.410 kg, ( 0.110 m, -0.380 m); (3) 0.200 kg, ( -0.280 m, 0.610 m). Find the x coordinate of the center of mass of the system of three...

Homework Statement I have 3 known point, with coordinate P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), P3-(X3, Y3, Z3). straight line is draw from P1 to P2, P2 to P3. they are "not" collinear. I would like to fit a round fillet to the conner with a "Known" radius of R, and I would like to know...

I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does. \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...

If we want to transform vector A from cooedinate ei to ei', then this formula occur: Aj' = aij Ai But I have a question, if I have found all components of Aj', then I want to transform it back to Ai, what should I do? I have tried Ai = aij Aj' but it won't give me the same number. Thanks...

Can anyone explain me what is the difference between inertial system and coordinate system in relativity? Please make me understand.

Homework Statement Describe in words the region of R3 (3 dimension) represented by the following inequality. 1)xyz=0 Homework Equations none i know of The Attempt at a Solution no idea where to start. I know that this means one variable must be equal to 0, but i don't...

Homework Statement Given that Z is a complex number with condition |Z-1|+|Z+1|=7 Illustrate Z on Argand Diagram and write out the equation of Locuz Z I attempted to figured out the equation of locus Z, |Z-1|+|Z+1|=7 |x+yi-1|+|x+yi+1|=7 \sqrt{}[(x-1)^2+y^2] + \sqrt{}[(x+1)^2 + y^2] =...

4 charts seem to cover it. BUt only 2 will do for a minimal number? Just like 2 charts will do to cover a sphere? Even though there are 6 all together.

Hi everyone, wondering if anyone can help me with this little problem... An object with mass m1 , resting on a frictionless horizontal table, is connected to a cable that passes over a pulley and then is fastened to a hanging object with mass m2. Find the acceleration of each object and the...

Question Statement The straight line y=mx -2 intersects the curve y^2=4x at the two points P(x1,y1) and Q(x2,y2). Show that 1) m>-1/2, m not equal to 0. 2) x1 + x2 = 4(m+1)/m^2 3) y1 + y2 = 4/m If the point O is the origin and the point T is a point such that OPTQ is a parallelogram, show...

Basically I want to find the new limits w,x,y,z when we make the valid transformation \int^{\infty}_0 \int^{\infty}_0 f(t_1,t_2) dt_1 dt_2 = \int^w_x \int^y_z f(st, s(1-t)) s dt ds I've tried putting in arbitrary functions f, and so getting 4 equations constraining the limits, but I end up...

I know there is: A gravitational length contraction by the factor of \sqrt{1-2GM/rc^2} A time slowing by the factor of \sqrt{1-2GM/rc^2} I would have thought the former and latter affect the notions of wavelength and frequency of light respectively, am I not right? However, then...

Homework Statement Given variables in one coordinate system, give the notation used to refer to the variables in another system. The known variable is x Homework Equations The transformation is an arbitrary one. My question has to do with notation and not mathematical procedures...

I was wondering about this, I've never seen any general theorem. Obviously it takes more than one, but I would think that in general it can take quite a few, for I can't see how to cover a torus with only 2. Is there any sort of general result on this?

Homework Statement Let L be the line y=7, x=7z. If we rotate L about the x-axis, we get a surface whose equation is Ax^2 + By^2 +Cz^2=1 What are the values of A, B, and C? Homework Equations Listed above. The Attempt at a Solution Since y=7, my first point that I plugged into...

Hello everyone, I was wondering where I could get complete ecliptic longitude/latitude data over the course of as many years as possible of the Sun and Moon. Of course, by definition the ecliptic latitude of the Sun would be zero. The equatorial coordinates would be fine. Thank you for...

Hey all, According to my physics textbook, if the potential energy of a particle is a homogeneous function of the spatial coordinate r, one can transform r by some factor a and t by some factor b=a^(1-.5k) such that the Lagrangian of the particle is multiplied by a^k. I understand all of this...

What is the difference, if any, between frame fields and coordinate bases?

I know basic 2D coordinate geometry/conic sections and some vectors and calculus. What I am trying to find out is, if you rotate a conic about its axis by an angle of pi, you should get a surface in 3D. How would you go about rotating this though?

How would you go about converting from a Cartesian coordinate plane to one where (0,0) is in the top left hand corner?

Homework Statement 1. Obtain an expression for operator of coordinate in momentum representation. To this end begin with definition of the average coordinate x = ∫ψ*(x)xψ(x)dx express the wave functions as wave packets in terms of plane waves, and rewrite the expression for average...