Coordinate Definition and 868 Threads

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...

I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help me...

...system, I mean as in the Cartesian Vector/Tensor definition. I get that if you have two mutually orthogonal basises which are theta degrees apart and the transformation from one basis to the other follows the same as a rotation by theta degrees i.e: V'i = Rij Vj then it is a Cartesian...

we know that in the cartesian plane, slope between two perpendicular lines is -1. but what about the x and y axis? if we find the slope between them it is not equal to -1. why is the slope between two perpendicular lines on the cartesian plane is -1 but the axes themselves do not behave such?

I have this problem where I need to convert from mouse coordinates on the screen with relative coordinates on an object that can be arbitrarily translated, scaled, and rotated around another arbitrary position. I've already normalized all of the units to be the same (pixels) but the trig is...

Homework Statement The y-axis marks the boundary between the area where the is no electric field (in the second and third quadrant) and the area where there is a constant electric field: E = 610j N/C (in the first and fourth quadrant). An electron travels along the negative x-axis toward the...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...

How can you tell when a compound will form a covalent bond or a coordinate bond? I know that a coordinate bond is a special type of covalent bond and if during covalent bonding, if the elements taking part do not obtain a noble gas configuration, they for coordinate bonds. But take for example...

Homework Statement Hi everyone. Here's my problem. I know that the volume element in spherical coordinate is ##dV=r^2\sin{\theta}drd\theta d\phi##. The problem is that when i have to compute an integral, sometimes is useful to write it like this: $$r^2d(-\cos{\theta})dr d\phi$$ because...

Homework Statement Transform the coordinates from the red c-system to the blue system. (Picture) Homework Equations Using(X Y) for the red cartesian system and (x y) for the blue system The Attempt at a Solution The solution to this problem gives x=Xcos▼ + Ysin▼ y=-Xsin▼+Ycos▼ Im not sure...

The question is to find the area of a disk, r ≤ 2a×cos(θ) as in the figure "example-just an illustration" I used two methods, each gave different wrong answers - integrate 2a×cos(θ) dθ dr - from θ=0 to θ=π/2 and from r=2a to r=2a×cos(θ) ; then I simply multiplied the answer by 2. - integrate...

Homework Statement Show that the uvw-system is orthogonal. r, \theta, \varphi are spherical coordinates. $$u=r(1-\cos\theta)$$ $$v=r(1+\cos\theta)$$ $$w=\varphi$$ The Attempt at a Solution So basically I want to show that the scalar products between \frac{\partial \vec{r}}{\partial u}...

This is a very basic question, but what type of coordinate system is this? When is it useful to use? er, eθ, eΦ sinθ

The point P rotates with angle α to point P'. the coordinates of the old P are x1 and x2 and for P': x'1 and x'2. Prove that: $$x'_1=x_1\cos\alpha+x_2\sin\alpha$$ $$x'_2=x_2\cos\alpha-x_1\cos\alpha$$ I drew on the left the problem and on the right my attempt. the line OA, which is made of...

The FRW cosmology is a solution of the FRW that can be foliated into 3D isotropic and homogeneous slices. This foliation is implemented mathematically first by the use of a not generally covariant coordinate condition https://en.wikipedia.org/wiki/Coordinate_conditions#Synchronous_coordinates ...

Hello, I'm running a galaxy formation simulation. The output specifies the coordinates in (x, y, z) of all the particles in a galaxy, which usually fall in a disk. The orientation of the disk depends on the initial conditions, but it is generally not aligned with any of the coordinate axes...

I have recently had a lengthy discussion on this forum about coordinate charts which has started to clear up some issues in my understanding of manifolds. I have since been reading a few sets of notes (in particular referring to John Lee's "Introduction to Smooth Manifolds") and several of them...

Homework Statement I am trying to use the equation ##B_{dip} (r) = \nabla \times A## to find the magnetic field due to a dipole at the origin pointing in the z direction (where A is the magnetic vector potential). The correct answer should be: ##B_{dip} (r) = \frac{\mu_0 m}{4 \pi r^3} \ (2...

Suppose that I have a two-dimensional coordinate system (x,y) and I change to a new coordinate system (u,v). What I know is that there is some function \theta(u,v) such that: \dfrac{\partial x}{\partial u} = cos(\theta) \dfrac{\partial x}{\partial v} = -sin(\theta) \dfrac{\partial y}{\partial...

When we obtain the velocity vector for position vector (r, θ, φ) Why do we take the time derivative of the radial part in the 3D Spherical Coordinate system only? Don't we need to consider the polar angle and azimuthal angle part like (dr/dt, dθ/dt, dφ/dt)?

So I know that this involves using the chain rule, but is the following attempt at a proof correct. Let M be an n-dimensional manifold and let (U,\phi) and (V,\psi) be two overlapping coordinate charts (i.e. U\cap V\neq\emptyset), with U,V\subset M, covering a neighbourhood of p\in M, such that...

How is it possible to distinguish a change of coordinate from a change o reference frame? I had this problem while i was studying Rindler' s coordinates: is it only another way to describe a Minkowsky space-time region or does it rappresent a region of the space time as described by an...

Hello, If for a curve in Cartesian coordinates ##||\dot{{\mathbf r}}||=\mbox{const}## (i.e. the curve is constant speed) will the speed of the curve change in cylindrical and spherical coordinates? Could someone experienced share how the transition from flat Euclidian space to curved space...

So I was asked to compute loop contributions to the Higgs and compute the integrals in spherical coordinates, I gave a look to Halzen book but did not found anything. Why, when and how to make that change?

Homework Statement Consider the bases B = {b1,b2} and B' = {b'1,b'2} for R2, where b1=(1, -1), b2=(2,0), and b'1=(1,2), b'2=(1,-3) a. Find the transition matrix P from B to B' b. Compute the coordinate matrix [p]B, where p=(4,3); then use the transition matrix P to compute [p]B' Homework...

Homework Statement I am given this state, which is the result of a lamba particle decaying into a proton and neutral pion. Initial j = 3/2. The final state can theoretically be written as: I have already determined that: alpha_p = Sqrt[2/3] beta_p = Sqrt[1/3] alpha_d = -/+ Sqrt[2/5]...

Hello, I'm trying to derive the perfectly matched layer for the TM mode Maxwell's equations using a complex coordinate stretching. As seen in http://math.mit.edu/~stevenj/18.369/pml.pdf . But I'm running in a bit of trouble somehow. \partial_t H_x =-\mu^{-1} \partial_y E_z\\ \partial_t H_y...

In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...

Homework Statement Our teacher said we can NEVER do an F=ma problem from an accelerating, or noninertial frame. (He said there are ways to do it, but we can not do it in his class), and I'm confused becuase often times he makes the "system" or makes a "free-body diagram" around an accelerating...

Homework Statement Start from the 'relevant equation' below and derive $$ (1) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{j}}={\hat{q}}_{i}\frac{1}{{h}_{i}} \frac{\partial{h}_{i}}{{\partial{q}}_{j}}, {i}\ne{j}$$ $$ (2) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{i}}= -\sum...

Consider a line charge with charge density λ and a electric charge q. A coordinate system moving at velocity v ,it will see the line charge as a current ,and the electric charge(which is also moving seen from the moving coordinate system) will feels magnetic force. Why does this happens?

Hello, firstly I have to make the usual apologies of ignorance and inexperience, but that's why I'm here! I have a library of XML files which each contain two sets of image data. Together they make something very similar to this:http://imgur.com/vjs7MRH The grey and red points are given in...

I'm looking at the extension of the Schwarzschild metric using Kruskal coordinates defined as ##u'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r+t)}{4M}}} ## ##v'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r-t)}{4M}}} ## In these coordinates the metric is given by...

So I have the metric as ##ds^{2}=-(1-\frac{2m}{r})dt^{2}+(1-\frac{2m}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}##* I have transformed to coordinate system ##u,r,\phi, \theta ##, where ##u=t-r*##(2), where ##r*=r+2m In(\frac{r}{2m}-1)## and to the coordinate system ##v,r,\phi, \theta ##, where...

Homework Statement The problem is: The ball B is traveling on a horizontal circle table. It is attached to the string that leads through a hole in the center of the circle. At the very beginning, the ball B is traveling around a circular path counter-clockwise, then the cord is pulled down...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] Find the equation of a line passing through point A (1, 2) and whose perpendicular distance from origin is maximum.

Suppose we have a block on an inclined plane. If we choose the x-y axis to be parallel and perpendicular to the inclined plane, then we have Fy = N - mgcos30 = 0 But if we choose our trivial x-y coordinate system, where y is parallel to the force of gravity, then we get: Fy = Ncos30 - mg =...

I think trig is assumed to be based upon triangles. This lumps trig next to squares, trapezoids, pentagons, hexagons, etc. Sure, triangles can be used to describe trig functions, but I think they do a disservice to your intuition. It's similar to Riemann sums versus integrals. True, integrals...

Warning: this may be totally trivial, or totally wrong. I've been working through Sean Carroll's lecture notes, and I've got to http://preposterousuniverse.com/grnotes/grnotes-two.pdf . I follow the derivation for showing that the tangent space bases are the partial derivatives (Carroll's...

Homework Statement Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes. Homework Equations Equation of a sphere with three dimensions X2 + Y2 + Z2 = R2 The Attempt at a Solution My equation is (x - 2)2 + (y +...

In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...

Question: Triangle ABC is a right isosceles triangle with hypotenuse AB. M is the midpoint of Line AB. Write a coordinate proof to prove that Line CM is perpendicular to Line AB.

How do you transform a curvy coordinate system to that in euclidean space? An example will be greatly appreciated.

V′μ=((∂yμ)/(∂xν))*Vν This is a contravariant vector transformation. (Guys I am really sorry for making the formula above looks so incomprehensible as I still new to this.) For the y in the partial derivative, is y a function in terms of x? In that sense, is it formula that maps x to y? Is it...

Hi guys, I have a GR question. It is usually said that black holes have event horizons in which time freezes/stops relative to an outside observer. This happens in the Schwarzschild coordinate system. But are there any coordinate systems in which the coordinate time of the black hole and its...

I am using an algorithm that transforms from my sensor frame to North West Up and I want to instead use North East Down. I have attached the current algorithm. I also want to skip the first step in my algorithm. Here is the current algorithm: http://www.filedropper.com/transformationalgorithm...

r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

Hi, this may be a very basic concept, but I'm trying to develop coordinate systems for other planets from their right ascension and declination and prime meridians so that, given a location on that planet, you could visualize the sky and its stars.. I've been reading...