Coordinates Definition and 1000 Threads

Homework Statement Well, if you have given a gradiant in cartisian coordinate system? what happened to the gradiant if we stretched the coordinates by factor of 2? Homework EquationsThe Attempt at a Solution I think gradiant should be the same as it's the rate of change of some function.

Homework Statement I'm currently trying to follow a derivation done by Shankar in his "Basic Training in Mathematics" textbook. The derivation is on pages 343-344 and it is based on the solution to the two dimensional heat equation in polar coordinates, and I'm not sure how he gets from one...

Find the coordinates of the expression (cos x + sin x)^3 in the basis {1, sin x, cos x, sin 2x, cos 2x, sin3x, cos3x}. I don't understand where to start since I am dealing with cos and sin now. :confused:

Consider the polynomial f(x) = x^5 − 5x^4. (a) Find coordinates of f′, f′′, f′′′ in the basis {1, x, x2, x3, x4, x5} I no f ' = 5x^4-20x^3 f " = 20x^3-60x^2 and f "' = 60x^2-120x but from there where to begin? do I make a matrix of like the following? 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0...

I am accustomed to ##x=rcos(\theta)sin(\phi)## ##y=rsin(\theta)sin(\phi)## ##z=rcos(\phi)## ##-\pi<\theta<\pi##, ##-\pi/2 < \phi < \pi/2## but see some people using these instead ##x=rcos(\theta)cos(\phi)## ##y=rsin(\theta)cos(\phi)## ##z=rsin(\phi)## ##-\pi<\theta<\pi##, ##-\pi/2 < \phi <...

Homework Statement A hollow cylinder with radius ##a## and height ##L## has its base and sides kept at a null potential and the lid on top kept at a potential ##u_0##. Find ##u(r,\phi,z)##. Homework Equations Laplace's equation in cylindrical coordinates...

I've learned that a vector in coordinate system can be expressed as follows: A = axAx+ayAy+azAz. ai, i = x, y, z, are the base vectors. The transformation matrix from cylindrical coordinates to cartesian coordiantes is: Ax cosΦ -sinΦ 0 Ar Ay = sinΦ cosΦ...

Given the force (derived from a potential in planar polar coordinates) F(p,w) = 2p+sin(w)e_p+cos(w)e_w Where e_p and e_w are unit vectors How do I calculate the line integral over a circumference that is defined as: p = 2 0 ≤ w ≤ 2pi Using the definition of a line integral \int_0^{2pi} \...

I have a course next semester on Classical Mechanics (mostly Lagrangian problems), for a second time. I'm ok for the theoretical preparation, but I'm trying to work ahead on problems and exercises, which was badly explained and without much of any resources. So, one of the sources to exercise on...

Homework Statement evaluate the double integral of cosh(6x^2+10y^2) dxdy by making the change of variables x=rcos(theta)/sqrt(3) and y=rsin(theta)/sqrt(5) let D be the region enclosed by the ellipse 3x^2+5y^2=1 and the line x=0 where x>0. Homework EquationsThe Attempt at a Solution first I...

Homework Statement Sorry for the long derivation below. I want to check if what I derived is correct, I can't find it anywhere else, feel free to skip to the end. Thanks! I am confused by how to write the EL equations if I have multiple constraints of multiple coordinates. For example, let's...

The potential on the side and the bottom of the cylinder is zero, while the top has a potential V_0. We want to find the potential outside the cylinder. Can I use the same boundary conditions as for case of inside cylinder potential? What is different?

Is A x B = | i j k | also true for Spherical Coordinates? | r1 theta1 phi1 | | r2 theta2 phi2 | Or I have to convert them to Cartesian Coordinates and do the cross product and then...

Hi everybody, I know that there are a lot of threads in this forum about Rindler coordinates but none of them have helped me :confused: I'll explain you my problem. First of all, my coordinates (x^0,x) (Cartesian coord., where x^0=ct) are related to the Rindler coordinates (\omega ^0,\omega)...

Homework Statement I'm feeling a bit ambivalent about my interpretation of spherical coordinates and I'd appreciate it if someone could clarify things for me! In particular, I'd like to know whether or not my derivation of the coordinates is legitimate. Homework Equations Considering...

Homework Statement I'm just having trouble understanding a step in my notes from class.. We're talking about how to derive the divergence in other coordinate systems. Homework Equations So, we are deriving this divergence formula in spherical coordinates \oint \vec{A}\cdot d\vec{A} = \int...

What is the relationship between the differentiable manifold that is space-time and the physical space around us? How does one relate the three seemingly Cartesian coordinates around us, those which we can measure out with a ruler, to the coordinates of the Lorentzian manifold? If i say, measure...

I was reading "Time scales in the context of general relativity" Bernard Guinot, and a few other papers whose names I forget, and was surprised that there was apparently some desire by some physicists to give coordinates units. It seems that the current recommended practice is that...

Homework Statement A cannon shoots a ball at an angle θ above the horizontal ground. (a) Neglecting air resistance, use Newton's second law to find the ball's position as a function of time. (Use axes with x measured horizontally and y vertically.) (b) Let r(t) denote the ball's distance...

Homework Statement The projectile A is being tracked by the radar at O. At a given instant, the radar readings are θ = 30degrees, R = 2000m, dR/dt = 200 m/s, and d^2R/dt^2 = 20 m/s^2. Determine the speed of the projectile at that instant. THE ANSWER AT THE BACK IS 299.7m/s [PLEASE SEE...

Homework Statement As a part of my self study I am trying to find the covariant basis vectors in the spherical polar coordinates. Since I have never done anything like this before I would appreciate if someone could tell me whether I am on the rigth track. Homework Equations...

Homework Statement Let \vec{F}=2\hat{i}-3\hat{j} act on an object at point (5,1,3). Find the torque about the point (4,1,0) Homework Equations \tau = \vec F \times \vec r The Attempt at a Solution Please tell me if my procedure is correct. Let the object occupy point A at (5,1,3) and let...

Sorry for a long post. I am looking for a clear and concise way to explain how to compute coordinates when changes of basis or linear operators are involved. I would like to avoid the summation notation as much as possible and use the definition of matrix multiplication only in the beginning...

The torque contribution due to the uniaxial anisotropy is given by the equation below \frac{\Gamma}{l_m K} = (2 \sin\theta \cos\theta)[\sin\phi e_x - \cos\phi e_y] (3) This contribution can be taken in the LLG equation to derive the LLG equation in polar coordinates \frac{\partial...

Homework Statement My answer seems to differ from the books answer, so I'm wondering where something has gone wrong. Find the volume inside the prism bounded by the planes ##y = x##, ##y = 0##, ##x = \frac{a}{\sqrt{2}}##, ##z = 0## and the cone ##az = h\sqrt{x^2 + y^2}##. Homework...

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...

I'm rather new here so please forgive me if this is answered somewhere else, but I was unable to find it while searching around. For some calculations I'm looking to perform I need to know the geocentric equatorial coordinates of the sun on a given date. However, the only place I know they...

Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...

When you have a general coordinate chart on spacetime you have a lot of freedom to pick your coordinates, but you are always going to have 4 coordinates and each 4-tuple uniquely (in that chart) identifies one event in the manifold. When you are choosing generalized coordinates for a...

Homework Statement Hi! This is not really a problem. I'm just confused on how to express the charge distribution of a set of point charges in spherical coordinates. From our discussion, ρ(\vec{r})=\sum\limits_{i=1}^N q_i δ(\vec{r}-\vec{r}') where \vec{r} is the position of the point where...

Homework Statement In spherical coordinates (ρ,θ,ø); I understood the ranges of ρ, and θ. But ø, still eludes my understanding. Why is ø only from 0 to π, why not 0 to 2π??

What am I doing wrong? Convert r = 2sin\theta to an equation in rectangular coordinates.. x^2 +y^2 = r^2 x^2 + y^2 = 2y x^2 + y^2 - 2y = 0 x^2 + y^2 - 2y - 1 = 1 x^2 + (y-1)^2 = 1 Coordinates are (0,1) yes?

Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...

Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...

Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...

If you rotate your rectangular coordinate system (x,y) so that the rotated x'-axis is parallel to a vector (a,b), in terms of the (x,y) why is it given by x'=ax+by y'=bx-ay I got x'=ay-bx, y'=by+ax from y=(b/a)x. By the way this is from solving the PDE aux+buy=0 by making one of the...

Hi, I'm working on a project that would take a 3d image using stereocopic camera and would record the depth and the 2d (x1,y1) , (x2,y2) coordinates of a single point in the image. The depth is found using the focal point, disparity, and the distance between the difference the camera sees on...

Dear all, As I was reading my book. It said that the line element of a particular coordinate system (spherical) in R^{3} is so and so. Then it said that the metric is flat. I don't get how the metric is flat in spherical coordinate. Could someone shed some light on this please? Thanks

I just derived the 3-D Cristoffel symbol of the 2nd kind for spherical coordinates. I don't think I made any careless mistakes, but once again, I just want to verify that I am correct and I can't find any place on line that will give me the components of the symbol so I can check myself. Here...

I recently derived a matrix which I believe to be the metric tensor in spherical polar coordinates in 3-D. Here were the components of the tensor that I derived. I will show my work afterwards: g11 = sin2(ø) + cos2(θ) g12 = -rsin(θ)cos(θ) g13 = rsin(ø)cos(ø) g21 = -rsin(θ)cos(θ)...

I am setting up a numerical simulation from a 2D discretization of the heat equation in cylindrical coordinates. my spatial variables are radius (r), height (z), and azimuth (ø). The assumption is that there is no gradient along the azimuth direction (if temperature is T then dT/dø = 0)...

hi fellas, i have been given a graph from which i can extract the coordinates and the slopes but all i need is to generate the function this graph represents. can you suggest me any manual procedure to do this mathematically or do i have to use software to generate polynomial functions? if...

So I'm wondering, should I use Cartesian or Polar Coordinates to store intergalactic objects in DB? I'm currently prototyping a game idea that can be oversimplified as a spaceship simulator in infinite space. I'm considering grouping objects together so that they have a "parent super-space"...

Lim (x, y)->(0,0)(X^3+y^3)/(x^2+y^2) The answer is -1, but I can't get it there. Here is what I did. ((Rcosx)^3 +(rsinx)^3)/((rcosx)^2+(rsinx)^2) Then by factoring out a r squared from top and bottom I'm left with a denominator of (sin^2(x ) + cos^2 (x)) which simplifies to 1. And a numerator...

The conic equation has 2 versions in cartesian coordinates: The general: ##Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0## And the parametric: ##y^2 = 2px + (e^2-1)x^2## In polar coordinates, I known just the parametric: ##r = \frac{p}{1+e\cos(\theta)}## But exist a general form too?

Homework Statement The points O,A and B are vertices of an equilateral triangle. Find a and b O=(0,0) A=(a,11) B=(b,37) Homework Equations ##c^2=a^2+b^2## The Attempt at a Solution Let AB =c Then ##c=\sqrt{(a-b)^2+(11-37)^2}=\sqrt{(a-b)^2+676}## Since it is an equilateral triangle...

Three unit circles $C_1$, $C_2$ and $C_3$ in a plane have the property that each circle passes through the centres of the other two. A square $ABCD$ surrounds the three circles in such a way that each of its four sides is tangent to at least one of $C_1$,$C_2$ and $C_3$. $A=(0,0)$, $B=(a,0)$...

Hello everyone ,i have captured car positons at differents frames.http://www.imagesup.net/pt-7140205392313.png%5D%5BIMG%5Dhttp://www.imagesup.net/dt-7140205392313.png Suppose car's(left side car which is coming towards us) centroid is at video frame1 is P(x1,y1) and Q(x2,y2) at video frame4...

Hello! :) From the relations: $$\partial_{r}=\cos \theta \cdot \partial_{x}+ \sin \theta \cdot \partial_y$$ $$\partial_{\theta}=-r \sin \theta \cdot \partial_x+ r \cos \theta \cdot \partial_y$$ we get: $$\partial_y=\sin \theta \cdot \partial{r}+\frac{\cos \theta}{r} \cdot \partial_{...