Coordinate Definition and 868 Threads

Hi Everyone, I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way: x = rcosθ Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...

Hello friends, If we consider ##{T}## as coordinate time and ##{\tau}## as proper time, the relationship between them is: ##\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}## so, ##{T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}## So we can consider this expression like this: If In...

Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra? If so, how?

Homework Statement Show that, owing to the rotation of the Earth on its axis, the apparent weight of an object of mass m at latitude λ is : m((g-ω^{2}Rcos^{2}λ)^{2}-(ω^{2}Rcosλsinλ)^{2})^{1/2} where ω is the angular velocity of the Earth and R its radius. The first space travellers to reach...

I've had to hit my books to help someone else. Ugh. Say we have the coordinate transformation \bf{x}' = \bf{x} + \epsilon \bf{q}, where \epsilon is constant. (And small if you like.) Then obviously d \bf{x}' = d \bf{x} + \epsilon d \bf{q}. How do we find \frac{d}{d \bf{x}'}? I'm missing...

1. Determine which of the three coordinate planes is closest to the center of the sphere(or indicate which planes are tied if two or more of the distances are the same) (s-7)^2+(y-7)^2+(z-7)^2=36 Homework Equations 3. Would i just try setting x,y,z in turns equal to 0 to find...

Homework Statement This is a 2 part question. I'm fine with the first part but the 2nd part I'm struggling with. The first part asks us to calculate the double integral, \int\intDx2dA for, D = {(x,y)|0≤ x ≤1, x≤ y ≤1} For this part I got an answer of 1/4. For the 2nd part we introduce a new...

Firstly; is there a difference between the "regular" polar coordinates that use \theta and r to describe a point (the one where the point (\sqrt{2}, \frac{\pi}{4}) equals (1, 1) in rectangular coordinates) and the ones that use the orthonormal basis vectors \hat{e}_r and...

Hey So, I was wondering how to convert from one coordinate axes to another... in particular, where the new axes are y = x and y = -x, as seen by the picture below I want it so that the Red dot in the new coordinate system will be (\sqrt2,0). Is there an easy way to do this? (My lookings on...

To specify a vector in cartesian coordinate systems,we assume its tail to be at the origin and give the cartesian coordinates of its head.What about other coordinate systems? For example,in spherical coordinates,is the following correct? a \hat{x}+b \hat{y}+c \hat{z}=\sqrt{a^2+b^2+c^2}...

I know that when you are integrated over dA in the xy plane, for your polar coordinates, x = rcosθ and y = rsinθ. However what about in the xz and yz plane? I noticed in one of the textbook problems, where the integration is over an area in the xz plane, x = rcosθ and z = rsinθ. How did the...

Homework Statement Tan A = -2/6 a) Draw two possible locations on the coordinate axis for the terminal arm of angle A b) Find two possible values for the measure of angle A and the related acute angle. Homework Equations c^2 = a^2 + b^2 SOHCAHTOA The Attempt at a Solution I know...

i don't really understand which quantities are thermodinamic coordinates and which are not. and what makes work and heat are not thermodinamic coordinates but temperature, volume, etc are thermodinamic coordinates?

I'm stuck on the second part of this question. Suppose a particle moves in a plane with its trajectory given by the polar equation $r=2b\sin(\theta)$ for some constant $b>0$. (i) Show that this can be written in Cartesian coordinates as $x^2+(y-b)^2=b^2$. This is the equation for a circle of...

In Wald's GR he makes use of a coordinate basis consisting of ∂/∂x^{n} where n runs over the coordinates, and I understand his argument that ∂f/∂x^{n} are tangent vectors, but I can't wrap my head around the operator ∂/x^{n} spanning a tangent space of a manifold. Any clarification on this would...

Dear All, I've been studying differential geometry for some time, but there is one thing I keep failing to understand. Perhaps you can help out (I think the question is quite simple): Can I use Cartesian coordinates to cover a curved manifold? I.e., is there an atlas that only contains...

Hi, could anyone tell me a reference on Navier-Stokes equation for the COMPRESSIBLE flow in CYLINDRICAL coordinate? Just can't find a good reference book. Thanks in advance. Jo

What Constitutes something being "coordinate free" People say that exterior calculus ie. differentiating and integrating differential forms, can be done without a metric, in without specifying a certain coordinate system. I don't really get what qualifies something to be 'coordinate free', I...

Homework Statement I've been reading through Spacetime Physics by Taylor & Wheeler, but this argument about the invariance of the y coordinate for inertial frames, one moving relative to the other on the x axis, is tripping me up. I'll just write the text word for word: I'm just not...

In general relativity, what are the total number of unknowns for a generic coordinate transform? Is it just 4 * 4 = 16? Is there a way to break those down into combinations of types, such as boosts, rotations, reflections (parity?), etc, or is it just left wide open from an interpretive...

Author: H.M. Schey Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus Amazon Link: https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20 Prerequisities: Calculus 1,2,3 Table of Contents: Preface Introduction, Vector Functions, and Electrostatics Introduction...

Consider a complex with Central Metal atom M A and B are monodentate ligands . Consider a compound with formula as [M A4 B2] . Textbook and the web says there can be only 2 possible isomers of this compound . What I say is, why can't I in the first image put A on the top and bring B...

I have this triangle and I know just the two sides indicated there. How can I find angle theta? I tried decomposing the triangle in two right triangles and using trigonometry find one side, but I can't figure how to do that using just the hypotenuse

I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...

let f = x2 + 2y2 and x = rcos(\theta), y = rsin(\theta) . i have \frac{\partial f}{\partial y} (while holding x constant) = 4y . and \frac{\partial f}{\partial y} (while holding r constant) = 2y . i found these partial derivatives by expressing f in terms of only x and y, and then in...

Hi all. What does it mean that a function in polar coordinates may not be a function in Cartesian coordinates? For example, r(\theta) = 1 + \sin\theta is a function because each \theta corresponds to a single value of r. However, in Cartesian coordinates, the graph of this function most...

Dear Friends Is there any coordinate tetrad in spacetime except Cartesian basis ? since tetrad basis should be orthogonal (( In Lorentzian description ))and the only orthogonal basis is Cartesian ( the metric is (+1,-1,-1,-1 ) but in any other coordinate basis like Spherical metric is (...

I would like someone to give this a quick check, I am really not sure if I am over thinking this question. I got the right ans, just would like a quick check of my method; big thanks in advance. question: P(-1,5), Q(8,10), R(7,5) & S(x,y) are the veritices of the parallelogram PQRS. Calculate...

Problem Solution answer For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.

We all know the ##\vec{i}##,##\vec{j}##,##\vec{k}## unit vectors for Cartesian space. But I've never been shown basis unit vectors in other coordinate systems. Do basis vectors exist in other coordinate systems? And if so what are they?

If i have a point at (0,0,5) in x,y,z system, then i make 2 rotation on the point with center at origin. i)the first rotation is on y-axis with angle P in clockwise direction. ii) the second rotation is on the point's new x-axis rotate in angle Q in clockwise direction. How can i find the...

Homework Statement How do I know that vector is invariant to changes of coordinate systems if i only have the components of the vector and not the basis vectors? Homework Equations let the vector in reference frame 1 be ds and the same vector in the reference frame 2 be ds1 The...

Hello! I have a problem. How can I convert a left part from picture which is in coordinate system (r, s) to coordinate system (x, y) and then to coordinate system (ζ, η) (right part). I need Jacobian matrix because of integration some function above this region. Any helpful links or...

Homework Statement Consider a function which depends only on a difference between two variables, and integrate it with respect to both: \int_a^b \int_a^b f(x-y)\, dxdy Is there any way to simplify this expression, like reducing it into a 1-D integral?

Hi PF, I have always wondered what was meant when my teachers told me that a vector is the same no matter what coordinate system it is represented in. What is it exactly that is the same? I mean the components change. So the only thing that I can see remains the same is the length of the vector...

I have an electromagnetic field with a Poynting vector that has the following form in spherical coordinates: $$\bar{P}(R,\phi,\theta)=\frac{f(\phi,\theta)}{R^2}\bar{e}_{r}$$ The exact nature of f(\phi,\theta) is not known. Suppose I measure the flux of this vector field by a flat area...

Hi, physics undergraduate here. I don't know much about differential geometry yet, but I'm curious about this idea: Say I encounter a boundary value problem, and I'm not sure what coordinate system would be 'easiest' to solve the problem in. Is there some way to put the differential...

Coordinate System--Spring Vertical Hi! This is a question on the use of a coordinate system. In the princeton review, I don't understand the coordinate system they are using it; it doesn't make sense. That is, for a vertical spring, the net force on the mass is kx-mg. But, shouldn't it be...

Hi all. I am very puzzled by the following. Let x_1 and x_2 be two coordinate systems related by x_1=1-x_2. Now if y(x_1) = x_1 and z(x_2) = 1-x_2, then clearly y(x_1)=z(x_2). Now integrating the function in each coordinate system gives Y(x_1) = \int y(x_1) dx_1 = \int x_1 dx_1 =...

Hi! I am currently working with a linear PDE on the form \frac{\partial f}{\partial t} + A(v^2 - v_r^2)\frac{\partial f}{\partial \phi} + B\cos(\phi)\frac{\partial f}{\partial v} = 0. A and B are constants. I wish to find a clever coordinate substitution that simplifies, or maybe even...

Consider a simple two particle system with two point masses of mass m at x1 and x2 with a potential energy relative to each other which depends on the difference in their coordinates V = V(x1-x2) The lagrangian is: L = ½m(x1')2 + ½m(x2')2 + V(x1-x2) Obviously their total momentum is conserved...

I am confused about one of the basic findings of relativity, that all coordinate systems are equal and there is no preferred coordinate system. A simple thought experiment is to consider three spacecraft called left, middle, and right. Left speeds off at half the speed of light in the left...

In McCauley's book Classical Mchanics: Transformations, Flows, Integrable and Chaotic Dynamics we are analyzing a coordinate transformation in order to arrive at symmetry laws. A coordinate transformation is given by q_i(\alpha) = F_i(q_1,...,q_f, \alpha). Then, to the first order Mccauley...

Hi I would like to know is there any way except using graph to find area element in cylindrical ( or Spherical) coordinate system? Thanks.

Just starting up school again and having trouble remembering some mathematics. Here's the problem. Find the inner product of ⃗a = (1, 45◦) and ⃗b = (2, 90◦), where these vectors are in polar coordinates (r, θ). Thanks =) 1st post here btw.

Homework Statement In the figure, let S be an inertial frame and let S' be another frame that is boosted with speed v along its x'-axis w.r.t. S, as shown. The frames are pictured at time t = t0 = 0: A) Find the Non-relativistic transformation (Galilean Transformation) between the two...

I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which represent the circle diameter and another point (P3) NOT on the circle but on its plane. Also known the length of the line from P2 to X, for example d. Another thing that may help, the...

Homework Statement For elliptical cylindrical coordinates: x = a * cosh (u) * cos (v) y = a * sinh (u) * sin (v) z = z Derive the relations analogous to those of Equations (168b-e) for circular cylindrical coordinates. In particular, verify that h_u = h_v = a * sqrt(cosh^2 (u) -...

Can someone help me with the conversion of this equation to Cartesian coordinates: [SIZE="4"]2cosθr + sinθθ (Due to formatting limitations, I just made the r_hat and theta_hat components bold-faced) I know the answer ought to be -(3y2)/[(x2+y2)+1] but I've tried every variation of the 3 main...

Okay I need to rotate a parabola on a cartesian coordinate system, y=x^2 by 90 degrees about the origin (either direction) without using piecewise, or inverse functions. Basically I am trying to use translations and deformations to accomplish this. Anyone thoughts?