Coordinates Definition and 1000 Threads

So I'm reading the Schaum's outlines while trying to prepare for a big test I have in September. And I'm trying to understand something here that maybe someone can offer some clarification and guidance. So, using Coulomb's Law, we can find the electric field as follows: \begin{equation} dE...

Yes, that is a serious title for the thread. Could someone please define GENERALIZED COORDINATES? In other words (and with a thread title like that, I damn well better be sure there are other words ) I understand variational methods, Lagrange, Hamilton, (and all that). I understand the...

Ok, the reason for my absence is I have been working on a project of building a multitasking Robot. Since the connection of Robots to Physics never entered my mind I assumed I have nothing of value to add to any discussion on the PhysicsForums. If anyone is interested in the problem that I am...

This might be a specialized question and hopefully people working in this area know it. I need to get atomic coordinates for a specific crystal in SpringerMaterial. It however gives two different coordinates, standardized and published coordinates. I looked through the website can cannot find a...

According to this video the length of basis is r. It grows as we further from the origin . Why?

hi, I really wonder what the difference between curvilinear coordinates in a Euclidean space and embedding a curved space into Euclidean space is ? They resemble to each other for me, so Could you explain or spell out the difference? Thanks in advance...

First, I'd like to say I apologize if my formatting is off! I am trying to figure out how to do all of this on here, so please bear with me! So I was watching this video on spherical coordinates via a rotation matrix: and in the end, he gets: x = \rho * sin(\theta) * sin(\phi) y = \rho*...

Homework Statement Hi everybody! I would like to discuss with you a problem that I am wondering if I understand it correctly: Find expressions for the cartesian components and for the magnitude of the angular momentum of a particle in cylindrical coordinates ##(r,\varphi,z)##. Homework...

hi, I am just curious about, and really wonder if there is a proof which demonstrates that curvature tensor is 0 in all flat space coordinates. Nevertheless, I have seen the proofs related to curvature tensor in Cartesian coordinates and polar coordinates, but have not been able to see that zero...

Homework Statement I need to find the work done by the force field: $$\vec{F}=(5x-8y\sqrt{x^2+y^2})\vec{i}+(4x+10y\sqrt{x^2+y^2})\vec{j}+z\vec{k}$$ moving a particle from a to b along a path given by: $$\vec{r}=\frac{1}{2}\cos(t)\vec{i}+\frac{1}{2}\sin(t)\vec{j}+4\arctan(t)\vec{k}$$ The Attempt...

Hi all, i am having a problem with question 3, as its not clear if i should use the Z value for the camera as 15 or 25 m or... Could you suggest me. Cheers The goal of this project is to obtain some understanding of the camera’s motion in space. Also, based on the camera’s motion, we will...

There have been many questions on this forum about celestial mechanics in general, and concerning position and velocity in an orbit in particular. So I offer this post as a summary and reference. Here's a method for finding heliocentric position and sun-relative velocity in ecliptic coordinates...

Homework Statement Use spherical coordinates to find the volume of the solid enclosed between the spheres $$x^2+y^2+z^2=4$$ and $$x^2+y^2+z^2=4z$$ Homework Equations $$z=\rho cos\phi$$ $$\rho^2=x^2+y^2+z^2$$ $$dxdydz = \rho^2sin\phi d\rho d\phi d\theta$$ The Attempt at a Solution The first...

Homework Statement "Slopes of tangent lines Find the slope of the line tangent to the following polar curves at the given points. At the points where the curve intersects the origin (when this occurs), find the equation of the tangent line in polar coordinates." ##7.##...

I have this exercise: > $V_t=${$(x,y,z) \in \mathbb{R}^3: 1\leq x^2+y^2\leq t, 0\leq z \leq 1, y >0$} >$F:[1,+\infty[ \rightarrow \mathbb{R}$ the function: >$$\iiint_{V_t} \frac{e^{t(x^2+y^2)}}{x^2+y^2} \,dx\,dy\,dz$$ > Calculate $F'(4)$ Ok so the firs thing I did was to apply directly a...

I am trying to evaluate \int\int xy dxdy over the region R that is defined by r=sin(2theta), from 0<theta<pi/2. I am struggling on where to begin with this. I have tried converting to polar coordinates but am not really getting anywhere. Any guidance would be really appreciated (Crying)

Homework Statement Hi everybody! I might have solved that homework but I struggle to properly understand some steps, especially concerning the gradient and partial differentiation: The potential Φ(r) of an electric dipole located at the origin of a coordinate system is given by: \phi...

Hello, I have been I am trying to optimize a molecule (crowded) with the chemical formula C60H52O18P4S4W2. The problem arises after 2 days, which means that the initial geometry was not a problem. " GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad Berny optimization...

Ok, so randomizing three random variables, X, Y and Z, each from a standard normal distribution, then plotting these in an ordinary cartesian coordinate system gets me a spherically symmetric cloud of points. Now I want to create this cloud having the same probability distribution but by using...

Homework Statement Evaluate ∫∫D (3x + 4y 2 ) dA, where D = {(x, y) : y ≥ 0, 1 ≤ x 2 + y 2 ≤ 4} with the use of polar coordinates. Homework Equations The Attempt at a Solution I made a sketch of the circle. It's radius is = 1 and it's lowest point is at (0,0), highest at (0,2), leftmost point...

Homework Statement Using the cylindrical polar co ordinates ##(ℝ,θ,z)## calculate the gradient of ##f=ℝ sin θ + z^2## the textbook says that the scale factors are ## h1=1, h2=ℝ & h3=1## how did they arrive at this?[/B]Homework EquationsThe Attempt at a Solution ##h1=|∂f/∂ℝ|= sin θ...

The Center of the Milky Way Galaxy is located at Sagittarius A*. https://en.wikipedia.org/wiki/Sagittarius_A* The J2000 position is: Right ascension 17h 45m 40.0409s Declination −29° 0′ 28.118″ Distance 25,900 ± 1,400 ly How do you find the Right Ascension and Declination for other Julian...

I was looking at the Static Weak Field Metric, which Hartle gives as: ##ds^2 = (1- \frac{2\Phi(x^i)}{c^2})(dx^2 + dy^2 + dz^2)## For a fixed time. Where, for example, ##\Phi(r) = \frac{-GM}{r}## I was trying to figure out how the coordinates (x, y, z) could be defined. Clearly, they can't...

H! I wonder how to solve: I=\int_{-\infty}^{\infty}e^{-u^2}\frac{1}{1+Cu} du I have solved: \int_{-\infty}^{\infty}e^{-u^2}du which equals \sqrt{\pi} and I solved it with polar coordinates and variable substitution. Thankful for help! Edison

1. A particle of mass m initially at rest at the origin is acted upon by a force (vector) F = xi+yj+zk. Its position vector after t seconds areI need instructions on solving this

Why is ##a_{ji}dG_j'=dG_i'## ? from the third last line below. ##G_i=a_{ji}G_j'## because a vector labelled by the space axes is related to the same vector labelled by the body axes via a rotation transformation. If ##a_{ji}dG_j'=dG_i'##, then we are saying a vector ##dG'## labelled by the...

The Schwarzschild radial coordinate ##r## is defined in such a way that the proper circumference of a sphere at radial coordinate ##r## is ##2\pi r##. This simplifies some maths but creates some rather odd side-effects, so to get a more physical picture I like to use isotropic coordinates...

I'm sure this is a simple concept but i just can't wrap my brain around it, the question is: a) Express the following vectors in terms of x-y coordinates: i)Vector V with direction π/6 and magnitude 4√3. ii) Vector W with direction 5π/4 and magnitude 4√2. b) Express the vector v + w in terms...

Homework Statement This is a physics olympiad problem; and I am still struggling with it. I will quote it here: " A particle moves along a horizontal track following the trajectory $$r=r_{0}e^{-k\theta}$$, where $$\theta$$ is the angle made by the position vector with the horizontal. Recall...

Hello, I am studying on my own from Weinberg's Gravitation and Cosmology and I cannot understand how he derives a solution (pg. 72). I did not know where else to post this thread since it is not homework exercise. He takes a coordinate system ## \xi^a## "in which the equation of motion of a...

Hi all I am conducting a fluid analysis on water flowing through a subsea pipe. Having used navier stokes equation, i derived the equation for velocity in the r-direction (using cylindrical coordinates. But when initially solving the energy equation to determine temperature distribution I...

How do you convert to "Of Date" or "Apparent" coordinates from "J2000" coordinates? The website: http://ssd.jpl.nasa.gov/horizons.cgi#results there are two options for displaying RA and DEC: Astrometric and Apparent. Astrometric is the J2000 coordinates and Apparent is the "Of Date"...

Homework Statement The problem asks for a single triple integral (the integrand may be a sum but there must be a single definition for the bounds of the integral) representing the volume (in the first octant) of the shell defined by a sphere of radius 2 centered around the origin and a sphere...

Homework Statement transform the following vectors to spherical coordinates at the points given 10ax at P (x = -3 , y = 2, z=4) Homework Equations x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ The Attempt at a Solution ax vector can be expressed ar,aθ,aφ so, I can change x ...

The problem is << transform the following vectors to spherical coordinates at the points given 10ax at P (x = -3 , y = 2, z=4)>> Actually, My first language isn't English, please understand that. x y z can be chage into x = rsinθcosφ , y=rsinθsinφ , z=cosθ ax vector can be expressed...

Homework Statement Determine the center of mass in cylindrical coordinates of a cone with constant density ##\rho(\vec{r})##. (The cone is inverted, i.e. it's thinnest point is at ##z=0##.) Homework Equations ##m=\int\int\int_C \rho r \, drdzd\theta## ##\overline{r}=\int\int\int_C r\cdot r\...

Hello! Good morning to all forum members! I am studying general relativity through the wonderful book: "General Relativity: An Introduction for Physicists" by M.P. Hobson (Cambridge University Press) (2006). My question is about Riemannian manifolds and local cartesian coordinates (Chapter 02 -...

Homework Statement B⃗ = -2.0ι^ + 3.0 j^. Find the polar coordinates r and theta. Homework Equations n/a The Attempt at a Solution r=sqrt((-2.0)^2+(3.0^2)) r = 3.6 theta = tan^-1(3/-2) = -56 degrees The answers seem to be wrong, can I get any guidance on this question please?

Homework Statement Derive the Lorentz Transformation using light cone coordinates defined by ##x^±=t±x## ##x^+ x^-~## is left invariant if we multiply ##~e^φ~## to ##~x^+~## and ##~e^{-φ}~## to ##~x^-~##, that is ##~x'^+ x'^-=x^+ x^-## Homework Equations ##t'^2 - x'^2 = t^2 - x^2...

Homework Statement Consider Minkowski space in the usual Cartesian coordinates ##x^{\mu}=(t,x,y,z)##. The line element is ##ds^{2}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}=-dt^{2}+dx^{2}+dy^{2}+dz^{2}## in these coordinates. Consider a new coordinate system ##x^{\mu'}## which differs from these...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's conversation on computations with tangent vectors and pushforwards ... in particular I need help with a further aspect of Lee's...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's conversation on computations with tangent vectors and pushforwards ... in particular I need help with an aspect of Lee's exposition...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I have some further questions concerning Lee's conversation on computations with tangent vectors and pushforwards ... The relevant conversation in Lee is as follows: In the...

Show that, in polar coordinates, the system is given by r′ = r(r^2 − 4) θ′ = 1x′1 = x1 − x2 − x1^3 x′2 = x1 + x2 − x2^3

Hello I've been having trouble finding the curl of A⃗ = r^2[e][/Φ]. Could someone help me please?

Hi, I'm trying to understand toroidal coordinates, that are a 3D version of bipolar coordinates. Well, I don't understand any of them, already cheked wiki and wolfram sites, but they don't give any clear explanation (in my opinion). Is there a way to get an intuition for obtaining the...

Homework Statement I have to find the Laplace operator asociated to the next quasi-spherical curvilinear coordinates, for z>0. Homework Equations \begin{align} x&=\rho \cos\phi\nonumber\\ y&=\rho \sin \phi\nonumber\\ z&=\sqrt{r^2-\rho^2}, \end{align} The Attempt at a Solution I computed...

I'm reading A. Zee's GR book and I'm in the section in which he is showing how to transform coordinates to be locally flat in a neighborhood of a point. He said that we can always choose our neighborhood to be locally flat for any space of any dimension D. "Look at how the metric transforms...

Homework Statement Find the locally flat coordinates on the Poincaré half plane. Problem I.6.4 by A. Zee Homework Equations [/B] Poincaré Metric: ##ds^2 = \frac{dx^2 + dy^2}{y^2}## The Attempt at a Solution First, I'm having problems with the explanation in Zee's book. He said that we can...

I know that an arc length in polar coordinates can be computed by integrating $$\int ds$$ using the formula ##ds=\sqrt{\rho^2 + \frac{dr}{d\theta}^2}d\theta##. But, seeing that ##s=\rho\theta## and ##ds = \rho d\theta##, why is it wrong to calculate arc lengths with this expression for ##ds##?