Coordinates Definition and 1000 Threads

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 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?

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...

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##?

The following integral arises in the calculation of the new density of a non-uniform elastic medium under stress: ∫dx ρ(r,θ)δ(x+u(x)-x') where ρ is a known mass density and u = ru_r+θu_θ a known vector function of spherical coordinates (r,θ) (no azimuthal dependence). How should the Dirac...

Homework Statement Provide an expression in Cartesian coordinates for a plane wave of amplitude 1 [V/m] and wavelength 700 nm propagating in u = cosθx + sinθy direction, where x and y are unit vectors along the x and y-axis and θ is the measured angle from the x axis. Homework Equations...

Homework Statement Homework EquationsThe Attempt at a Solution I have stared at this for hours and don't know where to start. I think I need to get r in terms of t but I don't really know how with the information given. I just need a good hint to get started.

Homework Statement Sketch each of the following vector fields. E_5 = \hat \phi r E_6 = \hat r \sin(\phi) I wish to determine the \hat x and \hat y components for the vector fields so that I can plot them using the quiver function in MATLAB. Homework Equations A cylindrical coordinate...

Homework Statement We need to find the shortest distance between two given cities. For this I'll use Bangkok, Thailand (13°N, 100°E) and Havana, Cuba (23°N, 82°W ). Earth is assumed to be perfectly spherical with a radius of 6.4x106m. These aren't the places we were given but the coordinates...

I have seen both rk and qj both used to represent generalized coordinates in the Lagrange equations. Are these both the same things? Does it matter which you use? Thanks!

Hello people! I have ended up to this integral ##\int_{φ=0}^{2π} \int_{θ=0}^π \sin θ \ \cos θ~Y_{00}^*~Y_{00}~dθ \, dφ## while I was solving a problem. I know that in spherical coordinates when ##\vec r → -\vec r## : 1) The magnitude of ##\vec r## does not change : ##r' → r## 2) The angles...

Hi this isn't my homework, but it is taken from a worksheet for a Maths course(trying to refresh my rusty math), so I hope it fits in here. 1. Homework Statement two cylindrical polar vectors with same origin: P(2,55°,3); Q(4,25°,6) units in m Homework Equations a) Express in cartesian...

What is the physical interpretation of Cartesian coordinates in GR? Say, e.g., a system centered at the center of a spherical mass. What are x,y, and z physically, i.e., how are they measured?

I'm stuck on a seemingly simple 2D electrostatics problem. The problem is as follows: A parabolic interface ($$x(y)=cy^2$$) separates two regions of different conductivities, with a uniform electric field at infinity aligned with the x-axis. I write the Laplace operator in parabolic...

I am looking at this derivation of velocity in spherical polar coordinates and I am confused by the definition of r, theta and phi. http://www.usna.edu/Users/math/rmm/SphericalCoordinates.pdf I thought phi was the co latitude in the r,θ,∅ system and not the latitude. Of course the two are...

First post ! I hope that my question will not make some long time physicists laugh. It is about geometrical quantization and the phase space in which we use : z=1/sqrt(2)(q+ip) My question is simple what is this 1/sqrt(2) ? And what is it is interpretation ? Thank you !

I am looking to understand more about ##a=(\ddot{r}-r(\ddot{\theta})^2)\hat{r}+(r\ddot{\theta}+2\dot{r}\dot{\theta})\hat{\theta}## I understand the terms ##\ddot{r}## and ##r\ddot{\theta}## ,but why ##-r(\ddot{\theta})^2## has opposite direction to ##\hat{r}## and why ##2\dot{r}\dot{\theta}##...

Homework Statement A sphere of mass M and Radius R had two spheres of R/4 removed. the centres of cavities are R/4 and 3R/4 from the centre of the original sphere (at x=0). what is the x coordinate of the centre of mass of this object? there is a drawing next to the question literally showing...

Homework Statement Find the volume of the solid lying inside both the sphere x^2 + y^2 + z^2 = 4a^2 and the cylinder x^2 + y^2 = 2ay above the xy plane. Homework Equations Polar coordinates: r^2 = x^2 + y^2 x = r\cos(\theta) y = r\sin(\theta) The Attempt at a Solution So I tried this...

I was just trying to write out the derivation for an object's trajectory from an inertial coordinate system if the object is rotating in another coordinate system (e.g. finding Coriolis, centrifugal acceleration). I seem to have gotten something close to what I was looking for, but after...

Homework Statement Homework EquationsThe Attempt at a Solutionhere is the setup for each, can someone check if they are correct before I evaluate the volume?