A set of numbers used to quantify location in space.

learn more… | top users | synonyms

2
votes
0answers
89 views

What do the components of light velocity look like in polar coordinates?

The Schwarzschild solution makes use of polar coordinates, and I'm wondering how the different components of velocity of light change with the position. Might I get some examples of light velocity ...
2
votes
1answer
186 views

Privileged coordinate system (or lack thereof) in general relativity

What does the following statement mean and why is it true? The Weak Equivalence Principle (WEP) implies that in general curved space-time there is no privileged coordinate system. I have looked ...
2
votes
0answers
153 views

Falling into a black hole emitter vs observer

Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole. Suppose we define the quantity $$u=t- v$$ where $$dv/dr= ...
2
votes
0answers
2k views

Rotate vector in spherical coordinates

I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
1
vote
1answer
4k views

In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?

I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a ...
1
vote
1answer
64 views

On the proof of the existence of geodesics coordinates [closed]

From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is $$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} ...
1
vote
1answer
39 views

$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
1
vote
3answers
240 views

How can we define a frame of reference in general relativity?

I have started reading general relativity. (A First Course in General Relativity, Bernard Schutz). I am finding very hard to understand a frame of reference. When I was reading special relativity ...
1
vote
2answers
283 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
1
vote
5answers
773 views

Is the polar coordinate system non-inertial or inertial?

Consider a car driving around in a circle lying in the plane and suppose we were interested in determining its acceleration as measured by an observer stationary on the "ground" or whatever. ...
1
vote
2answers
399 views

Coordinate and conformal transformations of the FRW metric

I'm considering a metric of the following form (signature $(+,-,-,-)$): $$ds^2 = (F(r,t)-G(r,t))dt^2 - (F(r,t)+G(r,t))dr^2 - r^2(d\Omega)^2$$ where $F(r,t)$ and $G(r,t)$ are arbitrary scalar ...
1
vote
1answer
141 views

From momentum to solid angle

Why $d^3\mathbf{p}=p^2\;dp \; d\Omega$ ? where $d\Omega$ is the solid angle that covers a particle with 3-momentum $\mathbf{p}$...
1
vote
1answer
510 views

Does change of coordinate system require acceleration?

This question came about from a side discussion that arose on this: Does GR provide a maximum electric field limit? Can we change our choice of coordinate system completely independent of physical ...
1
vote
2answers
107 views

Killing field in Minkowski space-time

If we look at the killing equation for a vector field $X$ in $\mathbb{R}^{(p,q)}$ (or on an open subset thereof) in coordinates with constant diagonal pseudo-metric we get: ...
1
vote
3answers
81 views

Prove that the spacetime interval is not invariant under Galilean transformations [closed]

The spacetime interval $(\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - c^2(\Delta t)^2$ is invariant under the Lorentz transformation and this isn't the case for the Galilean ...
1
vote
1answer
69 views

A particular coordinate transformation of a metric tensor

So, this was a problem set question for my GR class due yesterday, and I can't for the life of me solve it, it seems I am missing something very trivial. Either the given answer is wrong, or I am. ...
1
vote
1answer
1k views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
1
vote
1answer
875 views

How can I find the motion equations of the 2-dim harmonic oscillator?

First of all: I am no physicist, so I am rather helpless. I need to find the moving equations of the 2-dim. harmonic oscillator. If it is possible it should be rather elementary, because, as I said, ...
1
vote
2answers
892 views

What is the physical meaning of the Eddington-Finkelstein coordinates?

What is the physical meaning of the Eddington-Finkelstein coordinates? I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this ...
1
vote
1answer
2k views

Christoffel symbol for Schwarzschild metric

I know that the christoffel (second kind) can be defined like this: $$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
1
vote
1answer
730 views

Can false origin be anywhere in a graph?

Can I start labeling my $x$ and $y$ axes from non-zero values when drawing a graph? Or is there any convention to only label $x$-axis from non-zero value when using a false origin and not $y$-axis? ...
1
vote
1answer
927 views

Trajectories using Polar Coordinates

Once I asked my teacher how to find the trajectory of any particle that is acted upon any force.(Generally) He Told me that I couldn't do it as I did not know polar coordinate geometry as of then but ...
1
vote
1answer
265 views

Inverting Generalized Coordinates

In Corben's classical mechanics on pg. 9, it says that given generalized coordinates $q_m = q_m(x_1, ..., x_n,t)$, then if the Jacobian is non-zero everywhere, you may express $x_i = ...
1
vote
1answer
437 views

Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity

I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
1
vote
1answer
960 views

converting force from spherical to Cartesian coords

So I am working on my assignment, and have a question about converting coordinates. I dont know whether I should ask here or the math SE, so lets give it a try here. The force in question is ...
1
vote
1answer
63 views

Is it correct to think about a point in time as the set of positions of all “things”?

Is it correct to think about a point in time as the set of positions of all "things" (photons, electrons, etc) that exist in the universe at that moment, despite the fact that simultaneity is ...
1
vote
1answer
66 views

Difference between local inertial frame and coordinate chart

In the most cases the local inertial frame is definied "physically" but I'm searching for a mathematically meaningful definition of the local inertial frame to solve my problem: Is the local ...
1
vote
1answer
50 views

Shear stress in cylindrical coordinates?

In cylindrical coordinates the momentum flux is given by (in the $r$ direction): $$ \Pi=-\eta \frac{\partial (r\omega)}{\partial r}$$ Where $\eta$ is the viscosity. Therefore one would expect that the ...
1
vote
1answer
72 views

Clarification in deriving the radial momentum operator $p_r$

In deriving an expression for $p_r$, a particle's radial momentum, I am unsure what is happening at a certain step. The derivation given in The Physics of Quantum Mechanics by Binney and Skinner is as ...
1
vote
1answer
93 views

What is the function type of the generalized momentum?

Let $$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$ denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action ...
1
vote
2answers
259 views

Do rotation matrices rotate about inertial or body angles? [closed]

I have Yaw, pitch, and roll angles in that order (Euler 321) to apply to a body reference frame in cartesian coordinate system. I want to know what the body reference frame vector coordinates are ...
1
vote
1answer
73 views

Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality

In Roger's book, the following is stated: (I'm paraphrasing because my book is in spanish) "We consider time as part of a space, namely $\mathbb{E}^1$, instead of it just being a copy of the line ...
1
vote
1answer
159 views

Is metric tensor invariant under rotation?

It is said that metric tensor depend on the local coordinate system and therefore are not intrinsic to the surface of an 3d-object? How is it possible, kindly provide any proof or discussion. Also is ...
1
vote
2answers
558 views

Is a double integral required to find the moment of Inertia of a non-uniform sphere?

Consider some ball of given radius $R$, with a mass density function that depends on the radial variable, $\rho=\rho(r)$ where $r$ is the distance from the center of the sphere. What is the moment ...
1
vote
2answers
383 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
1
vote
1answer
114 views

How big or small is a reference frame in Relativity?

What exactly is a frame of reference? Does it have an objective existence and if so what is it? What's the size of a reference frame? Is a reference frame the same size for a stationary frame of ...
1
vote
1answer
2k views

Radians to Rotate Earth to Match ECI Lat/Lon with ECEF Lat/Lon

I am attempting to model GPS Satellite positions on the globe for a set of ephemerides. I have a verified set of ECI ( http://en.wikipedia.org/wiki/Earth-centered_inertial ) XYZ Coordinates and a ...
1
vote
2answers
217 views

What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
1
vote
1answer
110 views

Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?

In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime. If I ...
1
vote
2answers
152 views

How big is an inertial frame?

How big is an inertial frame? Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year. Thus light from its end closer to the fixed point to the end farther ...
1
vote
1answer
159 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
1
vote
2answers
483 views

What does “equinox of date used” mean?

The documentation for an API I often use for quick astronomical modeling and figure drawing says Positions are given in FK5 heliocentric coordinates in the equinox of the date used. What does ...
1
vote
4answers
4k views

When an object moves downward, is its height negative?

The question is: A ball is thrown directly downward with an initial speed of 8.00m/s from a height of 30.0m. After what time interval does it strike the ground. So I went through the problem ...
1
vote
3answers
15k views

Find radius of curvature, given a velocity vector and acceleration magnitude?

The particle P moves along a space curve. At one instant it has velocity $v = (4i-2j-k)$ $m/s$. The magnitude of the acceleration is 8 $m/s^2$. The angle between the acceleration and the velocity ...
1
vote
1answer
40 views

Time variable in Lorentz transformations

When an object goes with a speed near from the light celerity, it inflates in the direction of its speed. The inflation rate is given by Lorentz transformations as follows: $x'= γ(x-vt)$ where $v$ ...
1
vote
3answers
125 views

Is the local Lorentz transformation a general coordinate transformation?

There is a saying in Nakahara's Geometry, Topology and Physics P371 about principal bundles and associated vector bundles: In general relativity, the right action corresponds to the local Lorentz ...
1
vote
3answers
179 views

Covariant and contravariant 4-vector in special relativity

I've just learned about contra- and covariant vector in the context of special relativity (in electrodynamic) and I'm struggling with some concept. From what I found, an intuitive definition of ...
1
vote
2answers
178 views

How can I convert Right Ascension and declination to distances?

I am calculating galaxy rotation curves for various galaxies in Ursa Major cluster and I want distance of those galaxies from the centre of Cluster. The values referred as coordinated are RA and dec ...
1
vote
1answer
112 views

Conversion of satellite coordinates from ITRF to J2000

I have coordinates of various satellites in two coordinate systems: Cartesian coordinates in the international terrestrial reference frame (ITRF) RA / DEC in J2000 epoch, as derived from plate ...
1
vote
1answer
64 views

$\frac{d}{dr}=0$ and $\frac{d}{dz}=0$ (cylindrical coordinates) for a 1D ring

In http://ritchie.chem.ox.ac.uk/Grant%20Teaching/2010/Lecture%204%202010.pdf slide 21 of 26, he says "Radius of ring is fixed and so derivatives in $r$ are 0." Presumably this goes for ...