The coordinate-systems tag has no wiki summary.
-2
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1answer
27 views
How to take integral of a spherical function $f_{(t,r,\theta,\phi)}$? [closed]
I know that volume integral is possible for a function of $f_{(r,\theta,\phi)}$ but How to take integral of a spherical function of $r$, $\theta$, $\phi$, which depend on time too?
...
1
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0answers
34 views
Wick rotation and relativity
CMIIW, but as I understand it, Wick rotation replaces the Minkowski basis (t,x,y,z) with the Euclidean basis (it,x,y,z). Suppose that $t_2=t_1 cosh \beta+x_1 sinh \beta$ and $x_2=t_1 sinh \beta+x_1 ...
0
votes
2answers
43 views
Is it incorrect to explain the direction of a coded vector quantity?
For example, let's say that in a linear physics problem, all the data are given to a certain direction, and coded positively for direction to the right.
So +5m/s would be a velocity of 5m/s to the ...
4
votes
1answer
79 views
Is orthogonality = mutual exclusiveness?
What does Euclidian orthogonality of 90° have in common with mutual exclusiveness?
It is paradoxical to me to hear that spin up state is orthogonal to spin down. If two elements are orthogonal, it ...
1
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0answers
31 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 ...
1
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4answers
175 views
How to get the angle needed for a projectile to pass through a given point for trajectory plotting
I am trying to find the angle needed for a projectile to pass-through a given point.
Here is what I do know:
Starting Point $(x_0,y_0)$
Velocity
Pass-through point $(x_1, y_1)$
I also need to ...
0
votes
1answer
47 views
Electromagnetic Tensor in Cylindrical Coordinates
I understand that the Electromagnetic Tensor is given by
$$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\
E_{x} & 0 & -B_{z} & B_{y}\\
E_{y} & B_{z} & ...
2
votes
2answers
33 views
Velocity in a turning reference frame
I often see the relation that $\vec v=\vec v_0+ \vec \omega \times \vec r$ in a turning reference frame, but where does it actually come from and how do I arrive at the acceleration being $$\vec ...
1
vote
1answer
64 views
How to assign coordinates to the elements of a flat metric space
Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements,
and consider the assignment $c_f$ of coordinates to (the elements of) set $M$,
$c_f ...
3
votes
0answers
125 views
Tensor equations in General Relativity
In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent.
Question: why is this true?
I'm looking for a ...
2
votes
1answer
53 views
Why does the Kruskal diagram extend to all 4 quadrants?
Why is it that the Kruskal diagram is always seen extended to all 4 quadrants when the definitions of the $U,V$ coordinates don't seem to suggest that the coordinates are not defined in, say, the 3rd ...
0
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1answer
197 views
Christoffel symbol for Schwarzschild metric
I know that the christoffel (second kind) can be defined like this:
$$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
-2
votes
1answer
47 views
How to smooth a path (and speed calculation) based on randomly timed coordinates? [closed]
first my actual problem. then my try on improving the current way of solving this with the wish for feedback or even a solution :)
gpx file with lat/long, elevation and time. wanna calculate speed... ...
3
votes
2answers
115 views
Explanation for Negative $\rho$ (radial distance) in Cylindrical Coordinates
My question : What does it mean when we arrive at negative values for distance variables like $\rho$ in cylindrical coordinates? (after some discussion here,I revised the question, at the end of the ...
0
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0answers
24 views
Coordinate transform to exploit symmetry
I have a stochastic process that can be described the following master-equation:
$$
\partial_{t}P(x,y)=-\left(W_{12}(x,y)+W_{13}(x,y)+W_{21}(x,y)+W_{23}(x,y)+W_{31}(x,y)+W_{32}(x,y)\right)P(x,y)\\
...
1
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1answer
66 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? ...
0
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0answers
46 views
coordinate change differential equation polar
I noticed that v [in step (2.5)] is not the same as the terms from the first formula, even if they are related..
I tried to understand how did he reach to this ...
1
vote
2answers
86 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
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1answer
72 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 ...
2
votes
1answer
112 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 ...
1
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1answer
167 views
Degrees of freedom in the infinite momentum frame
Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no ...
0
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0answers
39 views
Curved space to flat space calculation
When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
1
vote
1answer
51 views
Can we change frame of reference twice in a single problem?
My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and ...
0
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2answers
106 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
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1answer
33 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
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1answer
57 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 $\mathbf{p}$...
0
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0answers
47 views
Vector identities equivalence under different coordinates
I've learned to represent curl, rot and Laplacian in the general form using scaling factors, Levi Civita symbol and delta.
I was asked to prove some general identities in vector calculus.
I was ...
2
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0answers
92 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
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0answers
66 views
Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?
Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
2
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0answers
553 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 ...
0
votes
2answers
291 views
Role of unit vectors in cylindrical coordinates
I know how the unit vectors are defined in cylindrical coords. If I have a point P, how do I express it as a combination of the unit vectors uρ, uφ and uz. In the case of Cartesian coordinates this ...
1
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1answer
243 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 ...
0
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1answer
375 views
How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates?
How do I express the Kepler general orbit $r(\phi)$ in rectangular coordinates?
I use the identities $x=r\cos\phi$, $y=r\sin\phi$, and $r^2 = x^2 + y^2$, but I block at some point.
1
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1answer
324 views
RA/dec to Alt/Az program or method
I've been looking for a program to convert from RA/dec into Alt/Az; having used a couple of online versions I haven't seemed to find one yet that works reliably. I've tried to do it myself and half ...
6
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3answers
139 views
From Manifold to Manifold?
Tensor equations are supposed to stay invariant in form wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor ...
5
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2answers
210 views
Lorentz transformation in light cone coordinates in string theory
What is the explicit form of the Lorentz transformation changing the light cone coordinates in the light cone gauge in string theory? The extended nature of the strings complicate matters, especially ...
4
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1answer
425 views
Convert ECI coordinates to latitude/longitude?
I have been given output in (what I believe to be) ECI format (from OrbitTools):
...
1
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2answers
99 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 ...
0
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2answers
300 views
Vector Nature Of Angular Velocity
I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
2
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2answers
303 views
Does the length of the sidereal day vary systematically?
I'm confused about some properties of the sidereal day, in particular whether its duration varies systematically over the course of the year.1 It seems to me that that must be the case, but the ...
0
votes
1answer
350 views
How to get the gradient potential in polar coordinate
In polar coordinate,
$$\nabla U = \frac{\partial U}{\partial r}\hat{\mathbf{r}} + \frac{1}{r}\frac{\partial U}{\partial \theta}\hat{\mathbf{\theta}} .$$
Can anyone show me how to get this result?
2
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4answers
301 views
Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system?
I am a Physics undergraduate, so provide references with your responses.
Landau & Lifshitz write in page one of their mechanics textbook:
If all the co-ordinates and velocities are ...
3
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2answers
280 views
Centrifugal Force and Polar Coordinates
In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
2
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2answers
188 views
Coordinate transformation from earth to solar
I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already ...
2
votes
1answer
123 views
Mass Shell in Light Cone Coordinates
I'm reading Zweibach's introduction to string theory, and don't understand one of his claims.
He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
3
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7answers
394 views
Relation between coordinates and frames of reference
I always get a little uneasy that all the theories I can think of (at least since Newton) are constructed in a way such that they would be true in heaven and on earth ... but we can never go ...
3
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3answers
196 views
First Postulate of Special Relativity: What does it mean?
Wikipedia has this quote:
Special principle of relativity: If a system of coordinates K is
chosen so that, in relation to it, physical laws hold good in their
simplest form, the same laws hold ...
2
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1answer
104 views
What is the physical intepretation of harmonic coordinates?
When I see harmonic coordinates used somewhere, what should my association be?
Is there some general use or need to consider the harmonic cooridnate condition?
I don't really see what's ...
4
votes
1answer
690 views
Why is light described by a null geodesic?
I'm trying to wrap my head around how geodesics describe trajectories at the moment.
I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
2
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1answer
502 views
The trajectory of a projectile launched from a hilltop
Here is the problem:
A boy stands at the peak of a hill which slopes downward uniformly at angle $\phi$. At what angle $\theta$ from the horizontal should he throw a rock so that it has the greatest ...
