The coordinate-systems tag has no wiki summary.
1
vote
0answers
75 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
49 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
votes
1answer
124 views
Christoffel symbol for Schwarzschild metric
I know that the christoffel (second kind) can be defined like this:
$$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
-2
votes
1answer
37 views
How to smooth a path (and speed calculation) based on randomly timed coordinates? [closed]
first my actual problem. then my try on improving the current way of solving this with the wish for feedback or even a solution :)
gpx file with lat/long, elevation and time. wanna calculate speed... ...
3
votes
2answers
105 views
Explanation for Negative $\rho$ (radial distance) in Cylindrical Coordinates
My question : What does it mean when we arrive at negative values for distance variables like $\rho$ in cylindrical coordinates? (after some discussion here,I revised the question, at the end of the ...
0
votes
0answers
20 views
Coordinate transform to exploit symmetry
I have a stochastic process that can be described the following master-equation:
$$
\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
vote
1answer
61 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
votes
0answers
44 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
78 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 ...
2
votes
1answer
109 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
vote
1answer
70 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 ...
0
votes
0answers
37 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?
0
votes
2answers
104 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
49 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 ...
1
vote
1answer
29 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
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
votes
0answers
45 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
votes
0answers
89 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= ...
1
vote
4answers
151 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 ...
1
vote
1answer
63 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 ...
2
votes
0answers
63 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
votes
0answers
495 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
215 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
163 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 ...
1
vote
2answers
94 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
votes
2answers
260 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
votes
2answers
294 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
2answers
281 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 ...
0
votes
1answer
319 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?
3
votes
2answers
272 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
votes
2answers
184 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
119 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
votes
3answers
193 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
votes
1answer
103 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 ...
3
votes
7answers
390 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 ...
2
votes
1answer
490 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 ...
4
votes
1answer
215 views
failing to see the conundrum in the Einstein hole argument
I've been reading about the Einstein hole argument, and i fail to understand what makes active diffeomorphisms "special" compared to passive diffeomorphismsm also known as good old coordinate ...
2
votes
4answers
292 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 ...
0
votes
0answers
75 views
is it possible to construct a contravariant basis in 1D
why is the magnitude of the basis vector at the point differ by a scale factor when considering the tangent as compared to the normal to the coordinate surface?
what exactly is the coordinate surface ...
1
vote
1answer
322 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 ...
0
votes
2answers
159 views
How was transformed an integral below?
I know how transform an integral below,
$$
\iint f(\mathbf v_{1})f(\mathbf v_{2})d^3\mathbf v_{1}d^3\mathbf v_{2},
$$
using relative speed coordinates: we just use
$$
m_{1} \mathbf v_{1} + ...
1
vote
1answer
302 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 ...
4
votes
1answer
628 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 ...
0
votes
1answer
1k views
Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?
I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
1
vote
1answer
110 views
How to explain relativistic mass with 2 moving systems, but not 3?
All the visual explanations I know work in some kind of "If you are moving relative to something A, while inside A something is moving, the stuff in A has to move slower due time dilation and ...
4
votes
1answer
395 views
Convert ECI coordinates to latitude/longitude?
I have been given output in (what I believe to be) ECI format (from OrbitTools):
...
3
votes
1answer
917 views
Force from point charge on perfect dipole
Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole.
I'm having more than a little difficulty ...
1
vote
1answer
178 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 = ...
0
votes
3answers
273 views
Need some basic help with notation and the Christoffel symbols
Apologies in advance if some of the questions below seem overly simple.
In an introductory GR book, I find the following expression for the autoparallel of the affine connection (the upper bound of ...
0
votes
1answer
221 views
Is spherical coordinates enough to calculate the exact position of a point with rotations included?
With "Geographic coordinate system" we only get the location, no rotations or anything. Translated into latitude and longitude.
Where with "Spherical coordinate system", we should be able to get the ...
