The coordinate-systems tag has no wiki summary.
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3answers
130 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 ...
6
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2answers
380 views
Is there any situation in Physics where the Right Hand Rule is not arbitrary?
We use Right Hand Rule in calculating Torque not because that's the direction torque is pointing in the real, physical world, but because it's a convenient way to indicate the "sign" of the rotation ...
5
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2answers
201 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
votes
1answer
625 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 ...
4
votes
3answers
253 views
Is the equivalence principle strictly fulfilled by general relativity?
The equivalence principle states
The outcome of any local experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
Any real local ...
4
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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 ...
4
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1answer
391 views
Convert ECI coordinates to latitude/longitude?
I have been given output in (what I believe to be) ECI format (from OrbitTools):
...
3
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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 ...
3
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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 ...
3
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2answers
104 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 ...
3
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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 ...
3
votes
1answer
167 views
Is General Relativity applicable for all coordinate systems?
My understanding was that relativistic physics can be expressed in any inertial coordinate system, but not arbitrary systems. That is, no experiment can determine if we are "still" or "moving" at a ...
3
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1answer
909 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 ...
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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 ...
2
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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 ...
2
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2answers
183 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
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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 ...
2
votes
2answers
306 views
What is a Kustaanheimo-Stiefel transformation?
What is a Kustaanheimo-Stiefel transformation? Which applications has it in physics? Can you point me to a reference, where this transformation is explained?
2
votes
2answers
293 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 ...
2
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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 ...
2
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1answer
489 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 ...
2
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1answer
106 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
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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 $$dv/dr= ...
2
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0answers
62 views
Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?
Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
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0answers
479 views
Rotate vector in spherical coordinates
I have two arbitrary vectors $\vec{x}$ and $\vec{x}'$ given in spherical coordinates $(|\vec{x}|=x,\theta,\phi)$ (as convention I take the "physics notation" given on Wikipedia ...
1
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1answer
211 views
In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?
I was reading through this question on time and big bang, and @John Rennie's answer surprised me.
In the immediate environment of a black hole, where does time stop ticking if one were to follow a ...
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2answers
76 views
Coordinate and conformal transformations of the FRW metric
I'm considering a metric of the following form (signature $(+,-,-,-)$):
$$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
55 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
365 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
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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? ...
1
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1answer
320 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
177 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
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1answer
258 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 ...
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1answer
483 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
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1answer
69 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
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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:
...
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2answers
93 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
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3answers
4k 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
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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 ...
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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
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1answer
298 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 ...
1
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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 ...
1
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1answer
61 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 ...
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4answers
146 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
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2answers
280 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
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2answers
102 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 ...
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2answers
258 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 ...
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1answer
311 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}} .$$
Can anyone show me how to get this result?
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2answers
159 views
How was transformed an integral below?
I know how transform an integral below,
$$
\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} + ...
0
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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 ...
