A set of numbers used to quantify location in space.

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1answer
1k 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
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1answer
399 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 ...
3
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4answers
475 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 ...
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0answers
86 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 ...
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1answer
568 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
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2answers
213 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
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1answer
901 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 ...
5
votes
1answer
2k 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
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1answer
3k 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
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1answer
158 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
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1answer
893 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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1answer
3k 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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1answer
231 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
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3answers
510 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
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1answer
300 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 ...
-1
votes
1answer
570 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.
6
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3answers
190 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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3answers
301 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 ...
1
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1answer
336 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 ...
5
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2answers
353 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 ...
0
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1answer
297 views

Accelerometer Orientation Conversion

Got two accelerometers that are measuring accelerations oriented at +/- 45 deg from horizontal. I am looking to determine the conversion of the accelerometer measured data to accelerations in the ...
5
votes
1answer
302 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 ...
14
votes
6answers
838 views

Proving that interval preserving transformations are linear

In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity: Prove ...
1
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3answers
8k 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 ...
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4answers
654 views

Why do Engineers manipulate coordinate systems? [closed]

When tackling a physics problem, An Engineer will manipulate the axes/coordinate system where a Mathematicians and/or Physicists will use the original coordinate system and math. Why do Engineers ...
2
votes
2answers
537 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?
0
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1answer
405 views

When are we now? Time coordinate system [closed]

The Second and the metre are well defined. We have those units available. Of course units are meant to express measurement, tools to compare with precision, and interchange that information ...
1
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1answer
435 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
721 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 ...
7
votes
2answers
496 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 ...