# Questions tagged [coordinate-systems]

A set of numbers used to quantify location in space.

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### What does spacetime interval really mean? [duplicate]

Is there any simple way to intuitively understand spacetime interval, proper time and proper length?
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### How to find position vector in Kepler orbit?

As the title says, I am trying to determine the position vector $r$, knowing true anomaly, semi-major axis, angular momentum and eccentricity vector. There is an equation describe the distance to the ...
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### Translation of coordinates to generalised coordinates

The translation form $r_i$ to $q_j$ language start forms the transformation equation: $r_i=r_i (q_1,q_2,…,q_n,t)$ (assuming $n$ independent coordinates) Since it is carried out by means of the ...
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### Canonical transformation such that Hamiltonian of a freely falling body becomes $H'(P,Q)=P$

Can someone please help me with this problem I am unable to find a suitable generating function? The question says: To find a canonical transformation such that Hamiltonian of a freely falling body ...
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### Linear algebra as a gauge theory

Is linear algebra a gauge theory? Is the gauge transformation a change of basis? This was the explanation that I received: "Take the principal bundle to be the frame bundle $LM$ of your space $M$...
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### How do you find the proper separation between two spacetime points?

Suppose you had two points in space-time A and B, where A = (t1, χ1, θ1, φ1) and B = (t1, χ2, θ1, φ1). How would you use the FLRW metric to find the proper separation? In this case the points occur ...
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### Computing total power from $x$, $y$, $z$ components of Poynting vector

I have (real parts) of $x$, $y$, $z$ components of Poynting vectors on the surface of a sphere. Since the total outward power flow from the sphere involves integrating the normal component of a ...
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### What are the Lorentz Transformations between polar coordinates? Or can Lorentz Transformations be Non-Linear?

This question rises from the comments on @G Smith's answer's to this question https://physics.stackexchange.com/a/603032/113699 Precisely I was trying to understand the Lorentz Transformations between ...
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### Understanding proper-time as “evenly spaced gradations” on the worldline?

In this video series on relativity, proper-time is explained as "evenly spaced gradations" along a particle's worldline. Here is a screenshot: Suppose I carry a clock with me that ticks at ...
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### Why is a metric necessary in SR?

Simple question since I don't fully understand the purpose a metric fulfills when looking at relativistic kinematics for example.
### Can I use the spacetime interval even if origins are not equal at $t=t'=0$?
Can I use the relativity formula $(\Delta s)^2 = (c \Delta t)^2 - (\Delta r)^2$ even when observers did not start at the same origin at $t=t'=0$? I know this is constant, but is it constant even if ...
Hello, I don't quite see why should the angle between $\hat{\dot{\theta}}$ and the projection of $\hat{\dot{\phi}}$ onto the $x_0$, $y_0$ plane be a right angle. Does it have something to do with pure ...