Questions tagged [coordinate-systems]
A set of numbers used to quantify location in space.
3,395 questions
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Definition of reference system in the context of General Relativity [closed]
I'm in trouble with the definition of reference system in the context of General Relativity intended as coordinate chart (i.e. no frame field).
Various sources define it as a one-to-one smooth mapping ...
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Relative motion interesting question [closed]
A rabbit begins at the origin, and the fox begins at the point (0,-a). The rabbit begins running east, with a constant speed v(x) along positive x axis. At the same time, the fox begins chasing the ...
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Is there a mistake in Susskind's "Theoretical Minimum" in chapter 4 "Systems of More than One Particle"?
On page 86, it says:
... the force on any one particle is a function of its location as well as the location of all the others. We can write this in the form
$$\vec{F}_i = \vec{F}_i(\{\vec{r}\})
$$
...
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Radar coordinates and smooth structures
Consider a time-orientable spacetime $M$ and two timelike particles Alice and Bob.
Radar coordinates are usually defined (operationally) in terms of messages and echos:
a particle Alice sends a pulse ...
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How do phase space coordinates represent field excitations within quantum optics?
I read this post that mentioned how phase space coordinates of position/momentum represent field excitations rather than physical position/momentum. I wanted to see if this could be expanded on with ...
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Proof verification for the necessary condition for a generating function to be a "generating function"
For a type 1 generating function $F(q,Q,t)$, the defining equations for a canonical transformation are
$$p_i = \frac{\partial F}{\partial q_i}(q,Q,t) \equiv f_i(q,Q,t), \qquad P_i = -\frac{\partial F}{...
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What is an inertial coordinate system? [duplicate]
A lot of posts have been made about the nature of inertial coordinate systems, but I did not find one that answered my doubts. I have a masters in math and am starting my PhD in mathematical physics ...
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Lorentz Transformations of a Sphere
My intuition is that a sphere is transformed into an ellipsoid by a lorentz transformation because the axes parallel to the boost must be contracted and the others, which are orthogonal to the boosts ...
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Radial coordinate transformation in General Relativity
I've been studying a paper by Alexander Vilenkin regarding Domain Walls and Cosmic Strings. Currently, I'm trying to reproduce the following coordinate change: We start we cylindrical coordinates and ...
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Physically allowed coordinate transformations between two inertial frames
I would like to derive that the Poincaré transformations are precisely the physically allowed transformations between inertial frames when imposing Einstein’s postulates of special relativity.
Using ...
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Christoffel symbols for Schwarzschild metric in cartesian coordinates
Some time ago I found the Christoffel symbols for Schwarzschild metric not only in the usual spherical coordinates but also in cylindrical coordinates and in cartesian ones. But I did not download ...
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Level Manifolds and Conserved Quantities
Define a dynamical system D, upon its manifold M. Say we have three quantities for D: $F_{1,2,3}$. Why is it that when taking a subsection of M as a level manifold $\text{M}_{f}$ defined by $F_{1} = ...
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Meaning of coordinate system 'varies smoothly' between neighbouring hypersurfaces
I am reading Gourgoulhon's 3+1 Formalism in General Relativity. In section 5.2, titled 'Coordinates Adapted to the Foliation', Gourgoulhon introduces coordinates on the spacetime manifold $\mathcal{M}...
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In differential geometry, is it possible to differentiate a basis without assuming a connection?
In classical mechanics and differential geometry, the notion of differentiation is often used in contexts where its underlying assumptions remain implicit. In particular, one frequently encounters the ...
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Question about the clock stopping in a moving frame
I am reading some pages about special relativity. I can understand and it seems that I have to agree that when I sit in a stationary frame, I have to conclude that a person moving in a constant speed ...
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