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Questions tagged [coordinate-systems]

A set of numbers used to quantify location in space.

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Having some trouble with acceleration in polar coordinates

So, I solved a question about acceleration in polar coordinates, but most people in my class (Classical Physics, first year at university studying Physics) disagree with my answer. So the question is ...
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What are the points in spherical coordinates?

Let's use the spherical coordinates so that $\vec P=(r, \theta, \phi)$. In this context i've read that it's possible to write $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$$...
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Metric tensor $g$ for static gravitational field referred to static coordinate system

Assume there is static gravitational field. I want to deduce that there exists a coordinate system where $$g_{m0}=0, \quad m=1,2,3.$$ Is this a reasonable result? Why would it be contradictory if ...
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Differentiation of metric tensor in new coordinate

I want to understand the explicit meaning of $g_{\mu'\nu',\lambda}=0$ where unprimed coordinates are coordinates of the the original coordinate systems and primed ones are for new coordinate system. ...
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What's the meaning of the coordinates if we use a polar coordinate system?

In general, the coordinates of a vector are defined as the projections of it onto the coordinate axis. Moreover, in a polar coordinate system, the basis vectors $\hat e_\phi$, $\hat e_r$ depend on the ...
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Can we detect a cyclic coordinate by just inspecting the Lagrangian?

I'm reading through Susskind-Hrabovsky's Theoretical Minimum. On page 126, where they are talking about cyclic coordinates, an example is given: Suppose two particles moving on a line with a ...
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Trajectories in space

I want to say that a set $T$ of vectors in $R^{\,4}$ is a "trajectory" if there is an interval $I$, and continuous functions $x,y,z$ on $I$, such that $T$ is the set of $[t,x(t),y(t),z(t)]$ for $t$ in ...
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Direct derivation of point-like particle metric in GR

The usual way to derive metric of a point mass in general relativity is (to my knowledge) based on assuming specific form of the metric that reflects spherical symmetry and independence on "time" (...
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Lagrangian form of acceleration

Reading the Wikipedia article on Lagrangian mechanics I have problems to understand one basic proposition in the motivation of Euler-Lagrange equation. The article says: For me is unclear how the ...
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How to interpret negative time in Lorentz transformation?

I am somewhat confused about how to interpret negative time in Lorentz transformation. In the usual case of two reference systems S and S' where the distance X (the one that measures S) to an event, ...
36 views

Interval invariance under galilean transformation

If we have the classical distance between two points in euclidean space, we define: $S=(x^1)^2+(x^2)^2+(x^3)^2=\eta_{\mu \nu}x^\mu x^\nu$ If we want to make a coordinate transformaction of the ...
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Does the relative speed of time mean there is less energy where time is slower?

Time runs relatively slower near a planet than in outer space. Does this mean that there is less energy near the planet? Is there a relationship between energy and the speed of time? If so, this ...
35 views

Non-holonomic constraints, degree of freedom and generalized coordinates

If a system has $N$ coordinates and $M$ number of holonomic constraints then number of degree of freedom $=N-M$ and generalized coordinates $=N-M$ too. But if there are $k$ non-holonomic constraints ...
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Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$ What would be the physical implications if different ...
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“Newtonian limit” property of special relativity

Books say that special relativity is indistinguishable from Newtonian mechanics when the speed of the primed frame ($v$) is small compared to the speed of light ($c$). This is what I mean by the "...
418 views

Global Frame of Reference in General Relativity

People have been saying that a global frame of reference does not exist in General Relativity. However, from Wikipedia: In Schwarzschild coordinates $(t,r,\theta ,\phi )$ the ...
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Why is the force of gravity positive for an oscillating spring?

When analyzing the movement of a weight attached to a spring, many sources set up the force equation using newton’s second law as follows. $$mg-k(L+x)=ma$$ where $L$ is the length that the mass $m$ ...
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Time Dependence on Landau & Lifshitz's Proof of Poisson's Bracket Canonical Invariance

I'm reading Landau & Lifshitz's Mechanics and, at a certain point when discussing canonical transformations, they prove that Poisson brackets are canonical invariants. The proof starts with ...
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Intrinsic curvature calculation

Gauss theorem egregium says that it is possible for the inhabitants of a 2d surface to calculate the surface curvature without knowing that it is embedded in a 3d euclidean space, simply calculating ...
In chapter 9, Goldstein ($3^{rd}$ ed.) includes a discussion and a few "trivial special cases" of Canonical Transformation which keeps the form of the Hamiltonian unchanged and named it Identity ...