# Tagged Questions

A set of numbers used to quantify location in space.

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### Why do Newton's laws hold in a normal and tangential coordinate system?

In my book it says: 'When applying the equations of motions, it is important that the acceleration of a particle be measured with respect to a reference frame that is either fixed or translates with ...
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### How is Riemann tensor related to the curvature in the coordinates?

I came across statements such as "the acceleration observed in a weak gravitational field is mainly due to curvature in the time coordinate. " I want to know how we can explicitly find the curvature ...
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### Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
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### Spherical phase space dynamics

I have a hamiltonian of the form $$H(\phi,z) = (1-z^2)\cos(2\phi) + \chi z^2$$ with position $\phi$ and conjugate momentum $z$. It has this form provided that $z \in [-1,1]$ and we have natural ...
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### Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
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### The most general way to write flat space metric [closed]

What is the most general way to write flat space (in d=4 in particular), but still preserving some isometries? In particular I'm interested in the case with 2 isometries, basically by using explicitly ...
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### Locally remove a gravitational field

Let $K$ be an inertial frame of reference on $\mathbb{R}^3$ and $g=g(t,x)$ a nonuniform and nonstatic gravitational field. How I can choose a system of reference $\bar K$ such that mechanical effects ...
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### What are the components of r-hat in spherical coordinates?

so I've found a lot of identities that relate the spherical unit vectors to cartesian unit vectors. What is the expression for the spherical unit vectors IN spherical coordinates? I'm tying my brain ...
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### Inertial coordinate systems [duplicate]

In Newtonian mechanics, by the following two assumptions: (i) The time is absolute. (ii) The length is absolute. it is easy find the relations betweem two coordinate systems with uniform motion ...
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### What's the difference between the diffeomorphism invariance and reparametrization invariance?

Can somebody tell me what's the difference between the diffeomorphism invariance and reparametrization invariance?
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I have problem in understanding the result of stream function in Axisymmetric 3D flow: I know that the result is (for spherical coordinates): $$u_r=\frac{1}{r^2sin\theta}\frac{\partial\psi}{\partial\... 1answer 37 views ### Coordinate Transformation in Classical Mechanics The coordinates in one inertial frame are represented by (x,t). Under coordinate transformation, the coordinates in another inertial frame can be represented by f(x(t),t). It can be shown that the ... 0answers 36 views ### Interpreting meaning of coordinates given a metric I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. ds^2=-(1+2 \Phi(r))dt^2 + (... 1answer 65 views ### On the proof of the existence of geodesics coordinates [closed] From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is$$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} {...
The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as \begin{align} u&=t-r^*\\ v&=t+r^* \end{align} where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$ The ...
For a circular motion centripetal acceleration can be expressed as $$a_{c}=\frac{v^2}{R} \hat{u_N}\tag{1}$$ Where $\hat{u_n}$ is the normal unit vector. Nevertheless in the expression for ...