A set of numbers used to quantify location in space.

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43 views

Description of charged circle with Dirac delta function in Cartesian coordinates [on hold]

I need to describe density of charge of uniformly charged circle ($x^2+y^2=R^2$; $z=0$, total charge $Q$) with Dirac delta function in Cartesian coordinates. In cylindrical coordinates it is: $$ \rho ...
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1answer
32 views

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 ...
1
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1answer
58 views

What is the function type of the generalized momentum?

Let $$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$ denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action ...
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1answer
38 views

Gradient and curl of a field in polar coordinates

How do we determine the gradient and curl of a scalar/vector field in polar coordinates? For instance, if we have the following potential energy function for a force, $$U = ...
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0answers
31 views

What are momentum, configuration and coordinate spaces? [closed]

What is a momentum space, a coordinate space and a configuration space? Are they in classical or quantum mechanics or both? What are their similarities and differences and when, where and how are they ...
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2answers
84 views

Do rotation matrices rotate about inertial or body angles? [closed]

I have Yaw, pitch, and roll angles in that order (Euler 321) to apply to a body reference frame in cartesian coordinate system. I want to know what the body reference frame vector coordinates are ...
2
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5answers
94 views

A reference frame is any coordinate system or just a set of Cartesian axes?

In Physics the idea of a reference frame is one important idea. In many texts I've seem, a reference frame is not defined explicitly, but rather there seems to be one implicit definition that a ...
0
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3answers
177 views

Finding the appropriate coordinate transformation given two metrics

Given the two-dimensional metric $$ds^2=-r^2dt^2+dr^2$$ How can I find a coordinate transformation such that this metric reduces to the two-dimensional Minkowski metric? I know that ...
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0answers
15 views

from right ascension and declination to angle from semi-major axis

I am working on a research project and having trouble converting from ascension and declination to angles with respect to the semi-major axis. The target coordinate system has its origin at the ...
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0answers
40 views

Boyer–Lindquist coordinates

In the Kerr solution to the vacuum Einstein Equation written in Boyer–Lindquist coordinates. Because it is not spherical polar coordinates, $r$ ranges from 0 to infinity does not cover all the space, ...
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0answers
28 views

Lagrangian of a particle on a torus. Calculations right? [closed]

I just want to calculate the motion of a particle on a torus. But it involves some complex calculation. I just want to see if I did everything right. $$f(\phi,\theta)= \begin{pmatrix} (R+ r \cos ...
2
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1answer
61 views

In the Heisenberg uncertainty principle

In Heisenberg uncertainty principle why do we only talk about uncertainty in position along $x$ axis, why not along other dimensions as well?
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1answer
47 views

Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
4
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3answers
94 views

If a Killing vector field is timelike, can it be set to $\partial/\partial t$?

If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to $\partial/\partial t$?
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1answer
72 views

Field transformations

I'm reading Maggiore's book "A modern introduction to quantum field theory" and I'm very confused by what he did in chapter 2.6 page 31 eq. (2.80). He basically wants to find the generators of the ...
4
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3answers
162 views

Coordinates for FLRW metric

In GR, coordinate are just a tool for us to describe the physics, they should be equivalent. However, in standard form of FLRW metric, it can be inferred that the universe is expanding, but we can do ...
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2answers
103 views

Locally flat coordinate and Locally inertial frame

I am having some doubts on myself regarding the above concepts in General Relativity. First, I want to point out how I understand them so far. A male observer follows a timelike worldline ($\gamma$) ...
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5answers
275 views

Is the polar coordinate system non-inertial or inertial?

Consider a car driving around in a circle lying in the plane and suppose we were interested in determining its acceleration as measured by an observer stationary on the "ground" or whatever. ...
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1answer
36 views

How is north defined for any point on the surface of the earth?

While studying about terrestrial magnetism, references were made to north direction, and the geographic meridian and later magnetic meridian defined using that. But what is actually the north ...
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1answer
54 views

Computing the angular momentum in spherical coordinates [closed]

How to compute the angular momentum of a particle in spherical coordinates? It's given by: $$x_1=r\cdot\cos(\phi)\cdot\sin(\theta)$$ $$x_2=r\cdot\sin(\phi)\cdot\sin(\theta)$$ ...
4
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2answers
77 views

Peskin and Schroeder passive and active translation

In peskin and Schroeder's qft book, in chapter two, they're discussing Noether's theorem with respect to translations of co-ordinates. They describe and "infinitesimal" translation $x^\mu\rightarrow ...
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3answers
107 views

Is there any use for non-orthogonal frames? [closed]

In regular three dimensional space we always limit ourselves to Cartesian (i. e. orthonormal) frames. This has lots of advantages: dot products are easy, no need to distinguish between vectors and ...
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1answer
47 views

Why we can omit some forces while applying linear momentum principle

While applying linear momentum principle, namely that if force is zero linear momentum of the system is constant, in textbook they don't count for $N$ force from $M \to m.$ This force have component ...
2
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2answers
105 views

Curved space-time VS change of coordinates in Minkowski space

I'm looking for a rather intuitive explanation (or some references) of the difference between the metric of a curved space-time and the metric of non-inertial frames. Consider an inertial reference ...
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0answers
56 views

Invariant Form of The Material Derivative

Why is the RHS of the following equation invariant to coordinate transformation and the LHS is not? And is there a way to show the equivalency between the LFS and RHS? \begin{align} \vec{V} \cdot ...
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0answers
38 views

Determine generalised coordinates in Lagrangian problems

Can someone teach me how to find out generalised coordinates in a particular system? I've been struggling few days about this...here are 2 cases... A body with mass $m$ is lying on a smooth, ...
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74 views

Is there an equivalent of Rindler coordinates for an object in centripetal motion?

Rindler coordinates are a parametrization of (a subset of) Minkowski space that are "natural" for an object experiencing constant acceleration - more specifically, an object experiencing constant ...
2
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0answers
71 views

Kleppner derivation of Lorentz transformation

I am reading Kleppner.(Lorentz transformations) He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form $$x'=Ax +Bt, y'=y, z'=z, ...
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2answers
63 views

Magnetic quantum numbers - axes correspondence

We know that the magnetic quantum number describes the space orientation of an orbital within an atom. For the $p$-orbital, the magnetic quantum numbers can be -1,0,1 (one for every axis). We have ...
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0answers
39 views

Euclidean AdS space in Poincaré coordinates

I have read anti-de Sitter (AdS) space and its Euclidean version both in Global and Poincaré coordinates. For Lorentzian case it is clear how one Poincaré patch cover only one half of the whole AdS ...
2
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3answers
43 views

Commutation Relationship

For the Hamiltonian of the hydrogen atom, does the square of angular momentum, $$L^2 = L_x^2+L_y^2+L_z^2$$ commute with Hamiltonian operator, $$H = \frac{1}{2m}(p_x^2+p_y^2+p_z^2) + V(r)~?$$ Should ...
0
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1answer
82 views

How to calculate the horizon line of a satellite?

I need an equation to calculate a list of Earth-centered, Earth-fixed (ECEF) XYZ coordinates on the earth that represent the visibility limit of satellite given its ECEF XYZ coordinates. For any ...
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0answers
76 views

Manifold for Schwarzschild and Bertotti-Robinson

In short: what is the manifold in discussion for Schwarzschild metric $$ ds^2 = -(1-\frac {2M}r)dt^2 + \frac1{1-\frac{2M}r} dr^2 + r^2 (d\theta^2 + \sin^2 \theta d\phi^2)$$ and Bertotti-Robinson ...
0
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1answer
34 views

What is the procedure (matrix) for change of basis to go from Cartesian to polar coordinates and vice versa?

I'm following along with these notes, and at a certain point it talks about change of basis to go from polar to Cartesian coordinates and vice versa. It gives the following relations: ...
2
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2answers
158 views

Are solutions coordinate invariant?

In the case of electromagnetism, we can solve the sorceless wave equation in Cartesian coordinates ($x$,$y$,$z$) getting plane waves as solutions: $$ u(x) = A(x-ct) + B(x+ct) $$ and actually I am not ...
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0answers
78 views

Free fall coordinates/Fermi (normal) coordinates

It makes sense intuitively given the equivalent principle, and I've seen many times it stated, that for a free fall (geodesic) path in an arbitrary spacetime, we can choose our coordinate system to ...
0
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2answers
57 views

Adding rotations onto a vector

I have a vector with spherical co-ordinates $(r_1,\theta_1,\phi_1)$, then I want this vector to be rotated by $\theta_2$ $\phi_2$ spherical angles but I cannot figure out how. I have tried using the ...
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1answer
43 views

A particular coordinate transformation of a metric tensor

So, this was a problem set question for my GR class due yesterday, and I can't for the life of me solve it, it seems I am missing something very trivial. Either the given answer is wrong, or I am. ...
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1answer
59 views

Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality

In Roger's book, the following is stated: (I'm paraphrasing because my book is in spanish) "We consider time as part of a space, namely $\mathbb{E}^1$, instead of it just being a copy of the line ...
2
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4answers
87 views

Why is coordinate time frame dependent? [duplicate]

Here is what I understand by coordinate time. It is the time difference measured between two events, using two synchronized clocks, one present at each event, and the difference is measured in an ...
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1answer
35 views

Plane-polar coordinates [closed]

I have to make a presentation about them (7 minutes long) and I was wondering in what projects where they used. Like real life application of Plane-polar coordinate system.
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0answers
86 views

Covariant Derivative Chain rule?

I want to prove that a covariant derivative of a vector $A^{\mu}(x(z))$ at the point $x(z)$ in general would be defined as $$D_z ...
0
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1answer
107 views

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 ...
1
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1answer
73 views

Is metric tensor invariant under rotation?

It is said that metric tensor depend on the local coordinate system and therefore are not intrinsic to the surface of an 3d-object? How is it possible, kindly provide any proof or discussion. Also is ...
0
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1answer
31 views

$y$-component of center of a cube that rolls without slipping [closed]

For the figure above, let $O$ be the origin point for $x,y$-axis, and $+x$ goes to the horizontal right direction while $+y$ direction goes to the up direction. The figure has one circle and one ...
3
votes
1answer
134 views

Langevin equations in translational and rotational direction

I want to describe the following system. A bead is connected with a tether. There is a force $\vec{F}_{up}=F_{up}\hat{y}$ that acts on the bead. The tether acts with a force on the bead, this force ...
1
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2answers
174 views

Is a double integral required to find the moment of Inertia of a non-uniform sphere?

Consider some ball of given radius $R$, with a mass density function that depends on the radial variable, $\rho=\rho(r)$ where $r$ is the distance from the center of the sphere. What is the moment ...
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0answers
37 views

Change to relative coordinates [closed]

I am looking at a weakly interacting bose gas and I am stuck on this integral: $$\frac{1}{V^2} \int_V d^3r_1 \int_V d^3 r_2 W(|\vec{r_1}-\vec{r_1}|)\, \exp{\frac{i}{\hbar}r_1(\textbf{p}_1 - ...
0
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4answers
1k views

When does acceleration due to gravity equal positive/negative? [closed]

For example a projectile is launched at an angle. What would $a$ in $y=vt +.5at^2$ be? Let's say I choose up to be positive. How do you not confuse yourself whether to use positive or negative $a$?
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1answer
67 views

A simple coordinate transformation

I'm currently taking my first shot at reading Einstein's 'On The Electrodynamics' (with plenty of mathematical background). With a few pictures, everything has been crystal clear to my intuition, up ...