A set of numbers used to quantify location in space.

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60 views

Which coordinate system confirms quantum-level experimental data?

We often use the Cartesian coordinate system, since it is the naive approach at macro level (placing a box just "next to" or "above" the other box). There are, however, many more such systems, incl. ...
2
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0answers
46 views

Solutions of PDEs in different coordinate systems

Suppose we have a PDE, for example the Helmholtz paraxial equation: $$ \nabla_\perp^2A+2ik\frac{\partial A}{\partial z}=0 $$ Solutions depend on the coordinate system we are using, i.e. we obtain ...
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49 views

How to prove the relations between the variables in bispherical coordinates?

When I was reading papers about the forces between two charged spherical conductors in a uniform electric field, I was confused with bispherical coordinates the author used to describe the spherical ...
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1answer
78 views

Coordinate-free derivation of the Lamé-Navier's elasticity equations

Linear static elasticity provides a local equation $-\mathrm{div}\sigma=f$, the constitutive law $\sigma=2\mu\epsilon+\lambda \mathrm{tr}(\epsilon)I$ as well as the strain-displacement relationship ...
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1answer
53 views

Electric field in a cylinder

We have electric charge density $\rho(r) = kr$ in a cylinder of infinite height and radius $a$. I'm asked to find the electric field. I'm doing it using two methods and I don't undesrtand why then ...
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1answer
65 views

Heliocentric Worldview [duplicate]

Isn't the whole historic Discussion of Heliocentric vs. Geocentric Worldview just about a Calculation-Technique. I mean I could also choose my coordinate-center to be in the middle of Earth and setup ...
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90 views

What coordinate system is used to describe planets positions in the universe?

How are planets positions described in the space and in respect to what? For example is Sun the origo and right now at this moment Earth has [coord_X, coord_Y, coord_Z]? or maybe [lng, lat]? ...
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1answer
381 views

failing to see the conundrum in the Einstein hole argument

I've been reading about the Einstein hole argument, and i fail to understand what makes active diffeomorphisms "special" compared to passive diffeomorphismsm also known as good old coordinate ...
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1answer
211 views

Optimal selection of generalized coordinates in Lagrangian system

EDITED: The number of bonds is actually 2, not 1 (look at edit history). Fixed for archiving purposes. Problem: The edge A of an homogeneous rod (of length $\ell$ and mass $m$) is performing a smooth ...
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1answer
225 views

Radians to Rotate Earth to Match ECI Lat/Lon with ECEF Lat/Lon

I am attempting to model GPS Satellite positions on the globe for a set of ephemerides. I have a verified set of ECI ( http://en.wikipedia.org/wiki/Earth-centered_inertial ) XYZ Coordinates and a ...
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1answer
56 views

Parametric equations of a hypersurface

In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations?
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1answer
100 views

Space-Time Continuum [duplicate]

In special relativity it is said that " Time and space cannot be defined separately from one another. Rather space and time are interwoven into a single continuum known as spacetime. " What is the ...
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2answers
137 views

What does it mean to divide space and time?

Goldstein's mechanics book, on the chapter on relativistic mechanics says that "We cannot assume that all observers make the same division into time and space in the same way." What does it mean to ...
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4answers
91 views

Special Relativity moving in space

Given that time is 'just another' dimension and people get hung up on the fact that we cannot go back and forth in time like the other dimensions. Is there any proof that the corner of 8th Avenue and ...
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1answer
133 views

Symmetry, Transformations and non-linear transformations

I am a physics student. My mathematical background is quite weak. I just want to know the similarities (if there are any) or differences between coordinate transformation of two kinds : Rotation of ...
2
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1answer
64 views

Riemann normal chart and special relativity

When you pick Riemann normal coordinates at a point, then the Christoffel symbols vanish and the metric is flat, but the Riemann curvature tensor does not necessarily vanish. Since Einstein said that ...
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3answers
301 views

Does the Relativity Principle of Special Relativity imply homogeneity and isotropy of all the reference frames?

In Rindler's book: Relativity, Special, General and Cosmological, is stated on page 40 that the Relativity Principle (RP), when applied to just one Inertial Frame (IF), guarantees the homogeneity and ...
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0answers
40 views

The inertia tensor is “global”, how do I make it local?

A solid cuboid has the following moment of inertia: $$I= \begin{pmatrix} \frac{1}{12}h^2+d^2 & 0 & 0 \\ 0 & \frac{1}{12}w^2+d^2 & 0 \\ 0 & 0 & \frac{1}{12}w^2+h^2 ...
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0answers
61 views

What is the physical meaning of the Eddington - Finkelstein metric?

I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this mathematical procedure. (really two transformations, but i think that is a ...
4
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1answer
102 views

Extent of coordinate freedom to set metric components along a spacetime path

If we describe spacetime with a Lorentzian manifold, it is always possible to choose a coordinate system such that at any particular point $x^\alpha$, the components of the metric are: $$ ...
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1answer
295 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
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3answers
654 views

Converting between Galactic and Ecliptic coordinates

I was hoping someone would be able to tell me the formula to convert between ecliptic and galactic coordinates. I've been able to convert values using ...
3
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1answer
160 views

Why does the Kruskal diagram extend to all 4 quadrants?

Why is it that the Kruskal diagram is always seen extended to all 4 quadrants when the definitions of the $U,V$ coordinates don't seem to suggest that the coordinates are not defined in, say, the 3rd ...
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2answers
2k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
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5answers
2k views

How to get the angle needed for a projectile to pass through a given point for trajectory plotting [closed]

I am trying to find the angle needed for a projectile to pass-through a given point. Here is what I do know: Starting Point $(x_0,y_0)$ Velocity Pass-through point $(x_1, y_1)$ I also need to ...
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2answers
190 views

Exercise about Lagrange-Euler equations

I'm solving an exercise about the Lagrange-Euler equations, that states the following: Let $\gamma (t) = \{ (t,q) : q = q(t), t_0 \leq t \leq t_1\}$ be a curve in $\mathbb{R} \times \mathbb{R}^2$. ...
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2answers
1k views

Expression of kinetic energy in polar coordinates

Expression for kinetic energy in Cartesian coordinate: Expression for kinetic energy in polar coordinate (applying the transformation of coordinates): Why can't we express it in the following ...
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1answer
122 views

Integrating Radial Vector Fields

Given a integral $$\int_vd^3{r} \;\vec{r}\;\rho(r)$$ and How do you convert it to spherical coordinate system, noting that $\rho(r)$ is indeed as it is without vector, i.e. it is spherically symmetric ...
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1answer
1k views

In general relativity (GR), does time stop at the event horizon or in the central singularity of a black hole?

I was reading through this question on time and big bang, and @John Rennie's answer surprised me. In the immediate environment of a black hole, where does time stop ticking if one were to follow a ...
4
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1answer
125 views

How to assign coordinates to the elements of a flat metric space

Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements, and consider the assignment $c_f$ of coordinates to (the elements of) set $M$, $c_f ...
5
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1answer
297 views

Is General Relativity applicable for all coordinate systems?

My understanding was that relativistic physics can be expressed in any inertial coordinate system, but not arbitrary systems. That is, no experiment can determine if we are "still" or "moving" at a ...
2
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1answer
203 views

Deriving the Schwarzschild solution

I am CS student and i want to create graphical simulation of black hole, so I need to use The Schwarzschild solution to calculate possible coordinates of given body every second. First try in 2D ...
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103 views

Whose reference frame to use for $d \theta$ near a black hole?

Using the Schwarzchild metric for a body circularly orbiting a nonspinning black hole (i.e. $dr=0$), the relation between $d\tau$, the time between two light pulses sent out infinitesimally close ...
2
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3answers
401 views

Jacobian, Lorentz and Fourier Transformation

Jacobian, Lorentz and Fourier Transformation. I am confused with the physical interpretation/meaning of all these transformations. As far as I understood, Jacobian transforms from one coordinate ...
2
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1answer
245 views

Lightcone coordinates

The Light cone coordinates are defined as $$x^+ = x^0 + x^3$$ $$x^- = x^0 - x^3$$ Then in the light cone coordinates the position 4-vector becomes: $(x^+, x^-, x^1, x^2)$ . Zwiebach in his A First ...
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2answers
428 views

Coordinate Transformation of Scalar Fields in QFT

By definition scalar fields are independent of coordinate system, thus I would expect a scalar field $\psi [x]$ would not change under the transformation $x^\mu \to x^\mu + \epsilon^\mu $. Correct? ...
2
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1answer
166 views

Expression of electrostatic field

An electrostatic field is characterized by the fact that it depends only by $r$, isn't it? If it is true, I don't understand why this expression, given in cylindrical coordinates, $${\bf ...
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1answer
219 views

Rotating point in 3D space by Unknown rotation vector [closed]

I have a random point defined by: int x = rand.nextInt(9)-4;//-4 to +4 int y = rand.nextInt(4)+2;//+2 to +5 int z = rand.nextInt(9)-4;//-4 to +4 Y happens to be ...
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0answers
68 views

equatorial-supergalactic conversion

What are the conversion formulas from equatorial to supergalactic coordinate system. Thanks for any help.
5
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2answers
203 views

A thought experiment on vision and curved spacetime

What follows is a long self-made example to deal with my conceptual issues of visualizing curved spacetime. Imagine an observer floating somewhere in space. He feels no strain on his body, ...
4
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1answer
147 views

Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
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2answers
440 views

Electric Dipoles and Spherical Coordinates

I've become confused over the use of spherical coordinates when working with dipole moments. It would probably be best o use an example to show where I'm confused. If we have a pure dipole, with a ...
2
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1answer
67 views

Why is it not possible to distinguish left from right by means of a coil?

Why is it not possible to explain to an alien "at the phone" which side is left and which is the right side by defining a simple experimental setup using induction? Defining for instance downwards ...
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1answer
104 views

Interchaning a position between two reference frames?

$\vec{r}_a$ is a positional vector from reference frame $a$. What is the position of same point from reference frame $b$ ? If required, assume position of origin of frame $a$ is $\vec{m}$ and ...
3
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1answer
69 views

Primary direction in planet-centered equatorial reference frame

I am given the classical orbital elements of the orbit of a spacecraft around a planet which is not the Earth, say Venus. I assume those are referred to a reference frame whose fundamental plane is ...
5
votes
1answer
356 views

What do up-left orthogonality has in common with up-down and what is their relationship?

I am familiar with the true (or general) notion of orthogonality, given in the Linear Algebra and Pythagoras theorem derived from the $\vec x \cdot \vec y = 0$. I have also recently got to know that ...
3
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0answers
99 views

Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?

Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
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0answers
64 views

Wick rotation and relativity

CMIIW, but as I understand it, Wick rotation replaces the Minkowski basis (t,x,y,z) with the Euclidean basis (it,x,y,z). Suppose that $t_2=t_1 cosh \beta+x_1 sinh \beta$ and $x_2=t_1 sinh \beta+x_1 ...
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2answers
55 views

Is it incorrect to explain the direction of a coded vector quantity?

For example, let's say that in a linear physics problem, all the data are given to a certain direction, and coded positively for direction to the right. So +5m/s would be a velocity of 5m/s to the ...
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0answers
58 views

What do the components of light velocity look like in polar coordinates?

The Schwarzschild solution makes use of polar coordinates, and I'm wondering how the different components of velocity of light change with the position. Might I get some examples of light velocity ...