A set of numbers used to quantify location in space.

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2answers
182 views

Can a curvature in time (and not space) cause acceleration?

I realize that the curvature of space-time causes acceleration (gravity). Is it possible to have a curvature only of space, or a curvature only of time? If so, would a curvature only of space, or a ...
3
votes
1answer
199 views

QM: How to compute position/momentum relation in polar coordinates

So if we are working in one dimensional space, we have the formula: $$\langle x|p\rangle = \frac{1}{\sqrt{2\pi\hbar}} e^{ipx/\hbar}$$ Suppose instead we are confined to a circle of radius $R$ so that ...
3
votes
1answer
85 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 ...
3
votes
1answer
4k views

Force from point charge on perfect dipole

Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole. I'm having more than a little difficulty ...
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 ...
3
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0answers
62 views

How coordinate system shifting is related to similarity transformations?

I know that coordinate system shifting can be represented using matrices. But how exactly are similarity transformations related to coordinate shifts ?
3
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3answers
2k 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
votes
0answers
109 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 ...
2
votes
3answers
653 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
votes
3answers
278 views

Why don't we define absolute coordinates?

Why don't we chose a random point in the void present between galaxy clusters and define it as the absolute origin? I know that rest is not absolute and that space expands, but we can easily keep ...
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 ...
2
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5answers
236 views

On the coordinate independence of general relativity

I've been having a bit of trouble with the idea of coordinate independence in general relativity. Let me start with a simple example that I think illustrates my question conceptually: Say you have ...
2
votes
3answers
168 views

Two-rotation coordinate transformation

I've designed an electronic device that uses a 3-axis accelerometer to measure the acceleration of an automobile. I'm only interested in accelerations in the plane of the road surface, so I want to ...
2
votes
2answers
109 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
votes
2answers
5k 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 ...
2
votes
1answer
422 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 ...
2
votes
2answers
76 views

Show that two families of curves are orthogonal (without using orthogonal trajectories)

I'm reading through Hartle's General Relativity and came across this question: Consider the following coordinate transformation from rectangular coordinates $(x,y)$, labeling points in the plane ...
2
votes
2answers
3k 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 ...
2
votes
2answers
291 views

Coordinate transformation from earth to solar

I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already ...
2
votes
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 = ...
2
votes
2answers
322 views

A few questions on passive vs active Lorentz transformations

1.) How do we physically interpret an active Lorentz transformation? The passive transformation seems simple enough: you view a fixed object from the perspective of a new observer. When we actively ...
2
votes
2answers
175 views

Momentum vector transformation

I am confused about the way momentum vector transforms in the following case: $$q_k \to q_k'= q_k + \epsilon f_k(q)$$ The Jacobian is thus $\Lambda_{ij} = \frac{\partial q'_i}{\partial q_j} \approx ...
2
votes
4answers
95 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 ...
2
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1answer
398 views

Electromagnetic Tensor in Cylindrical Coordinates

I understand that the Electromagnetic Tensor is given by $$F^{\mu\nu}\mapsto\begin{pmatrix}0 & -E_{x} & -E_{y} & -E_{z}\\ E_{x} & 0 & -B_{z} & B_{y}\\ E_{y} & B_{z} & ...
2
votes
2answers
104 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 ...
2
votes
2answers
65 views

How do I modify a 3-D simulation grid to be 2-D?

I am creating a particle in cell simulation that models an electron plasma in a cylindrical container. Part of this process is assigning charge density to grid points based on the position of each ...
2
votes
1answer
139 views

Curvilinear coordinate system around body of revolution

In Boundary-Layer Theory by Schlichting he gives the boundary-layer equations for a body of revolution according to the paper by Boltze$^1$. Unfortunately, this paper is in German. He apparently uses ...
2
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1answer
76 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 ...
2
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2answers
391 views

Local inertial coordinates/Fermi normal coordinates

It is said that we can introduce local inertial coordinates/Fermi normal coordinates for any timelike geodesic. But why only for timelike geodesics? What about null geodesics? Perhaps it has to do ...
2
votes
1answer
137 views

What is the physical intepretation of harmonic coordinates?

When I see harmonic coordinates used somewhere, what should my association be? Is there some general use or need to consider the harmonic cooridnate condition? I don't really see what's ...
2
votes
2answers
627 views

What is a Kustaanheimo-Stiefel transformation?

What is a Kustaanheimo-Stiefel transformation? Which applications has it in physics? Can you point me to a reference, where this transformation is explained?
2
votes
1answer
276 views

How to transform material permittivity tensor from Cartesian coordinates to another orthogonal coordinate system?

I have a material specified by a permittivity tensor written in Cartesian coordiantes: $$\begin{pmatrix} \epsilon_{xx} & \epsilon_{xy} & \epsilon_{xz}\\ \epsilon_{yx} &\epsilon_{yy} ...
2
votes
2answers
270 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 $\mathbb{R} \times \mathbb{R}^2$. ...
2
votes
1answer
261 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 ...
2
votes
1answer
206 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 ...
2
votes
1answer
68 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 ...
2
votes
2answers
74 views

Velocity in a turning reference frame

I often see the relation that $\vec v=\vec v_0+ \vec \omega \times \vec r$ in a turning reference frame, but where does it actually come from and how do I arrive at the acceleration being $$\vec ...
2
votes
1answer
329 views

Degrees of freedom in the infinite momentum frame

Lenny Susskind explains in this video at about 40min, as an extended object (for example a relativistic string) is boosted to the infinite momentum frame (sometimes called light cone frame), it has no ...
2
votes
2answers
475 views

Does the length of the sidereal day vary systematically?

I'm confused about some properties of the sidereal day, in particular whether its duration varies systematically over the course of the year.1 It seems to me that that must be the case, but the ...
2
votes
1answer
234 views

Mass Shell in Light Cone Coordinates

I'm reading Zweibach's introduction to string theory, and don't understand one of his claims. He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
2
votes
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 ...
2
votes
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?
2
votes
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 ...
2
votes
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 ...
2
votes
1answer
126 views

Black holes and Time Dilation at the horizon

What is the difference between proper time and the observer time? Whilst thinking about Black holes, when we see the Schwarzschild metric $$c^2\tau ^2 = \left ( 1 - \frac{r_{s}}{r} \right )c^2t^2 - ...
2
votes
1answer
213 views

Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
2
votes
1answer
131 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 ...
2
votes
1answer
673 views

Calculate the latitude / longitude coordinates of the location where the Sun is at the zenith

There are plenty of resources showing how to calculate zenith and azimuth of the Sun when the time and the location are given. However, I need to calculate the location where the sun is at the ...
2
votes
1answer
1k views

The trajectory of a projectile launched from a hilltop

Here is the problem: A boy stands at the peak of a hill which slopes downward uniformly at angle $\phi$. At what angle $\theta$ from the horizontal should he throw a rock so that it has the greatest ...
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, ...