A set of numbers used to quantify location in space.

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Eulerian angle understanding

I have alot of confusion with Eulerian angle so first of all I would like to address something I don't understand from the book and maybe that would shed some light on the intuition of eulerian ...
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2answers
86 views

What coordinate systems allows the magnitude of the basis vectors to change with position?

I'm familiar with coordinate systems where the direction of the basis vectors changes with position, but I haven't come across any where the relative magnitude of the basis vectors themselves are ...
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0answers
34 views

Is Lorentz Transformation about the difference of coordinates or coordinates of itself?

I have seen different authorities talking about different interpretation of Lorentz transformation. In his book 'Introduction to Classical Mechanics', David Morin states We always talk about eh ...
3
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1answer
159 views

Non-inertial frames in Lagrangian mechanics?

Building on this Phys.SE post I am interested in how non-inertial frames can be considered in Lagrangian mechanics. My understanding is that changing the reference frame causes a transformation of the ...
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0answers
21 views

Transform velocities from one frame to an other within a rigid body

I come from non-physics background but just came to face the following problem. I have a rigid body with two attached frames of reference A and A'. I know: the rotation and translation between A ...
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1answer
26 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
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1answer
60 views

Free-fall path into a black hole in Kruskal Coordinates

If an object at t=0 begins to free-fall into a black hole from X in Kruskal coordinates (https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates), what does its path on the Kruskal-Szekeres ...
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1answer
41 views

Non-inertial system [duplicate]

Supposing I am in a non-inertial system and I don't know what forces are acting. How can I test EXPERIMENTALLY and in practice to be in a non inertial system? If I am in a system and I don't know how ...
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4answers
100 views

Why is displacement negative during free fall?

I am confused by this question. Displacement is shortest path travelled by an object, but I had seen in my book that during free fall displacement is negative.
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1answer
38 views

$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
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0answers
13 views

Coordinate Transformation across different media

I have an arrangement that is as follows : (1) inner cylinder(radius r1) filled with water (2) outer cylinder(concentric, radius r2>r1) made of glass I have a sensor S1 at radius r(r1) at angle beta. ...
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1answer
26 views

Euler Angles with respect to base body when Euler Angles with respect to another body is known

Let's say I have a fixed base body $B_0$ with a reference frame $X_0Y_0Z_0$, and two other bodies, $B_1$ and $B_2$, rotated arbitrarily with respect to this base body. Coordinate systems fixed to ...
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1answer
21 views

E field using cylindrical coordinates

Can someone explain why, when I am going to calculate the $\vec{E}$ or $\vec{B}$ field of a charged ring in its axis (using cylindrical coordinates), the position of source field is $(R,0,0)$ and not ...
2
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1answer
73 views

Do Einstein's equations allow multiple solutions that agree in a neighborhood of a spacelike hypersurface?

This question is an extension of my a question that I have recently asked: Why doesn't a global frame of reference exist for GR?, where it was recommended that I post another question (so I am ...
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5answers
2k views

Why do we need coordinate-free descriptions?

I was reading a book on differential geometry in which it said that a problem early physicists such as Einstein faced was coordinates and they realized that physics does not obey man's coordinate ...
2
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2answers
147 views

Why doesn't a global frame of reference exist for GR?

I only have at best a layperson's familiarity with GR, so forgive me if I am asking a basic question, but I have heard that in GR, we cannot have a global frame of reference, that is a frame of ...
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2answers
62 views

Stationary v/s Static

Blau, in his GR book, says that a stationary and spherically symmetric metric is automatically static. He says this easily follows from the fact that for a stationary metric, and in spherical ...
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1answer
53 views

Spherical Symmetric Metrics

In the case where all books try to illustrate a spherical metric, the procedure goes this way: First they impose isotropy in terms of polar coordinates so that one can write: $$ds^2=-A(r)dt^2 + ...
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2answers
87 views

Meaning of Proper time

Sorry for a bit of a basic question, but want to clarify things in my head. Is proper time quantified by the amount of physical process that an object, or physical system undergoes, for example the ...
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0answers
32 views

Change of variables for integral operator

One can write the operator $L=(\sqrt{1-i\partial_x^2}-1)$, as an integral, that is $$(\sqrt{1-i\partial_x^2}-1)B(x,t)=\frac{i}{4\pi^2} \int_{-\infty}^{\infty}(\omega(k_o+\kappa)-\omega(k_o))e^{i ...
2
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2answers
113 views

How are FRW metric and Minkowski metric physically different?

According to GR, matrices are coordinate invariant. Does this mean we can transform FRW metric to Minkowski metric with a coordinate transformation like $$dx'=dx\cdot a(t), dy' = dy\cdot a(t), dz' = ...
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0answers
39 views

Test bodies general relativity

I'm studying section 82 of the Landau & Lifshitz Field Theory vol.2 In this page it's written that the relative position of test bodies can't remain unchanged during time. And ok with this. But ...
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1answer
79 views

Invariant equations of motion under Lorentz transformations

My question regards the statement that an equation of motion may be invariant under a Lorentz transformation I just finished watching the Stanford University special relativity lectures on special ...
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0answers
47 views

Flat Slicing De Sitter to Static De Sitter

I wonder how one transforms from flat slicing de sitter metric given below $$ds^2=-dt^2+e^{Ht}d\bar r^2$$ where $H$ is Hubble expansion rate as a function of time, to static coordinate, ...
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2answers
82 views

Are spherical coordinates distances or angles?

I've become confused about spherical coordinates when dealing with electric fields. The way I always understood spherical coordinates is something like the below picture. To define a vector, you give ...
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2answers
52 views

Best coordinate system for Projectile motion [closed]

What is the best coordinate system for describing the projectile motion? Rectangular coordinate system or n-t(normal and tangential) coordinate system.
3
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1answer
55 views

Manifolds, unit 2-sphere and stereographic projection

I am always passing through this example while reading about manifolds that I don't quite get. It is when describing the unit 2-sphere $S^2$ as an example of a manifold. They say, initially it may ...
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0answers
17 views

How do I compute the galactic cooridinates of the Earth for a given date?

The question is simple enough, but I wasn't able to find any tools online. Does anyone know of one, or a simple formula?
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3answers
344 views

Is there a quick way of finding the kinetic energy on spherical coordinates?

Assume a particle in 3D euclidean space. Its kinetic energy: $$ T = \frac{1}{2}m\left(\dot x^2 + \dot y^2 + \dot z^2\right) $$ I need to change to spherical coordinates and find its kinetic energy: ...
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1answer
70 views

Components of acceleration in spherical polar co-ordinate

I wanted to calculate two component of acceleration in polar co-ordinate. Starting from the lagrangian $$L= \frac{1}{2}m( \dot{r} ^{2}+ r^{2} \dot{ \theta } ^{2} ) -V(r, \theta )$$ I ...
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0answers
43 views

commutation relation of angular momentum operator in non cartesian coordinates

The angular momentum operator $J$ in quantum mechanics with the commutation relation \begin{equation*} [J_i,J_j]=i\hbar\epsilon_{ijk}J_k \end{equation*} has the structure of a Lie-algebra. It is ...
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0answers
43 views

What exactly are generalized coordinates and how do they differ from regular coordinates?

I'm trying to learn the basics of Hamiltonian mechanics, which typically distinguishes itself from Newtonian mechanics as being described in terms of "generalized coordinates and momenta". What ...
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2answers
70 views

How to calculate centre of mass

How do I find the centre of mass with given coordinates? For example if we have four objects with mass $m$ at coordinates of a square $(0,0,0),(0,0,a),(0,a,0),(0,a,a)$ or another example with eight ...
2
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1answer
90 views

What is the most general definition of a coordinate system?

What is the most general definition of a coordinate system? Specificly: given a suitably general metric space $(\mathcal S, s)$ consisting of a set $\mathcal S$ of elements (for instance: a set ...
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3answers
144 views

How can we define a frame of reference in general relativity?

I have started reading general relativity. (A First Course in General Relativity, Bernard Schutz). I am finding very hard to understand a frame of reference. When I was reading special relativity ...
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0answers
19 views

How do I calculate the right ascension of the ecliptic at the points where it intersects the horizon?

Given an observer's location on the Earth's surface, and time, how do I calculate the right ascensions of the points along the ecliptic where it intersects the observer's horizon?
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1answer
72 views

Solving Lagrangian equations of motion for two point-bodies with gravitational interaction

I would like to solve the equations of motion with the Lagrangian function for two point-bodies that interact gravitationally via the potential $$V= {-Gm_1m_2 \over r_{12}} $$ where $$r_{12} = **r_1 ...
3
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2answers
81 views

Under what representation do the Christoffel symbols transform?

I often read the statement, that the Christoffel symbols aren't tensors. But then, under which representation do they transform?
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2answers
182 views

At what point does force stop translating an object and start purely rotating it? [duplicate]

At what point (or distance) from the axis of rotation, does force applied on a rigid body stop translating and purely rotating the body? Can such a point even exist? Does the body always have to ...
1
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1answer
62 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
79 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 ...
2
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1answer
85 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 = ...
1
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2answers
145 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
241 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 ...
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3answers
244 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 ...
0
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0answers
37 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 ...
1
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0answers
129 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, ...
2
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1answer
80 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
67 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
128 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 $\partial/\partial t$?