A set of numbers used to quantify location in space.

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80 views

Wick rotation and special 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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64 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 ...
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69 views

coordinate change differential equation polar

I noticed that v [in step (2.5)] is not the same as the terms from the first formula, even if they are related.. I tried to understand how did he reach to this ...
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1answer
165 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 ...
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5answers
3k 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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3answers
136 views

Is this webcomic accurate?

I was considering this xkcd comic from 5/10/14, with the alt-text "Trains rotate the Earth around various axes while elevators shift its position in space." I'm wondering about its accuracy. I ...
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2answers
174 views

Free fall and projectile motion

I'm wondering if something is falling say from a roof, would the distance it falls be the final $y$ position? Also would all the $y$ components (velocity, displacement) be negative?
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3answers
594 views

Need some basic help with notation and the Christoffel symbols

Apologies in advance if some of the questions below seem overly simple. In an introductory GR book, I find the following expression for the autoparallel of the affine connection (the upper bound of ...
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2answers
34 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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2answers
110 views

Kinematic sign convention

For example, if I drop a ball from a $50$ meters building, then I will consider the ground is $0$ meter downward is positive ( which makes gravity positive, downward velocity positive, etc) so ...
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2answers
90 views

How to know the Direction of the Acceleration Vector?

If the exercise doesn't give you the direction, how to know the correct one? Sometimes I assume its to the right and it was actually to the left, and I get everything wrong. Example here: How can I ...
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2answers
672 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 ...
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2answers
823 views

Role of unit vectors in cylindrical coordinates

I know how the unit vectors are defined in cylindrical coords. If I have a point P, how do I express it as a combination of the unit vectors uρ, uφ and uz. In the case of Cartesian coordinates this ...
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2answers
70 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. ...
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2answers
909 views

Vector Nature Of Angular Velocity

I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
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2answers
49 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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4answers
450 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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4answers
105 views

Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
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1answer
75 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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2answers
57 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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2answers
133 views

How big is an inertial frame?

How big is an inertial frame? Consider a huge rod which is rotating about a fixed point in a plane, its length is 1 light year. Thus light from its end closer to the fixed point to the end farther ...
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1answer
1k views

How to get the gradient potential in polar coordinate

In polar coordinate, $$\nabla U = \frac{\partial U}{\partial r}\hat{\mathbf{r}} + \frac{1}{r}\frac{\partial U}{\partial \theta}\hat{\mathbf{\theta}} .$$ Can anyone show me how to get this result?
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222 views

How was transformed an integral below?

I know how transform an integral below, $$ \iint f(\mathbf v_{1})f(\mathbf v_{2})d^3\mathbf v_{1}d^3\mathbf v_{2}, $$ using relative speed coordinates: we just use $$ m_{1} \mathbf v_{1} + ...
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1answer
3k views

Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

I have earlier posted the same question here on math stackexchange but without any answer. As the question concerns tensors, I guess that I have come to the right ...
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1answer
426 views

When are we now? Time coordinate system [closed]

The Second and the metre are well defined. We have those units available. Of course units are meant to express measurement, tools to compare with precision, and interchange that information ...
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1answer
30 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 ...
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1answer
63 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 ...
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2answers
30 views

How can I calculate the center of an object relative to a focal point and a moving observer? [closed]

I'm developing an app that contains a 3D scene which the user can navigate. As the user moves it gives the illusion that you are browsing a real landscape but for the illusion to work I need to know ...
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1answer
51 views

Inconsistent integral and distance in spherical coordinates

I am currently studying this problem: 14 b) There you see an integral $$A(r) = \int f(\theta) (-\sin(\phi), \cos(\phi),0) d \Omega$$ where $f$ is the function containing all the rest of the integrand ...
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1answer
69 views

How do I find the generalized coordinates in a certain system?

I'm learning about constraints and I know the following: If there are $N$ particles in 3 dimensional space, I have $3N$ degrees of freedom. If I have $n_b$ holonomic constraints and I switch over to ...
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1answer
309 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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1answer
1k views

Christoffel symbol for Schwarzschild metric

I know that the christoffel (second kind) can be defined like this: $$\Gamma^m_{ij} = \frac{1}{2} g^{mk}(\frac{\partial g_{ki}}{\partial U^j}+\frac{\partial g_{jk}}{\partial U^i}-\frac{\partial ...
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1answer
314 views

Is spherical coordinates enough to calculate the exact position of a point with rotations included?

With "Geographic coordinate system" we only get the location, no rotations or anything. Translated into latitude and longitude. Where with "Spherical coordinate system", we should be able to get the ...
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1answer
324 views

Accelerometer Orientation Conversion

Got two accelerometers that are measuring accelerations oriented at +/- 45 deg from horizontal. I am looking to determine the conversion of the accelerometer measured data to accelerations in the ...
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0answers
27 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 ...
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1answer
39 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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1answer
22 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: ...
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0answers
57 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 ...
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1answer
91 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 ...
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1answer
98 views

Calculation of the partition function for a classical 2D gas lying on the surface of a sphere of constant radius $R$

I'm kind of confused with this system. My first question is. Is the Hamiltonian of one particle of this gas the following? ...
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2answers
76 views

Projections in Polar coordinate system

I really understand what projections in Cartesian coordinate system, I can imagine this, but I absolutely do not understand projection in polar system. For example, I have a speed, $U$, and I must ...
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0answers
53 views

Jacobian of a transformation on Maxwell equations in cylindrical coordinates

In an area called transformation optics, they transform Maxwell equations from one space coordinate system to another, and then using the fact that Maxwell equations retain the same format under ...
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0answers
83 views

Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
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0answers
72 views

Compatibility between solutions of explicit Maxwell equations vs. wave equation?

When trying to solve for the allowed propagation frequencies in a cylindrical waveguide, I approached the problem by solving the wave equation for all three components of $\bar{E}$, and subsequently ...
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0answers
51 views

Active and passive transformations and the change in potential energy

Under active transformation, the particle moves. On the other hand, for a passive one, the coordinate is just relabel. I've read that the passive one will not affect the potential energy and the ...
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0answers
80 views

Transforming components of the angular momentum operator

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...
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43 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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1answer
60 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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50 views

Curved space to flat space calculation

When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
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87 views

is it possible to construct a contravariant basis in 1D

why is the magnitude of the basis vector at the point differ by a scale factor when considering the tangent as compared to the normal to the coordinate surface? what exactly is the coordinate surface ...