A set of numbers used to quantify location in space.

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268 views

Can false origin be anywhere in a graph?

Can I start labeling my $x$ and $y$ axes from non-zero values when drawing a graph? Or is there any convention to only label $x$-axis from non-zero value when using a false origin and not $y$-axis? ...
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569 views

Trajectories using Polar Coordinates

Once I asked my teacher how to find the trajectory of any particle that is acted upon any force.(Generally) He Told me that I couldn't do it as I did not know polar coordinate geometry as of then but ...
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1answer
231 views

Inverting Generalized Coordinates

In Corben's classical mechanics on pg. 9, it says that given generalized coordinates $q_m = q_m(x_1, ..., x_n,t)$, then if the Jacobian is non-zero everywhere, you may express $x_i = ...
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1answer
336 views

Understanding P-, CP-, CPT-violation etc. in field theory and in relation to the principle of relativity

I can never get my head around the violations of $P-$, $CP-$, $CPT-$ violations and their friends. Since the single term "symmetry" is so overused in physics and one has for example to watch out and ...
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1answer
722 views

converting force from spherical to Cartesian coords

So I am working on my assignment, and have a question about converting coordinates. I dont know whether I should ask here or the math SE, so lets give it a try here. The force in question is ...
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1answer
57 views

Timelike curves in Special Relativity

I have a question that probably might sound silly to most of you. We know that a natural Lorentz-invariant parametrization of a timelike curve is provided by: $$\tau$$ the Lorentz-invariant proper ...
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2answers
60 views

Euler angles derivation

I have been trying to grasp the idea of Euler angles for a while. Can anyone point out if my understanding is correct or not. Situation: We have 3 axes known as principal axes of inertia which define ...
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1answer
81 views

How big or small is a reference frame in Relativity?

What exactly is a frame of reference? Does it have an objective existence and if so what is it? What's the size of a reference frame? Is a reference frame the same size for a stationary frame of ...
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1answer
92 views

Can the fuzzball conjecture be applied to microscopically explain the entropy of a region beyond the gravitational observer horizon?

In this article discussing this and related papers, it is explained among other things, how the neighborhood of an observer's worldline can be approximated by a region of Minkowsky spacetime. If I ...
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1answer
81 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
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2answers
242 views

What does “equinox of date used” mean?

The documentation for an API I often use for quick astronomical modeling and figure drawing says Positions are given in FK5 heliocentric coordinates in the equinox of the date used. What does ...
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3answers
8k views

Find radius of curvature, given a velocity vector and acceleration magnitude?

The particle P moves along a space curve. At one instant it has velocity $v = (4i-2j-k)$ $m/s$. The magnitude of the acceleration is 8 $m/s^2$. The angle between the acceleration and the velocity ...
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1answer
50 views

Convenient coordinate systems and symmetries

I recall in my basic electromagnetism and quantum mechanics lectures that choosing one coordinate system over another may greatly simplify the equations involved in solving a problem (think about ...
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1answer
35 views

When to pull out a negative sign from a variable

I get confused about when there should be a negative sign in certain equations or not. I will give three short examples (that I will make long with explanation) that show my confusion. Example 1: ...
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1answer
73 views

Derivative chain rule in a triangle, confusing but interesting problem

I asked the question in math.stackexchange. But I think it is better to ask here again. I am new to these sites. Please forgive me if it is not polite. http://math.stackexchange.com/q/921001 You can ...
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1answer
88 views

Rotation operator for a point in a coordinate system linearly derived from Cartesian coordinates

For some experimental and practical reason, I have created a new coordinate system in the form $$x^\prime_i=T_{ij}x_j$$ where $T_{ij}$ isn't a square matrix. $x_i$ is standard Cartesian coordinates, ...
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2answers
273 views

Calculating the electric potential in cylindrical coordinates from constant E-field

I am having so much trouble with this problem. I feel like I shouldn't be, but I am. A uniform electric field, $\vec{E} = E_0\hat{x}$. What is the potential, expressed using cylindrical ...
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1answer
88 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
57 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
324 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
219 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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2answers
150 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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1answer
118 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 ...
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1answer
71 views

Can we change frame of reference twice in a single problem?

My question has an inclined plane of mass $M$ and simple block kept on it, of mass $m$ (Both on a table). All surfaces are friction-less. Both of the objects would move, block down the incline and ...
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1answer
901 views

RA/dec to Alt/Az program or method

I've been looking for a program to convert from RA/dec into Alt/Az; having used a couple of online versions I haven't seemed to find one yet that works reliably. I've tried to do it myself and half ...
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1answer
158 views

How to explain relativistic mass with 2 moving systems, but not 3?

All the visual explanations I know work in some kind of "If you are moving relative to something A, while inside A something is moving, the stuff in A has to move slower due time dilation and ...
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55 views

The Effect of Tortoise Coordinates

Referring particularly to http://arxiv.org/abs/hep-th/9909056 in regard to the wave equation for Schwarzschild-AdS black holes (p.4), I'm trying to understand tortoise coordinates. So starting ...
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1answer
27 views

Degrees of Freedom for an Asymmetric top

How many degrees of freedom does an asymmetric top have if it is rotating about a fixed point?What are the generalised coordinates used then?
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51 views

Double dot product in Cylindrical polar coordinates - Strain Energy

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: $$2W=σ_{ij}ε_{ij}$$ Where σ and ε are symmetric rank 2 tensors. For cartesian ...
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72 views

About the proof of the second Bianchi Identity

The second Bianchi Identity is $$ \nabla_{[a}R_{bc]de}=0 $$ As far as I know, the proof (say, Walfram Mathword) start by stating the representation of Riemann tensor in local inertial coordinates $$ ...
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79 views

Compute and plot satellite position on 2D Earth map

I would like to create a simple satellite tracking software, that will compute the position of a satellite at any time, and show its location on a 2D map of Earth. Let's assume it is possible to ...
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125 views

How to solve the Laplace equation in ellipsoidal coordinates?

It seems that popular textbooks on electrodynamics do not discuss how to solve the Laplace equation in ellipsoidal coordinates. I could not find any reference, but there must be references about this. ...
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53 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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76 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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62 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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1answer
149 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
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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3answers
129 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
69 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
510 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
57 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
485 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
742 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
65 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
825 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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4answers
79 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
71 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
56 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
132 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?