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Questions tagged [coordinate-systems]

This tag involves questions on various coordinate systems. The usual Cartesian coordinate system can be quite difficult to use in certain situations. Some of the most common situations when Cartesian coordinates are difficult to employ involve those in which circular, cylindrical, or spherical symmetry is present. For these situations it is often more convenient to use a different coordinate system.

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Transforming normals into a specific coordinate system

Let's say I have normals defined from points of latitude and longitude on a sphere (represents the satellite object). The coordinate system we want to transform these normals into is z points to ...
AGJADSGK's user avatar
-1 votes
1 answer
69 views

Is there any two-coordinate system where X, Y is the same point as Y, X? [closed]

Is there any two-coordinate system where e.g., (10,36) is the same point as (36,10)? You see we here at the Rescue Centre are at our wits' end. Half our reports come in with latitude first, half with ...
Dan Jacobson's user avatar
-3 votes
1 answer
34 views

Find the value of the interior angles of a polygon [closed]

I have coordinates of points $(x, y)$. By connecting these points we get a polygon in which I have to get values of its internal angles. For example points = $[3,1], [3,3], [1,3], [3,5], [7,5], [7,1]$ ...
Paul's user avatar
  • 97
-2 votes
0 answers
26 views

Number of parameters needed to find a point on $S^n$

Firstly, let me point out that the following argument can be easily extended to $S^n$ for every natural number $n$, so I will just focus on $S^1$. Consider the circumference $x^2+y^2=1$, centred at $O=...
Davide Masi's user avatar
0 votes
0 answers
41 views

Changing coordinate system

Someone please explain how did we get second term in equation 2.15.
Mr. Wayne's user avatar
  • 111
1 vote
1 answer
50 views

Equation of line passing (1,4) having minimum sum of intercept on positive axis?

We have to find Equation of straight line passing through $(1,4)$ having minimum sum of intercept on positive axis? So I have two approaches: Method 1 First $a+b$ ($a$ and $b$ are intercept on ...
Guess's user avatar
  • 169
1 vote
2 answers
59 views

Sierpinski Gasket coordinate description

I was reading Gerald Edgar's "Measure, Topology, and Fractal Geometry" when I came across this exercise Let coordinates $(u,v)$ be defined in the plane with origin at one corner of the ...
Rubén Sales Castellar's user avatar
2 votes
0 answers
31 views

Variational formulation of the vector Laplace equation in cylindrical coordinates

I want to solve the vector Laplace equation $\nabla^2 \mathbf{v}=\mathbf{f}$ in arbitrary coordinate systems using finite-elements. The usual way to derive the variational form necessary for the ...
pfloutch's user avatar
1 vote
0 answers
44 views

How to combine the $4$-dimensions of spacetime into 1 dimension?

I have been thinking about the possibility of representing all points in a $4$-dimensional spacetime coordinate system $\mathbb{R}^{1,4}$, as points on one line $P$ (or axis of a $1$-dimensional ...
A.M.M Elsayed 马克's user avatar
2 votes
0 answers
49 views

Analytical solution to Stokes equation with cylinderical symmetry but with a curved region

Is there any way one could solve the following Stokes equation analytically in a system with cylindrical symmetry but with a curved region? The set of equations in the cylindrical coordinate read \...
questionerno8's user avatar
2 votes
1 answer
69 views

In a 2d coordinate plane, how can I find the position of point S given the angles to 3 known reference grid points on the x and y axis.

I need to understand how to find the position of a mobile robotic camera that is positioned in a defined grided area. I rotate the camera so that it points at 3 different grid reference points named B,...
Robert's user avatar
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1 vote
0 answers
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Linear approximation of the magnetic dipole field

Summary: using 3 angles to represent a magnetic dipole's orientation is redundant because the rotation around the $z$-axis of the dipole does not change the magnetic field, there are only 2 DOFs for ...
William Lin's user avatar
0 votes
0 answers
14 views

Finding the coordinate of four points of imaginary intersecting lines which passes through end points of two intersecting lines

image I want to find the coordinates of the points A,B,C,D where two imaginary lines intersect each other, where this imaginary lines passes through the end points of the two lines L1 and L2, the ...
Basavaraj Kittali's user avatar
0 votes
1 answer
63 views

Best Coordinate system - Lagrangian problem

In $\Bbb R^3$ consider an heavy point $P$ whose mass $m$ on a circumference $\Gamma$ of radius $R$, centered in the origin. Now consider that $\Gamma$ lives in the plane $$\Pi = \{( x,y,z) \in \Bbb R^...
Turquoise Tilt's user avatar
2 votes
2 answers
42 views

Covariant and contravariant velocity

I'm facing the following problem in tensor calculus: I want to calculate the velocity of a mass particle in spherical coordinates. So I'm using the following coordinate functions for spherical ...
user avatar
2 votes
3 answers
19 views

Covariant (absolute) derivative of a vector along a curve -- compare cartesian vs. polar coordinates

BACKGROUND: Suppose $A^μ$ is a vector field and $x^μ(λ)$ is a curve in spacetime. A first guess at measuring the change in $A^μ$ along the curve might be $$\frac{dA^μ(x(λ))}{dλ} = \frac{∂A^μ}{∂x^ν} \...
Khun Chang's user avatar
1 vote
1 answer
103 views

Parametric Equation of a unit circle when the angle between $x$-axis and $y$-axis is not $90$ degrees

I know in regular Cartesian coordinates the parametric equation for a unit circle is $x=\cos(\theta)$, $y=\sin(\theta)$, and if the $x$ coordinates are stretched by an amount $a$, and the $y$ ...
Anders Gustafson's user avatar
0 votes
1 answer
42 views

Equivalence of solutions to PDE in different coordinate systems

Wave equation in two dimensions can be solved either in Cartesian or polar coordinates. One can derive the expressions for Laplacian by putting in the coordinate transformations directly. However, ...
Sanjana's user avatar
  • 265
-1 votes
1 answer
24 views

Transformations of Function

Im having trouble conceptualizing why when we transform a function, we need to describe $x$ and $y$ as functions in the new coordinate system. For example with polar coordinates $x$ and $y$ are now ...
TreyarchPi's user avatar
1 vote
1 answer
198 views

How to obtain the pucker angles of a molecular ring?

The structure of the system is a ciclohexane whose conformational preference is describe in the following image: The name of this conformational preference is "chair". Because it resembles ...
Another.Chemist's user avatar
0 votes
1 answer
26 views

Frames of reference in Coriolis' equation

I feel like I should be able to work this out but keep confusing myself, so I thought I'd ask here. Coriolis' equation (this seems to have different names depending on where you look) lets us find the ...
Count Dirac-ula's user avatar
1 vote
1 answer
42 views

Question about Euler angles and rotation about relative and fixed frames?

I'm studying linear algebra, and one of the topics is rotation through euler angles. Depending on the sequence, we obviously get different results. One thing that I'm confused about however, is that ...
JerSci's user avatar
  • 59
0 votes
1 answer
9 views

How to find the basis vector of a transformed frame?

I have a frame B that is rotated w.r.t to frame A about the z axis by 30 degrees clockwise and translated by [2, 0, 0]. Frame A is translated by [1, 0, 0] w.r.t to the world frame. The goal is to ...
JerSci's user avatar
  • 59
1 vote
1 answer
54 views

What is the 'easiest' coordinate system for categorizing points on a sphere according to the following rule?

I am in 3D space. I have a collection of unit vectors (with all positive Cartesian coordinates) that I would like to categorize in 7 sections (see the diagram below). By 'categorize', I mean I want to ...
Marco Froelich's user avatar
2 votes
1 answer
53 views

Converting 3d coplanar points to space of 2d plane then back into 3d

I have the equation of an arbitrary plane of the form $Ax+By+Cz+d= 0$. I also have a set of points lying on this plane, $\{p_1, p_2, ... , p_i\}$ where each $p_i$ is an $(x,y,z)$ coordinate. I would ...
wkacct acctwk's user avatar
0 votes
1 answer
36 views

In concentric circles Triangle formed from intersection of a line making 45 degree with x axis where inner circle meets x axis to outer circle [closed]

I have two concentric circles one of radius 5 cm and outer one of 10 cm, their centers being 0,0 I want to calculate P B and H of the triangle formed by intersection of a line on outer circle making ...
Ken Kaneki's user avatar
1 vote
0 answers
35 views

What is an angle? [duplicate]

I am a high school student and recently I started trigonometry and one question that comes to my mind every time is that "What is an angle?" I mean when we say that angle between two sides ...
Himanshu Singh Nirwan's user avatar
0 votes
0 answers
18 views

Creating a transformation matrix for a 2d coordinate system with some known points

I have this system There are 2 different coordinate spaces. one in red and one in blue. I know the values of cp and p in the ...
munHunger's user avatar
  • 181
-1 votes
1 answer
56 views

Definition of a local coordinate system as a mapping of region of $\mathbf{R}^n$ to the manifold (and not the inverse)

I am looking for differential geometry or analysis books that define a local coordinate system in $M$ as a mapping $U\to M$, where $U\subset\mathbf{R}^n$. All that I've seen so far use the inverse ...
Alexey's user avatar
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0 votes
0 answers
12 views

How to represent a point's velocity seen from a moving coordinate system?

let us consider a three-dimensional point $x$ that is fixed in the world coordinate system, ie. its velocity is zero, $\dot{x}=0$. Consider another coordinate system that is defined by a rotation ...
Beram's user avatar
  • 21
3 votes
2 answers
96 views

Common Tangent to hyperbola and circle using parametric coordinates

The circle $x^2+y^2-8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ are given Find equation of a common tangent with positive slope to the circle as well as to the hyperbola is (A) $2x - \sqrt{5}y ...
Nandini's user avatar
  • 159
0 votes
1 answer
80 views

Trying to understand coordinate transformations

So, I don't really understand why $\mathrm{d}x$ or generally any differential is equal to the sum of this differential over each one of the corresponding spherical coordinates times each spherical ...
Andronikos's user avatar
2 votes
1 answer
43 views

Are they called "cardinal" subspaces? If not, what else?

A Cartesian coordinate system for an N-dimensional space S has, obviously, N axes. However, it also has $\tbinom{N}{2}$ planes spanned by those axes, and $\tbinom{N}{3}$ 3D spaces likewise spanned, ...
Xirdal's user avatar
  • 186
0 votes
1 answer
35 views

Volume integral of vector field in spherical and cartesian coordinates

I am trying to reconcile the different results obtained when integrating a vector field in either spherical or cartesian coordinates. Take for example the vector field in spherical coordinates (...
ZehDeckel's user avatar
9 votes
5 answers
2k views

Can a straight line be drawn through a single node on an infinite square grid without passing through any other nodes?

The problem is from an advanced 8th grade math curricula, and marked with a star: *The topic is "Real numbers" The plane is covered by an infinite square grid. Is it possible to draw a ...
curioushuman's user avatar
2 votes
2 answers
61 views

Method to find the longest and shortest distance on a circle from origin with less computation

The sum of the least and greatest absolute value of $z$ which satisfies the condition $|2 z+1-i \sqrt{3}|=1$ is A. 1 B. $\frac{3}{2}$ C. 2 D. none of these In this problem, I'm able to reduce this ...
math_learner's user avatar
3 votes
1 answer
69 views

Question on concurrent normals in a Parabola

Normals drawn at points A, B and C of a parabola are concurrent at $N (4,2)$. If $A \equiv (3,3)$ and $B \equiv (1,-1)$. Then which of the following can be true? I) Focus is at S $\displaystyle\equiv \...
Tanish Agarwal's user avatar
1 vote
1 answer
97 views

Differential geometry: what are coordinates, and what is their relation to a basis set?

I'm self-studying differential geometry (from several different places) and have run into what I think is a high-level conceptual confusion. As with most conceptual confusions, I am not exactly ...
IMK's user avatar
  • 23
1 vote
0 answers
25 views

How does the del operator work exactly? [duplicate]

In Cartesian coordinates, vector operations are as simple as if we were treating the del operator as like a vector. $$\nabla = \Big(\frac{\partial}{\partial x}\hat{\textbf{i}} + \frac{\partial}{\...
Researcher R's user avatar
0 votes
0 answers
15 views

Using Geocentric or Geodedic latitude with Great Circle Distance

I've recently started working on a system does some work using geodetic coordinate systems. The data it uses is WGS84 and some of the modern components use a Vincenty Algorithm for distance but there ...
loxias's user avatar
  • 1
0 votes
0 answers
8 views

Given a vector field in spherical coordinates, compute the flux through a disk at z = -d

I want to compute the flux of the magnetic field $B = \frac{\mu_0m}{4\pi r^3}(2cos(\theta)\vec{e_r}+sin(\theta)\vec{e_\theta})$ through the disk at $z=-d$ with radius b centered around the z-axis. ...
Merkel_Bot's user avatar
0 votes
0 answers
12 views

Transformation and image of a plane under a given transformation when one of the variables is constant.

Consider the transformation given by: \begin{cases} x = \frac{\sin(\sigma)\cos(\phi)}{\cosh(\tau) - \cos(\sigma)} \\ y = \frac{\sin(\sigma)\sin(\phi)}{\cosh(\tau) - \cos(\sigma)} \\ z = \frac{\sinh(\...
Angelo's user avatar
  • 47
0 votes
0 answers
17 views

Question regarding minimum time taken to move a point onto a line joining two points

This question is regarding the following problem A bird is at a point $P(4, –1, –5)$ and sees two points $P_1(–1, –1, 0)$ and $P_2(3, –1, –3)$. At time $t = 0$, it starts flying with a constant speed ...
koiboi's user avatar
  • 356
0 votes
0 answers
32 views

Instance spaces - donut hypothesis

I am working on an assignment that specifies an origin-centered donut hypothesis in an instance space. The formula is as follows: $$ h \leftarrow \Bigl\langle a < \sqrt{x^2 + y^2} < b \Bigr\...
Gerhardus Carinus's user avatar
2 votes
2 answers
53 views

How many intersections are there for two confocal parabolas with their axis perpendicular to each other? [closed]

I assumed it to be 4 but I was wrong. I tried to write the equations of the parabolas by making them in standard form through origin shifting and rotation of axis and also wrote coordinates in ...
S K's user avatar
  • 81
0 votes
0 answers
21 views

Decomposition of many particle coordinate system into translation, rotation, and vibration

Consider the space $\left(\mathbb{R}^3\right)^N$ of configurations of $N$ three-dimensional points. Given for each point a "mass" $m_n$ and a reference configuration $x^o_n$, is it always ...
creillyucla's user avatar
2 votes
3 answers
59 views

Why does the equation $x = 1$ represent a line in a 2-dimensional coordinate system?

I'm posting a question because I was curious about something while studying linear algebra. As we all know, $x = 1$ is a point in a one-dimensional coordinate system. I understand this part. But why ...
Normalbut_Genuine's user avatar
1 vote
0 answers
23 views

Do coordinate changes only affect antisymmetric matrices linearly?

Let there be an antisymmetric tensor field $\Omega_{ab}(q)$ where $q^i$ are coordinates on a 2N dimensional manifold. For context, this is a general symplectic form on phase space. I want to find a ...
P. C. Spaniel's user avatar
3 votes
1 answer
173 views

Distance of a point from a line measured parallel to a plane

Determine the distance of the point $(3,8,2)$ from the line $\frac{x-1}{2}=\frac{y-3}{4}=\frac{z-2}{3}$ measured parallel to the plane $3x+2y-2z+15=0$. I am getting two different answers using two ...
a_i_r's user avatar
  • 689
0 votes
3 answers
39 views

Finding vector equation of a line

Show that the equation of a straight line passing through the point with position vector $\vec{b}$ and perpendicular to the line $\vec{r}=\vec{a}+\mu \vec{c}$ is of the form $\vec{r}=\vec{b}+\beta \...
a_i_r's user avatar
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