Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [coordinate-systems]

Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

0
votes
2answers
53 views

From $dxdy$ to $\rho d\rho d\phi$. Where am I doing wrong?

A small area element in the xy plane reads $da=dxdy$. In plane polar coordinates, it reads $da=\rho d\rho d\phi$. We also know, $$x=\rho\cos\phi,~ y=\rho\sin\phi.$$ So using partial derivative formula,...
0
votes
0answers
10 views

Local polar coordinate system to global polar coordinate system

Let's have a point located in the local polar coordinate system at $(r,\phi)$. The origin of this local system is located at $(R_0,\Phi_0)$ in a global coordinate system. I would like to express $(r,\...
1
vote
0answers
32 views

Questions on coordinate representation of a map between smooth manifolds (sphere with stereographic projections)

On the sphere $S^n$, consider the atlas given by the stereographic projection: $\{(U_1, \phi_1), (U_2, \phi_2)\}$, where $U_1 = S^n \backslash \{N\}$, $U_2 = S^n \backslash \{S\}$, $N$ and $S$ are ...
1
vote
0answers
16 views

Questions about the basics of coordinate systems and their basis

Since I think I am missing some basic understanding about coordinate systems and their basis, I would really appreciate your help answering my questions. Also if something isn't written mathematically ...
0
votes
1answer
29 views

Change of base matrix between displaced and rotated coordinate systems

I have a function that solves a problem when a specific angle equals $0$. The same function can be used with non-zero angles if you compute the problem from other coordinate system. The scheme of the ...
0
votes
1answer
22 views

Coordinates of 3D vector in rotated coordinate system (without using a matrix)

The problem: There is a vector with coordinates X,Y,Z. This vector is in a coordinate sytem that has been rotated by A degrees along the X axis and B degrees along the Y axis. I would like to know ...
0
votes
4answers
31 views

Is it possible to know the equation of a line by only knowing the slope and where the line intercepts the x axis?

I do not know where my line intercepts the $y-$axis. I know it intercepts the x axis at coordinate $(10, 0)$. At an angle of $30^{\circ}$. So would $$y = mx + b = (10\tan(30)) + b$$ be correct? ...
0
votes
1answer
20 views

I have 3 objects in the real world that I want to mark on a x y graph, I know where to plot 2 of them but how to mark the third point?

In the real world I have 3 points of interest ABC. A B and C are each 20 cm apart and are placed in a equilateral triangle formation. A coordinates are (-10, 0) and C coordinates are (10, 0). I'm ...
0
votes
1answer
16 views

Given a set of points, find maximum area of triangle

Given a finite set of 2-d points, I need to find the maximum area of triangle formed. My solution steps : Take mean of points , lets call it (x_m, y_m). Take 3 most distant points from (x_m, y_m). ...
1
vote
1answer
30 views

1 Coordinate Geometry [closed]

In a Quadrilateral ABCD ,if the bisectors of angle A and angle C meet on BD ,prove that the bisectors of B and D meet on AC. Can someone please help me with a coordinate geometry proof .
2
votes
0answers
38 views

Geodesics under coordinate transformation

Consider components of metric tensor $g'$ in a coordinate system $$g'= \begin{pmatrix} xy & 1 \\ 1 & xy \\ \end{pmatrix} $$ We can transformation rule which brings $g'$ to euclidean metric $...
1
vote
1answer
21 views

How to designate a coordinate system

Imagine I have a coordinate system where the coordinates are $a$ and $b$ How to designate this system? $a-b$ $ab$ $a,b$ $aOb$ (where $O$ stands for origin). Is there an accepted standard? I have ...
0
votes
0answers
14 views

Calculating point B given point A and Euler angles in 3D [closed]

Given 3D cartesian coordinates for point $\mathbf{A}$ relative origo, $\vec{OA} = (x_A,y_A,z_A)$, Euler Angles from point $\mathbf{A}$ facing point $\mathbf{B}$, yaw-pitch-roll order, and length of $\...
0
votes
0answers
15 views

Relation between Normal coordinates and Cartesian coordinates in flat space

Let $\gamma_v$ be the unique maximal geodesic with initial conditions $\gamma_v(0)=p$ and $\gamma_v'(0)=v$ then the exponential map is defined by $$exp_p(v)=\gamma_v(1)$$ If we pick any orthonormal ...
1
vote
1answer
40 views

Help a robot avoid computing the matrix inverse using the Gram-Schmidt process

Imagine you have a robot whose position is recorded as $t_1, t_2, t_3, \dots$ in its coordinate frame. Check the visualization here. We can write down the robot's basis in our 2D image plane, i.e. ...
0
votes
0answers
9 views

Vectors and Coordinate planes with non-perpendicular axis

Given two vectors $A$ and $B$ with $|\theta_A-\theta_B|=\frac{\pi}{2}$ and $r_a$ and $r_b$ are any real numbers, can every possible vector be represented by $A+B$ with some constant $r_a$ and $r_b$? ...
1
vote
0answers
19 views

How to fill a rectangle with smaller specific rectangles that have cardinal information about their adjacent neighbours

Lets say its 6x6 grid that is represented by top left(0,0) and bottom right(1,1) in coordinate system. Next, I have set of objects with their cardinal directional information about each of their ...
1
vote
2answers
33 views

How can I apply a sign to a calculated angle?

apologies in advance as I'm a software engineer and not a mathematician so I will probably explain this very poorly. Thanks for muddling through it. I have a system with three points in three-...
0
votes
0answers
13 views

How do I use a set of orthogonal vectors as a new coordinate system?

I'm dealing with a problem where I need to apply a coordinate transformation to a set of data, but am not sure how. This is probably very simple, but I want to make sure I do it right. Suppose that ...
0
votes
1answer
28 views

Find the grid number of a X,Y coordinate

Let's say we have a grid separated in chunks. Each chunk contains multiple points. Grid and chunks Each chunk has a number : Chunks numbers Let's say we have a point X,Y, how do we find its grid ...
0
votes
1answer
18 views

About the definition of divergence

The divergence is defined as: $\nabla . \mathbf{A}=\lim \limits_{V \to 0} \dfrac{ \unicode{x222F}_{\partial V} \mathbf{A}.d\mathbf{S}}{V}$ My question is of two parts: $(1)$ If we are using ...
0
votes
1answer
10 views

Calculating projected coordinates for rotations on a Cartesian plane

There are four points Blue (4,1), Purple (6,3), Red (9,3) and Green (4,5) plotted on a 1 cm Cartesian grid. I want to rotate the diagram about the Blue point anticlockwise (2nd layout) and clockwise (...
1
vote
0answers
26 views

Cross product of unit vector in cylindrical and spherical coordinate system [closed]

For cartesian, the unit vectors are $(ax, ay, az)$ For cylindrical, the unit vectors are $(ar, a\theta, az)$ for spherical, the unit vectors are $(aR, a\theta, a\phi)$ How can one compute cross ...
0
votes
0answers
31 views

Find joints positions in 3D robotic manipulator?

I have been trying to solve this 3D mechanics problem, but can't seem to be able to figure out what the best way to do it is. I have this $3D$ robot manipulator with $3$ rotary joints $(B, C, D)$. I ...
-1
votes
1answer
12 views

Cartesian Coordinate system and straight lines

It's just a random doubt that came to my mind but it has really got me confused. If we say that a straight line makes an angle, say 60 degrees, with the negative direction of the X axis, then does ...
0
votes
1answer
27 views

How to Calculate Point on an Arc (Given: Center, Arc Endpoints, Direction, and Distance along the Arc)? [duplicate]

I need to calculate the grid coordinates for a point on an arc using the distance traveled along it. I'm given the endpoints, radius, center, clockwise direction, and distance. How can I calculate ...
0
votes
1answer
31 views

Computing endpoint coordinates of point P of a line of known length d that ends perpendicularly at the known mid-point coordinates of another line

Is there a simple formula that gives the coordinates of a point P, which is the endpoint of a line of length d that passes perpendicularly through the midpoint of another line? The distance d of the ...
-1
votes
0answers
39 views

How to prove $\displaystyle \int_V \dfrac{dx\ dy\ dz}{r^2}$ doesn't contain singularity?

Let's consider the transformation from spherical to Cartesian coordinates: $r, \theta, \phi\overset{T}{\rightarrow}x,y,z$ Let: $\vec{a}=\vec{r} (r+\Delta r,\ \theta,\ \phi)-\vec{r} (r, \theta, \phi)$...
1
vote
1answer
55 views

A quotient space by group action is manifold $???$

The aim of this question is to construct a exmaple of quotient manifold. First, I set notations and difnitions. Let $\mathbb{R} , \mathbb{C}$ be real and complex numbers with usual topology. We ...
0
votes
0answers
11 views

Question about Helmholtz's paper “ON THE CONSERVATION OF FORCE”

Below follows the exact extract from Helmholtz's paper "On the conservation of force". Let us now imagine, instead of the system $A$, a single material point $a$, it follows from what has been just ...
0
votes
1answer
26 views

Do I abuse notation ? $\mu(dx)=f(x)dx=f(g(t))g'(t)dt=\mu(dt)$?

I have that $$\mu(A)=\int_A f(x)dx=\int_B f(g(t))g'(t)dt.$$ Do I abuse notation when I right $$\mu(dx)=f(x)dx=f(g(t))g'(t)dt=\mu(dt) \ \ ?$$ In fact in an exercise of physic I have that $dF=F(x)dx$. ...
0
votes
0answers
20 views

pass Euler angles from a coordinates system to another

I have a coordinates system $(\vec{x},\vec{y},\vec{z})$. In wich there is three known perpendicular vectors of length 1 that define another coordinate system: $(\vec{x'},\vec{y'},\vec{z'})$. ...
0
votes
2answers
33 views

Oblate Spheroidal coordinate system graphic representation of ellipse

I am having difficulty understanding how to interpret the coordinate system proposed by Spencer. From his handbook Field Theory Handbooks ISBN 9783540184300 proposed a system with the domains ...
0
votes
0answers
7 views

what is the result type 3D vector, point and scalar arithmetic operations?

I doing programming but I am not good at math. I want to represent point and vector in different type. Both point and vector are tuple of 3 elements, where point represent location and vector ...
2
votes
1answer
30 views

Getting equation of a curve which touches a given curve

There was a Q in my class, "From any point on $ b^4x+2a^2y^2=0$ pair of tangents PQ and PR are drawn to hyperbola $ x^2/a^2-y^2/b^2=1$. Prove that QR touches a fixed parabola and also find it's ...
1
vote
0answers
14 views

Prove that there exists a $m×m$ lattice square in the $x-y$ plane such that none of its coordinates are visible [duplicate]

Call a lattice point 'visible' if the $gcd$ of its coordinates is 1. Then there exists a $m×m$ square in the $x-y$ plane such that none of its coordinates are visible. You can actually define such ...
1
vote
1answer
22 views

Elementary Problem on Coordinates

If I invented a coordinate system of 3 parameters - just like in Cartesians $(x,y,z)$, should those 3 parameters have directional vectors that are mutually perpendicular?
1
vote
1answer
75 views

Why is $y = x^{1/3}$ not differentiable at $x = 0$?

It seems like the differentiability of a curve should morally speaking be part of the curve itself. More specifically, whether or not a curve is differentiable should not depend on the coordinates. ...
0
votes
1answer
35 views

Isometric Drawing Tool: Converting 2D information to 3D

I was drawing with the NCTM Isometric Drawing Tool, and produced the image seen here. I also noticed that it is possible to view the isometric drawing in 2D, and was wondering if/how it is possible to ...
0
votes
2answers
28 views

Matrix free linear map decomposition

Consider $a_1,\dots,a_n\in\mathbb{R}^n$ and identify $a_j\in\mathcal{L}(\mathbb{R},\mathbb{R}^n)$ via $\varphi\mapsto \varphi1$. Also, consider $A\in\mathcal{L}(\mathbb{R}^n)$ given by $$A\colon (x_1,...
1
vote
0answers
13 views

Representing position vector

I know the position vector in spherical coordinates: $\vec r = rsin\theta cos\phi \hat r + rsin \theta sin\phi \hat \theta + rcos \theta \hat\phi$ But I do not know the derivation of it. How is the ...
1
vote
0answers
28 views

Shortest distance to a spheroid

I have a point $P'$ given by known Cartesian coordinates $(x',y',z')$ and an oblate spheroidal surface parameterized by \begin{align} x &= a \cosh{\mu} \cos{\nu} \cos{\phi} \\ y &= a \cosh{\mu}...
0
votes
0answers
17 views

Interpolation on curvilinear grid

How could someone interpolate spatial data on a curvilinear grid, like the one in the picture shown?
0
votes
1answer
46 views

The coordinate of a circle [closed]

Suppose two circles intersect and form three regions A, B, and C. The center of circle A is (2,2) and the center of circle B is (x,y). The three regions formed by the two circles are equal in area. ...
0
votes
0answers
20 views

Laplacian Identity in Tensor Notation

I am working through a problem in this book where it asks for the proof of the following identity: $\nabla^2f=g^{ij}\nabla_if_{,j}$ This is what I came up with: $\nabla^2f=\nabla\cdot\nabla f$ $\...
1
vote
0answers
25 views

When does a conic represent an empty set?

In my textbook of Arihant publications it says: If a conic represents an empty set then, ∆ not= 0 and h^2 I don't understand what is meant by an empty set represented by the conic and how this ...
0
votes
1answer
35 views

How many straight lines and circles can be drawn in the plane so that they are equidistant from all four points?

Four points on a plane are given which are not collinear or all on one circle. How many straight lines and circles can be drawn in the plane so that they are equidistant from all four points? If not ...
0
votes
0answers
15 views

Rotation with roll pitch and yaw in different coordinate system

Say I am given a point in an x1,y1,z1 coordinate system. I have a different coordinate system, x2,y2,z2 that has the same origin as the x1,y1,z1 system, but the axis are not aligned. I have roll, ...
2
votes
2answers
64 views

Finding the area of shaded region using co-ordinate system

I am trying to solve the problem above by co-ordinate geometry. Here is what I have done: I flipped the figure (just for simplicity) such that the point B is to the right of AC. Then I took C as the ...
1
vote
0answers
23 views

How to perform these two conversions from a symmetric metric

Suppose in Cartesian coordinate system a Minkowski metric for flat spacetime can be written as : $$ ds^2 = a^2 (t)[-(1 + 2ψ(t,x,y,z))dt^2 - 2B_idx^idt + (1 - 2ψ(t,x,y,z))dx^{(i)2}] $$ This is a ...