# 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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### Finding Cartesian unit vectors in terms of cylindrical unit vectors

When we want to find what the unit vectors of a cylindrical coordinate system would be in Cartesian we can use the following strategy. First we define a position vector in Cartesian: \begin{align}\vec{...
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### How to Convert Equations of Motion from Cylindrical to Custom Coordinates for a Cylindrical Shell?

I have derived the equations of motion for a cylindrical shell using cylindrical coordinates. However, I would like to switch to a specific coordinate system that is commonly used in mechanical ...
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### Find the volume and total surface area of the solid formed

Let the planes be defined by $$|x|+|y|+|z|=1$$ Find the volume of the solid enclosed and the total surface area of the solid thus generated. I am not able visualise the solid. What will it be$?$ I ...
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### Show that |E×F|=EFsinα

Given are the two vectors E=5.2ar + 6.5 az and F=8.3ar + 12.8aφ - 3az The question is Show that |E×F|=EFsinα
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### How would Cartesian Plane look at infinity?

I’m relatively new to mathematics, and I admit I’m still trying to grasp the concept of infinity, so there might be some errors in my thinking. I understand that $\infty$ is not a real number, which ...
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### For what value of "a" the line and the plane are parallel in real coordinate space? [closed]

The question that I am facing is the following: "For which choice of a real number $a$ are the line $x = y-1 = \frac{(z+1)}{2}$ and the plane $ax+y+2z=3$ in $\mathbb{R}^{3}$ parallel? a) $a=-5$ b)...
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### Find the points at which the diameter intersects the circumference of the circle.

I am working on an optic simulation program. I reached a stage where I am unable to find an algorithm for the desired points. Here is the required problem, I figured out how to find the equation of ...
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### Is a polynomial having $d+1$ coefficients related to how it uniquely satisfies $d+1$ points? [closed]

A degree $d$ polynomial $p(x)=a_d x^d+a_{d-1} x^{d-1}+\cdots+a_1 x+a_0$ has $d+1$ coefficients. Is this fact related in any meaningful way to how a polynomial uniquely satisfies $d+1$ points with ...
1 vote
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### How to convert Cartesian coordinate to polar coordinate in $-180°$ to $+180°$

I wanted to plot temperature at circumference of a circle. I extracted the data by converting cartesian coordinates into polar coordinates by using ATAN2 function, but the plot is having negative and ...
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### Position of a point with respect to parallel lines. [closed]

Prove the fact that if a point in the X-Y plane $(x_1,y_1)$ lies between two parallel lines $ax+by+r=0$ and $ax+by+s=0$ then: $(ax_1+by_1+r)(ax_1+by_1+s)<0$ I tried to assert the above by using the ...
1 vote
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### Could Hilbert Spaces offer the vehicle to make Synergetic's IVM System Functional?

This one is a bit out there in left field, and hope it doesn't draw too much flak. Intended more for the "Mathematically Adept" out there ... which I am not. Please understand that I am not ...
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### Parametric form of Parabola [closed]

Recently I was going through co-ordinate geometry. While studying about parabola I encountered something called "parameteric coordinates". In my textbook some parameteric coordinates were ...
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### A Problem on Family of circles and family of corresponding orthogonal circles

Problem Statement: Let $P(x_1,y_1)$ and $Q(x_2,y_2)$ be two fixed points on xy plane and $R(\alpha , \beta)$ is a point such that $PR:QR=k , \ (k≠1)$ and locus of R for different values of k be ...
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### Is it possible to construct a coordinate system which gets "pulled in"

I really hope i can explain our issue adequately and keep this purely math bound, even if it is technically a graphics programming related question. But over on their exchange ill never get an answer. ...
1 vote
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### What's the equivalent for spheres to homogeneous coordinates for projective spaces?

Projective or homogeneous coördinates are an extremely useful parameterization of projective spaces (indeed often used to define them!), but they are redundant -- a projective space of dimension $n$ ...
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### Coordinate system for the region between a circle and a square

Consider the region outside a circle of diameter $a$ and inside the square of side length $b$ where $b>a$. I would like to represent this region using a coordinate system $(u,v)$ where the circle ...
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### About the definition of a vector in "Mechanics I" by Akira Harashima. Do I understand this definition?

I am reading "Mechanics I" (in Japanese) by Akira Harashima. A quantity is given by three real numbers $(A_x, A_y, A_z)$ in an orthogonal coordinate system $S$, and for another orthogonal ...
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### Nonlinear Coordinate Transform via Intersections?

I've defined a sort of 'warp' procedure for 2d shapes, and I'm curious whether it's familiar within the math canon or even has a name. Given its simplicity I'm sure that there's a formal definition ...
1 vote
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### Are Non-Rectangular Coordinate Systems Ever Used?

In my study of coordinate geometry, I am using the textbook provided by S.L. Loney. In the textbook, he derives various formulas for rectangular coordinates as well as coordinates inclined at a ...
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### Coordinates equipped with equivalences in other conventional (or unconventional) ways

I know coordinates with equivalences of the type : (a,b,c, ...) ~ (a+k, b+k, c+k, ...) (a,b,c, ...) ~ (ak, bk, ck, ...) Does exist some other type of coordinates (and its geometry associated) that ...
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### Understanding The Parabola $x^2 + 2y = 8x –7$

Now, I am reading S.L. Loney's book on coordinate geometry, and am having a hard time figuring the way he examines parabolas. The standard equation to the parabola is introduced to be $y^2 = 4ax$ ...
1 vote
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### If length AB, $(x_1,y_1)$ angle POQ are given. Is it possible to get point B $(x_2,y_2)$ ? Yes or No ? Or is the information insufficient?

This is a modification of my previous question here: Is it possible to get the value of angle BAC in this case? If length AB (say $100$m), $(x_1,y_1)$ say $(-50,0)$ and angle POQ ($30$ degrees) are ...
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### Intersecting lines could have same direction cosines?

When direction cosines of a line are calculated as (per their definition states) the 'cosines' of the angles made by the line with positive X, Y, Z axis (angles measured counterclockwise), we get a ...
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### Doubts Regarding the group structure on Lie groups.

I have some conceptual doubts on the notion of a lie group, or perhaps on the notion of topological group. A lie group is manifold equipped with a continuous group structure of multiplication and ...
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### How to relate a derivative in tortoise coordinates with the radial coordinate?

Since the radial coordinate and the tortoise coordinate are related by r* = r + 2M Log (r/2M-1) How can I write the derivative ... 32 views