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

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Getting coordinate vector in linear algebra

I know how to get the coordinate vector of single matrices by just joining them and doing a gauss jordan. But these are a 2x2, I don't know how to go about this, apparently no elimination can take ...
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17 views

How many kinds of simple coordinates are there in a 2D space?

The question comes form an idea to solve a motion-with-potential problem in 1D space by finding a mathematically equivalent uniform-motion problem in 2D space. ...
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How do points change in a curved surface?

In the middle picture it shows a row of sticks at certain points along a flat surface. Now in the outer left picture (never-mind the outer right one), when the surface becomes curved the points ...
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3answers
50 views

If there are $N$ people on the positive $x$-axis and one man can send a message to another one only if the distance between them is $\leq k $.

The question is how to determine a function which would decide if a pair of persons can communicate with each other, where communication is possible only if the distance between two individuals are ...
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35 views

Converting from set of Cartesian equations to Polar Equation

Is it possible to convert the set of Cartesian equations: $$x(t) = (20-30)*\cos(2t)+45*\cos(2t*(20-30)/20))$$ $$y(t) = (20-30)*\sin(2t)+45*\sin(2t*(20-30)/20))$$ where $$t \in [0,2\pi)$$ Into a ...
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36 views

Partial differentiation in transformed coordinates

Following lecture notes from MIT it says that, given some variable $A = A(x, y, z(x, y, r, t), t)$ where $r$ is a transformed vertical coordinate $\left. \frac{\partial A}{\partial x} \right|_r = ...
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2k views

Minimum moves to reach destination [closed]

Given that a person is standing at $(0,0)$ and initially look in direction of $X$-axis. Now he can walk only at right angle to previous move. Like if he has to go to $(3,3)$ then $6$ moves are ...
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2answers
41 views

Locating a point on a circle

I am having trouble getting the $(x,y)$ of a certain point on the circle. Please look at the image: The circles are the identical, the radius is $1000 \text{ units}$, $S$ is the center with ...
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1answer
35 views

cylindrical and rectangular coordinates

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be ...
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15 views

Vocabulary of line coordinates

We can represent a line in 2 and 3 dimensions using 2 and 4 parameters respectively. For example, in 2 dimensions, we can represent a line using the angle $\theta$ of the normal and orthogonal offset ...
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1answer
26 views

Estimate Rotation and Translation from two sets of points in different coordinate systems

I got one set of 3d $(x,y,z)$ points $( \# \geq3 )$ located in two diffent coordinatesystems. Is it possible to estimate the rotation and translation between these systems? Something like $$ ...
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34 views

Dividing an infinite plane into regions

I am currently working on a computer program for computing layout of graph-based diagrams. Their content is placed in an "infinite" 2D plane with cartesian coordinates in the center of the diagram. ...
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1answer
26 views

How many lines are larger lines made of in a dotted grid?

In a dotted 2d grid, lines can be drawn between the dots. But every dot that the line touches breaks the line up into smaller lines. I want to be able to work out how many lines this bigger line is ...
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1answer
31 views

Equation of pair of reflected straight lines given the equation of pair of incident straight lines

If $ax^2 + 2bxy + by^2 = 0$ represents a pair of lines, then find the combined equation of lines that can be obtained by reflecting these lines about the x-axis. I know that this can be done by ...
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1answer
23 views

How does the transformation $u=x+y$, $v=x/y$ transform the first quadrant?

How is the region $(x,y) \in [0,\infty] \times [0,\infty]$ transformed under the change of coordinates given by $$u=x+y$$ $$v=x/y$$ Would appreciate any hints on how to find the image of such ...
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1answer
22 views

What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...
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3answers
56 views

Alternatives to polar coordinates for mapping point onto one dimensional coordinate

I can map a point (x,y) to polar coordinates (angle,length). However, let's say in this (angle, length) pair, "length" doesn't actually interest me, so I can map (x,y) to a one dimensional ...
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19 views

Example of a Problem Made Easier with Skew Coordinates

I'm looking for an example of a problem which would be hard (or significantly harder) to solve in orthogonal coordinate systems, or at least the Cartesian coordinate system, but is reduced to an ...
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1answer
36 views

Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
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1answer
40 views

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through the points $(1,0)$ and $(3,0)$ and touches the circle $x^2+y^2-2x-8=0$ and have its ...
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1answer
34 views

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r.$.

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r_2>r_3 \cdots r_n$ and $r_1=10$ The circles are such that the chord of contact of ...
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1answer
19 views

Longitude and Coordinates

Let $X=(x_1,x_2,x_3)$ and $Y=(y_1,y_2,y_3)$ be two points on the unit sphere $S^2=\{(x_1,x_2,x_3)\,|\,x_1^2+x_2^2+x_3^2=1\}$. Is there a "nice" necessary and sufficient condition on the coordinates ...
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2answers
38 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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119 views

Using paraboloidal coordinates

I have the 3-dimensional paraboloidal coordinates $$s_{\pm}=\sqrt{x^2+y^2+z^2}\pm z$$ $$\phi=ArcTan(y/x)$$ with the inverse transformation $$x=\sqrt{s_+ \cdot s_-}\cdot cos(\phi)$$ $$y=\sqrt{s_+ ...
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Locus of point moving with circle

Consider the circle of radius $1$ unit with its centre at the point $(0,1)$. From the initial position, the circle is rolled along the positive $x$- axis without slipping. Find the locus of the point ...
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1answer
68 views

Pi for non mathematician

I've been long gone from math (shamefully) and have trouble using some quite familiar concepts... Consider the following picture in which I render two circles with radius 32 (...
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1answer
20 views

2-dim. pendulum: Which coordinates?

I have a rather elementary question: I have a 2-dim pendulum and I do not know how I can descrive the coordinates. In the 1-dim case one coordinates is enough_ the angle. But I do not know how it is ...
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2answers
40 views

how to calculate the coordinates center of a squar [closed]

I need to calculate the center of square cells each cell has 4 (x,y) coordinates. Can one help me to Know how can I calculate the coordinates of the center of each cell?
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69 views

Global and local coordinates on a manifold, and their relations to curvature

I would be pleased to have some information about coordinates in differential geometry. A) First I would like to check whether or not the definitions I use are correct. (Mainly for the sake of ...
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Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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1answer
46 views

Dot product in Curvilinear Coordinate Systems

I came across the dot product in polar, cylindrical, and spherical coordinates, today. After checking they were equivalent to the Cartesian versions, I started wondering how one would figure them out ...
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1answer
20 views

Find the nature of the curve

Given: $x=t^2+t+1, y=t^2-t+1$ Find the nature of the curve. My approach: I was trying to relate $x$ and $y$. However I haven't been able to. Please suggest some methods to solve such kind of ...
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1answer
33 views

Coordinates of specific points on a triangle, given the triangles coordinates

I'm working on a programing project. For that project I have a triangle with points $A,B,C$, where $A(a_1,a_2,a_3);B(b_1,b_2,b_3);C(c_1,c_2,c_3)$. Given the coordinates of the points $A,B$ and $C$, I ...
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2answers
57 views

Better way to denote position on a sphere's surface

TL;DR: Read the bold text. If you have a rectangular plane, you can use two coordinates (X, Y) to define any position on the plane. If you have a sphere, you can still use polar coordinates to denote ...
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2answers
84 views

What is a coordinate system?

What's a coordinate system? I was watching a Khan video about coordinates with respect to orthonormal bases. It is mentioned that orthonormal bases make for "good coordinate systems". I didn't ...
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Ellipsoidal Coordinates Geometrically

Is there a quick, geometric, way of writing down (the square root of?) the Cartesian coordinates $$\begin{align} x^2 &= (a^2+\xi)(a^2+\eta)(a^2+\zeta)/(b^2-a^2)(c^2-a^2)\\ y^2 &= ...
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79 views

converting kph and heading to xyz velocity vector

I am writing software (in C++) that is required to send out messages from our simulation system to another simulation system. Problem is we track the simulation object's current speed (kph) and ...
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1answer
20 views

How to find the $ x,y$ coordinates of a point in between $2$ points in $3$ dimension

Point $1 = (0,0,0)$ Point $2 = (5,6,7)$ Given that point $3$ have a $z$-coordinate of $3$, how can I find the $x,y$ coordinates of point $3$?
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1answer
46 views

How many different ways are there to go from $(0,0,0)$ to $(3,3,3)$?

There is a cube that is on the $(x, y, z)$ coordinates. How do I construct a systematic way to go from $(0,0,0)$ to $(3,3,3)$? Which subject should I study for this question? Please help me! I'm ...
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1answer
50 views

Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
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1answer
67 views

Point transformation of ODEs

I am trying to understand a passage in the introduction to this book, which deals with algorithmical procedures to analytically solve ODEs. Specifically, I do not understand how the ODE $$ y''(y+x) + ...
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1answer
37 views

maximum radius of a circle inscribed in an ellipse

Consider an ellipse with major and minor axes of length 10 and 8 resp. The radius of the largest circle that can be inscribed in this ellipse, given that the centre of this circle is one of the focus ...
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1answer
41 views

N points in a circle around a point on a sphere.

Consider a 3D sphere: $(x_{c}, y_{c}, z_{c})$ : cartesian coordinates of the center $r$ : the radius Consider a random point on the surface of this sphere of coordinates : $(x_{0}, y_{0}, ...
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Separation of the centre of mass coordinates for an N-electron atom

Can anyone tell me how to derive [A8.5] and [A8.6] in Appendice 8 of "Bransden: Physics of solid state matter", in this screenshot: http://i.imgur.com/zSCkVnI.jpg ? It should be easy, but damn me I ...
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What does the phrase “uncoupled across coordinate directions” mean in this text?

The following paragraph is from a paper about comparison of maneuvering target tracking models.In the paragraph it talks about constant acceleration models. The above models are simple but crude. ...
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14 views

create local coordinate system with one axis aligned with a line

I have a line from p1=(x1,y1,z1) to p2=(x2,y2,z2) in global coordinate system. I am trying to create a local coordinate system with origin at p1, whose local z axis i.e. z' is aligned with (parallel ...
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24 views

Integration over length

Trying to integrate over length with natural coordinates I stumbled upon the following equation. Where can I find the explanation of it? Thanks. $$ \int_H L_1^\alpha L_2^\beta \,dH = ...
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11 views

New Axis calculation

I have a task whereby I use an accelerometer to calculate acceleration for a vehicle. The problem I am attempting to solve is to allow the accelerometer to be in any oriertaion. Basically I have a ...
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30 views

Differential Operators in different coordinates

How does one show this identity? $$\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}=\frac{\partial^2}{\partial r^2}+{1\over r}\frac{\partial}{\partial r}+{1\over ...
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132 views

Alternative form of equation of circle?

In a problem set I was solving, one of the solutions used the equation of a circle in the form $$(x-h)^2 + (y-k)^2 + \lambda(ax + by +c) = 0$$ where, $(h,k)$ is any point on the circle $ax+by+c ...