What is Coordinate system: Definition and 200 Discussions
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.
Hello,
I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates).
Griffiths gives the definition of the maxwell stress tensor...
Lets say I have Coordinate Frame's A and B.
and...
I have the coordinates of the 3 principle axes of B in terms of Frame A,
So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A:
XA -> -YB
YA -> XB
ZA ->...
Homework Statement
Starting from one oasis, a camel walks 82.021 ft in a direction 30 degrees south of west and then walks 30 km toward the north to a second oasis. Without using a coordinate system, calculate the magnitude and the direction of the displacement from the first oasis to the...
A charged particle in a magnetic field is spiralling along a path defined in cylindrical coordinates by r
= 1 m and θ = 2z rad (where z is in meters). The speed along the path is constant at 3.87 km/s. What is
the z-component of the velocity, vz, in cylindrical coordinates?
My attempt...
Hi!
I see there are three 3D coordinate systems based on either 3 number (cartesian), 2 numbers and 1 angle (cylindrical) and 1 number and 2 angles (spherical). So can't there be a system based on 3 angles? Thank you.
Homework Statement
I will to explain this without a diagram. Consider a coordinate system(1st quadrant) where the x and y-axis both stop at 7 units (i mean the boundary), there are two points P(3,3) and Q(4,4). How many points can R be positioned such that PQR is an isosceles triangle...
Currently I am using a graphying application called "Autograph" and modeling a building with a dome shaped roof on top. I need to define parabolic shapes in 3d system.
But i can't do it ( my math knowledge is pretty elementary)
What would be the basic parabolic function in 3d that i can base...
Hello to all,
I am currently studying computer graphics and I have came up with the following problem. Consider that we have three coordinate systems, let's say CSA1, CSA2 and CSA3 that have the same origin and differ by a rotation. That is to CSA2 connects to CSA1 by R12 and CSA3 to CSA1 by...
if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is
B=(r2,\theta2,z2)
(if ar,a\theta,az are unit vectors)
then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az>
and the position vector of B is =
r2<ar>+\theta2<a\theta>+z2<az>
so vector BA=...
I'm working with a cartestian system that has certain periodic properties I'd like to exploit with a new coordinate system, but I don't know one that would work. The trajectory of the state of the system is symmetric across non-adjacent squares (ie a checkerboard of sorts), so that (x,y) can...
Hello,
I've been searching all over for the epoch time of the WGS84 coord system. A GPS I'm using says its 06/01/1980, but I don't know if starts from 12:00:00 ET. Is there an epoch by definition or is it arbitrary?
I am reading Differential Topology by Guillemin and Pollack.
Definition: X in RN is a k-dimensional manifold if it is locally diffeomorphic to Rk.
Suppose U is an open subset of Rk and V is a neighborhood of a point x in X.
A diffeomorphism f:U->V is called a parametrization of the...
A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?
Homework Statement
In the xy-plane, sketch the coordinate system [ a; b] corresponding to the basis
{ (1, 1 ) , (1, -1) } by drawing the lines a = 0, \pm1 and b = 0, \pm1. What point in the xy-plan corresponds to a = 1, b = 2?Homework Equations
Not sure of any in this caseThe Attempt at a...
Homework Statement
A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...
Homework Statement
2 coordinate systems are given:
1st: \vec{a}, \vec{b}, \vec{c}
2nd: \vec{m}, \vec{n}, \vec{p}
in system \vec{a}, \vec{b}, \vec{c} basis vectors of 2nd system have values:
\vec{m}=\{2/3, 1/3, 1/3\}, \vec{n}=\{-1/3, 1/3, 1/3\}, \vec{p}=\{-1/3, -2/3, 1/3\}
also known that...
I want to caculate length of curve in Polar coordinate system like this: if r=r(a)
then length of the curve is ∫r(a)da Is this right? if not ,why ?
What's the right one ?
I konw the way in rectangular coordinate system,I just want to do it in Polar coordinate system .
I do not understand Spherical coordinate system.
I'm asked to compare the differences with Cartesian coordinate but I have no idea how to start.
So I would like some help that will at least give me a understanding of the spherical coordinate system, thx
Does "coordinate system" = "gauge"?
Are "coordinate system" and "gauge" the same thing?
What about "coordinate transformation" and "gauge transformation"?
I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element".
2D: polar coordinates - dA = r dr dtheta
3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr
4D: ?
Hi,
I have a certain NON-orthogonal curvilinear coordinate system in 3D (in the metric only g_{13}=g_{23}=g_{31}=g_{32}=0) and I want to take the curl (\nabla\times\mathbf{v}) of a vector.
Any idea on how to do this? The only information I can find is about taking the curl of a vector in...
Hi there, does anyone know where can I found a material or note about how to deduce momentum operator in coordinate system other than linear coordinate (especially in spherical coordinate system)?
Thanks in advanced.
A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system?
30°
180°
90°
60°
45°
Is this problem too simple or am i missing something? if the x and y components are equal in...
Homework Statement
a 3D solid is bounded by 2 paraboloids. The binding condition in cartesian coordinates is
-1+(x2+y2) < 2z < 1-(x2+y2)
a) rewrite the binding condition in parabolic coordinates
b) using parabolic coordinates and the (already derived) metric tensor, find the volume of...
Question Details:
Convert the following equation into cylindrical coordinates...
x^2 + y^2 + z^2 = 4
It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to:
r^2 + z^2 = 4 ... is there a better way to do this?
Consider the line element:
ds^2=-f(x)dt^2+g(x)dx^2
in a coordinate system (t,x) where f(x) and g(x) are two functions to be determined by solving Einstein equation. But I can always make a transformation
g(x)dx^2=dy^2
and then calculate everything in the (t,y) coordinate system. My...
2. In the figure below the particle P is in uniform circular motion. The motion is centered on the origin of an xy coordinate system.
(a) At what values of \vartheta is the vertical component r_{y} of the position vector greatest in magnitude?
(b) At what values of \vartheta is the...
Guys,
Any ideas on how to calculate distance between two points in Polar coordinate system without converting their coordinates to Cartesian?
Ps. I know that if I converted from Polar (r, t) to Cartesian (x, y) by x = r.cos(t), y = r.sin(t), then the distance between two points would be d =...
I wonder if there are coordinate systems that gobally curve and twist and turn and curl, that do NOT admit local orthonormal basis. I know that the Gram-Schmidt procedure converts ANY set of linear independent vectors into an orthnormal set that can be used as local basis vectors. And I assume...
What are the r and θ limits for the triple integral of y where there's a parabloid cylinder x=y^2 and planes x+z=1 and z=0?
I rearranged x+z=1 to get z=1-x => so 1-rcosθ; 0 ≤ z ≤ 1-rcosθ
but I don't know how to get the limits for θ or r. How do I do this?
Greetings,
Regarding a mass on a spring – I know the classic differential equation is
m \frac {dx^2(t)}{dt^2} + B \frac {dx(t)}{dt} + kx = f(t)
F(t) = outside force applied
B = damping coefficient
“X” is in the vertical direction and +x direction is down.
In reading I have...
Homework Statement
which of the following is a coordinate system for specifying the precise location of objects in space?
a. frame of reference
b. diagram
c. x-axis
d. y-axis
Homework Equations
The Attempt at a Solution
I thought it would be a diagram since it would use vectors...
Homework Statement
Can someone give me a real rigorous definition of what a right-handed coordinate system is? I can't find one on the internet.
Is this true:
A coordinate system is right-handed IF AND ONLY IF x-hat cross y-hat = z-hat
?
Homework Equations
The Attempt at a...
Homework Statement
Describe in words the region of R^3 represented by the equation or inequality.
Homework Equations
xyz=0
The Attempt at a Solution
I'm not really sure how to look at the equation. I would think its just the point (0,0,0). Can someone explain if this is wrong.
I have problem with getting normal coordinates offset. I have cube1 and cube2. cube1 position is 10,10,10 and cube2 position is 10,9,10. Cube 2 offset refers to local coordinate system of cube1. If rotation of cube1 is 0,0,0 i get position offset 0,-1,0. But if cube1 rotation is 45,0,0 i get...
(a) A point is observed to have velocity v_A relative to coordinate system A . What is its velocity to coordinate system B which is displaced from system A by distance R ? ( R can change in time)
I think its v_B = v_A - \frac{dR}{dt} . But I am not completely sure why this is the...
I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does.
\frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and...
A general orthogonal coordinate system (u,v,w) will have a line elemet of the form:
ds^2 = f^2 du^2 + g^2dv^2 + h^2dw^2
I have done a lot of vector calculus, but for some reason I can't figure out what this means! What is a line element? I know about the differential length element and its...
Local coordinate system in GR observed.
If one considers coordinate systems in General Relativity.
I think, if I understand it well enough, that in GR space & time and or in space-time a coordinate system depends on locality, e.g. on an average distance between galaxies an the total amount...
Hello guys, at the link
http://mathworld.wolfram.com/Superellipse.html
you can find the definition of superellipse. Now consider the particular super ellipse
\frac{x^{2n}}{A^{2n}} +\frac{y^{2n}}{B^{2n}} = 1
In which A,B, are constant and n is a positive integer.
What is the...
Hello, I have a "simple" problem for you guys. I am not expert in math and so try to be simple.
I explain the problem by starting with one example. The polar coordinate system has the following main property: with two parameters, rho and theta, each point is described as the intersection of...
What is the difference between a frame of refernce and a coordinate system. For example, I know that a rotating frame of reference is non-intertial, but is this also a non-intertial coordinate system?
Thanks.
i have been set the following question
theta = 3r^2
find the magnitude of the acceleration when
r=0.8 m
dr/dt = 4ms^-1
d^2r/dt^2 = 12 ms^-2
my working followed the process of calculating angular velocity with these conditions and angular acceleration with these conditions then...
Say, i have a vector a, defined in a coordinate system, x-y-z and i rotate the axes by an angle theta around the z-axis, so i have my z-component invariant in this change of basis. Can someone show me why,
a_x' = a_x cos\theta + a_y sin\theta and
a_x' = -a_x sin\theta + a_y cos\theta...
Identify a convenient coordiante system for analyzing each of the followling situations:
A. a dog walking along a sidewalk
B. an acrobat walking along a high wire
C. a submarine submerging at an angle of 30 degrees to the horizontal.
This should be rather easy, it was number one of the...
Ok, so if a ball is thrown vertically upward with velocity v on the Earth's surface. (Air resistance being neglected). I have to show that the ball lands a distance (4wsin(beta)v^3/3g^2) to the west where w is the angular velocity of the Earth's rotation and beta is the colatitude angle...