What do you mean by "Curvilinear Co-ordinate Systems" of Vector Analysis?

Answer 1

The usual coodinate system for the plane, say, is a rectangular coordinate system. The curves of constant x or y are straight lines. Similarly, for three dimensions, the usual x,y,z coordinate system is rectangular: surfaces of constant x, y, or z are flat planes.

On the other hand, it is possible to use polar coordinates for the plane or either cylindrical or spherical coordinates for space. So the curve of constant radius is a circle in the plane; the surface of constant radius is a sphere in space. These coordinate systems are called curvi-linear since the level curves or surfaces have curvature. There are other coordinate systems (parabolic, elliptical, etc) which are also, but less frequently used.

Anyway, treating vectors in such coordinate systems tends to be a bit more difficult than in simple rectangular coordinates. But often a spherical coordinate system (say) is more adapted to specific problems than a rectangular coordinate system is, so it becomes important to learn how to express vector quantities in these systems. One important difference: in curvilinear coordinate systems, vectors are based at specific points and do not maintain their components when moved to other places. This alone can cause a lot of confusion at first.

Answer 2

Cartesian co-ordinates (commonly written x,y) use 2 perpendicular linear axes to describe all points on a plane (or x,y,z and 3 axes in 3-D).

Curvilinear co-ordinates are co-ordinate systems that use one or more angles to describe 2-D or 3-D space. For example, instead of x,y you could use P,r where P is a distance and r is an angle. Both systems can describe a point.

Answer 3

If it helps to understand the importance of curvilinear coordinate systems, Einstein's General Relativity is entirely based on it. And since he needed to study only those physical properties which was independent of choice of curvilinear coordinate system, he expressed all of his laws in terms of tensors, which are invariant under transformations in curvilinear coordinate systems. This was a way of breaking free from being dependent on Euclidean physics, which may not necessarily be reflected in physical reality. String theories today are quantum extensions of Einstein's curved spacetime.

Answer 4

I am a math major at FSU...so I can help you here.

Vector's basically deal with the direction in space/time that a line can travel. It is not the regular highschool x y plots you made. This is x y and z. It is in 3 dimensional space. Now Cuvilinear will deal with infinity problems, a lot of 0's, 1's, and negatives. So get ready for it.

I hope you arne't taking a class and you are expected to know this. If that is the case, DROP THE CLASS. It takes awhile to fully understand vectors.

Just wikipedia "vector" for more information on it. AND get a Dummy's Guide to Calculus...it will explain vectors to you. But before you learn vectors, you need to know other equations and math problems that will eventually lead up to it.

Goodluck and Godspeed.

Answer 5

not pegs. I do colour co-ordinate with the coat hangers when I've ironed the garments. i imagine i'd have become somewhat obsessed; determining to purchase extra hangers only for a million or 2 colorations i choose. i'm off to get a existence now..... Edit: basically seen smoothie's answer, imagine we ought to continually both bypass to counselling. Least i'm not on my own!

Answer 6

Different ways to indentify position. In 2D there is the standard (x,y) system but there is also the polar system (r, theta) where r=distance from origin and theta=angle from positive x-axis. Go to a college bookstore and look for polar graph paper and you will get a picture of what is going on. Or browse on the net.

Google "polar graph paper" or try

http://images.google.com/imgres?imgurl=http://www.math.ttu.edu/~kesinger/polar.gif&imgrefurl=http://www.math.ttu.edu/~kesinger/&h=586&w=668&sz=14&tbnid=T0O4Fa_vPatmEM:&tbnh=121&tbnw=138&prev=/images%3Fq%3Dpolar%2Bgraph%2Bpaper&start=1&sa=X&oi=images&ct=image&cd=1

for a picture

Answer 7

Check it here.
http://newton.ex.ac.uk/teaching/CDHW/EM/CW970129-3.pdf