Cartesian Definition and 561 Threads

Homework Statement See the picture for the situation of the problem. I'm told that any ray starting from S and getting through the "Cartesian Oval" reach point P. I must show that the equation of the interface curve is l_0n_1+l_i n_2=K where K is a constant. So far I've showed that...

Hi there, just a pretty straight forward query I need cleared up... If a question asks for the null space of A in cartesian form how do I set it out? This is what I've got: X = ( -2; 1; 1)*x3 for all values of x3 Therefore, Null(A) corresponds geometrically to the line through the...

Goldstein(3rd) 1.15 Generalized potential, U as follows. U( \stackrel{\rightarrow}{r} ,\stackrel{\rightarrow}{v})=V(r)+\sigma\cdot L L is angular momentum and \sigma is a fixed vector. (b) show thate the component of the forces in the two coordinate systems(cartesin, spherical...

Homework Statement "Determine the Cartesian equation of the plane that passes through the origin and contains the line \vec{}r = (3,7,1) + t(2,2,3) Homework Equations Ax + By + Cz + D = 0 The Attempt at a Solution Well. The way that I was taught to find the Cartesian Equation...

Homework Statement Transform the equilibrium equations from cartesian to polar coordinates using x = rcos(theta) and y = rsin(theta): \frac{\partial\sigma_{xx}}{\partial{x}} + \frac{\partial\sigma_{xy}}{\partial{y}} = 0 \frac{\partial\sigma_{yx}}{\partial{x}} +...

I'm trying to sharpen up my maths before I go back to university to start my PhD and am working through Roel Snieder's excellent book 'A Guided Tour of Mathematical Methods for the Physical Sciences'. The problem I am working on is how to evaluate the volume of a sphere in Cartesian...

Homework Statement (2 CIS (pi/6))*(3 CIS (pi/12)) Homework Equations Also what is CIS? I believe it's Cos+i*sin but how do you use it? The Attempt at a Solution i simplified it to 6 CIS (pi/12) How do i turn it into cartesian?

Problem solved!

Homework Statement Find the cartesian equation for the curve r=csctheta The Attempt at a Solution I understand how to get the answer, by changing it to r=1/sin, and then rsin=1, and then since y=rsin, then y=1. What I'm not understanding is the relationship between y=1 an r=csc. I...

I'm attempting to get an output of a specific Cartesian oval (or oval of descartes, the perfect imaging system in physical optics- viz. perfectly stigmatic imaging). Algebraically I've deduced the equation to be 3/2 Sqrt[(30 - x)^2 + y^2] + Sqrt[x^2 + y^2] == 7/20 (Mathematica input). I'm...

I'm attempting to get an output of a specific cartesian oval (or oval of descartes, the perfect imaging system in physical optics- viz. perfectly stigmatic imaging). Algebraically I've deduced the equation to be 3/2 Sqrt[(30 - x)^2 + y^2] + Sqrt[x^2 + y^2] == 7/20 (Mathematica input). I'm...

Homework Statement Transform the vector A = x2 - y5 + z3 into spherical coordinates at (x= -2, y= 3, z=1 ).Homework Equations http://www.equationsheet.com/eqninfo/Equation-0348.html http://en.wikipedia.org/wiki/Spherical_coordinate_system The Attempt at a Solution I know the transformation...

Homework Statement I have a rather complicated vector field given in cartesian coordinates that I need to evaluate the line integral of over a unit square. I know to use Stoke's Theorem to do this, and I suspect that the integral would be greatly simplified if it were in cylindrical...

Homework Statement (1)If C is a set with c elements , how many elements are in the power set of C ? explain your answer. (2)If A has a elements and B has b elements , how many elements are in A x B ? explain your answer. Homework Equations The Attempt at a Solution (1)The...

Is it correct that the angle of intersection of two curves is the same in x,y coordinates as in r,theta coordinates? If so, why is this?

Homework Statement Establish an equation in polar coordinates for the curve x^2+y^2=4y-2x Homework Equations n/a The Attempt at a Solution I know that x^2+y^2=r^2 so I used substitution, and now have r^2=4y-2x. Now this next part, I'm really not sure if I'm allowed to do this... i...

Double Integrals: cartesian --> polar and solve here is everything: #19: I am stuck...This is to be solved using cylindrical polar coordinates and a double integral. I understand simpler ones such as find the volume of the solid under the cone z= sqrt(x^2 + Y^2) and above the disk (x^2 + y^2...

Homework Statement Particle is moving with velocity v= ui along the line y=2. What is its v in polar coordinates Homework Equations The Attempt at a Solution I think I'm being really stupid here but not entirely sure where to start. If you integrate to find position you have it as...

Homework Statement eliminate the parameter to find cartesian equation of the curve Homework Equations The Attempt at a Solution @ means delta x = 4cos@, y=5sin@, -pi/2 <= @ <= pi/2 i have no idea how to do it.. i read the whole chapter and it doesn't make any sense.. so i...

Can anyone suggest how to calculate the semi major axis of a body in an elliptical orbit when all I've got is x,y,z,vx,vy and vz? I'm guessing I need to calculate the eccentricity too. I really suck at conversions like this. :(

Homework Statement Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. int(-1to1)int((sqrt(1-y^2))to(sqrt(1-y))[x^2+y^2]dxdy Homework Equations x=rcostheta y=rsintheta The Attempt at a Solution...

Is it possible to do general relativity but avoid the difficult mathematics of generalized coordinates, tensors, and computing the metric of a space-time manifold by using ordinary cartesian coordinates in a 5 dimensional space? We can picture a curved 4 dimensional spacetime as being...

I'm trying to prove that the cartesian metric g_{mn}=\delta_{mn} doesn't change under a transformation of coordinates to another cartesian coordinate set with different orientation. As a starting point I am using ds^2=\delta_{mn}(x)dx^m dx^n=\frac{\partial x^m}{\partial y^r}\frac{\partial...

Homework Statement Find the Cartesian equation of the parametric surface: [2cos(t)cos(s), 3sin(s), sin(t)cos(s)] Find eqn. of the tangent plane when S = 0, t = pi/2Homework Equations The Attempt at a Solution I'm not quite sure what to do. All I've done is squared each term, which gave me...

Homework Statement Find the gradient of 3r^2 in spherical coordinates, then do it in Cartesian coordinates Homework Equations \nabla f=\hat r \frac{\partial f}{\partial r} + \hat \theta \frac{1}{r} \frac{\partial f}{\partial \theta}+ \hat \phi \frac{1}{r\sin \theta}\frac{\partial...

Homework Statement how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Homework Equations z = ( a + i b) The Attempt at a Solution r= -2 tan inverse = pai/4 / pai/4 ?? Thank you very much for helping me out

Express -2(cos pai/4+i sin pai/4 ) in Cartesian , Polar and Exponential form ? how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Thank you very much

Hi there, I am getting confused about how to work this out. I know that to convert cartesian coordinates to spherical coordinates you can use: theta=arccos(z) phi=arcsin(y/sin(theta)) my problem is that I have a list of coordinates, let's call them THETA and PHI. I change them into X,Y,Z...

Hello, How can i calculate compass heading from cartesian vectors? Specifically, a planet of radius R is located at (0,0,0), with north pole being at (0,R,0). An airplane is located at POS, and is flying in DIR direction. How can i determine the (true north) compass heading of the plane...

Proposition: Let \{A_n\}_{n\in I} be a family of countable sets. Prove that \bigotimes_{i=1}^n A_i is a countable set. Proof: Since \{A_n\}_{n\in I} are countable, there are 1-1 functions f_n:A_n->J (J, the set of positive integers) Now let us define a function...

Homework Statement Solve: \iint_{\frac{x^2}{a^2}+\frac{y^2}{b^2} \leq 1} \sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}} dx dy Homework Equations Cartesian to Polar The Attempt at a Solution Well - this Integral should be solved as a polar function (the radical should be...

I'm talking about E \times F, where E,F \subseteq \mathbb{R}^d. If you know E and F are compact, you know they're both closed and bounded. But how do you define "boundedness" - or "closed", for that matter - for a Cartesian product of subsets of Euclidean d-space? The only idea I've had is...

Suppose a group G and it acts on a set X and a set Y. (a) A simple group action on the cartesian product would be defined as such: G x (X x Y) --> (X x Y) to prove this is a group action could I just do this: Suppose a g1 and g2 in G. g1*(g2*(x,y))=g1*g2(x). This is obvious...

Homework Statement What is the proper notation for writing the set of all ordered pairs of real numbers that are in quadrant 1 and 3 of the real plane? Homework Equations The Attempt at a Solution I was thinking something like $\left\{...

I have an integral \int \int_S x^2 + yz \ dS and wish to transform to spherical polar coordinates. How does dS become dS = r^2 \sin \theta d\theta d\phi ?? Where surface S is x^2 + y^2 + z^2 = 1

I am hoping to find the coordiantes of all 4 vertices when the rectangle is in any orientaion knowing the length l, the width b, the coordinate of its center mark (xcen,ycen), and the coordinate of vertex A as shown below: This is NOT HOMEWORK so although I think it is possible to do, I am...

Homework Statement The equation of a conic in polar coordinates is: r = \frac{r_o}{1-\epsilon cos(\theta)}. \epsilon is the eccentricity, 0 for a circle, (0,1) for an ellipse, 1 for a parabola, and >1 for a hyperbola. What is this equation expressed in Cartesian coordinates...

[b]1. Was wondering if anyone could help me confirm the polar limits of integration for the below double integral problem. The question itself is straight forward in cartesian coordinates, but in polar form, I'm a bit suspect of my theta limits after having sketched the it out. any help much...

Homework Statement Solid horn obtained by rotating the points {[x=0], [0 \leq y \leq 4], [0 \leqz \leq \frac{1}{8}y^{2}] } circles around y-axis of radius \frac{1}{8}y^2. Set up the integral dzdxdy.Homework Equations Cartesian coordinates.The Attempt at a Solution I don't understand how the...

converting cartesian to parametric equation R3 hi, I can't convert cartesian to parametric equation this equation 3x-y+4z-6=0 In example is given only 3x-y+4z-6=0 and says to convert it to parametric form ? how this can be done ?

So I wonder why the gradient in coordniates other than cartesian ones bears coefficients. Let's take spherical coordinates for example. We have (Source) - Sorry if image doesn't work - too lazy to get the TeX right. From what I know, I don't see anything that raises cartesian coordinates...

Homework Statement Find a Cartesian equation of the plane P containing A (2, 0, −3) , B(1, −1, 6) and C(5, 5, 0) , and determine if point D(3, 2, 3) lies on P. Homework Equations vector cross product ax + by + cz = 0 The Attempt at a Solution Take the cross product of AB and...

I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley. On slide 6 they give the usual...

The problem is to prove that if M and N are orientable manifolds, then MxN is an orientable manifold

Homework Statement I need to convert this to a polar coordinate \vec{F} = 5xz\vec{i} + 5yz\vec{j} + 4z^3\vec{k} Homework Equations The Attempt at a Solution I have no idea to do this, can someone help?

Homework Statement convert double integral from line one to polar integral and then evaluate see problem 12 attachment Homework Equations y=rsinx x=rcosx r^2=x^2+y^2 The Attempt at a Solution see problem 12 attachment I calculate a area of zero. are my limits wrong and if...

When converting an AC waveform (from polar) to a rectangular form, a source quotes v(t) as x + jy. But how is this possible?...I mean v(t) is clearly the x-axis length of r (vm). Further more how does complex number come into the picture?...every thing is real.

Homework Statement Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates. Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z ... (divergence in Cartesian coordinates) I need to...

Homework Statement Well, it's all in the title. I just need to show that Gauss's theorem applies to this fluid flow and have converted all my (x,y,z) components to their respective (r,theta,phi) versions, but I can't remember the spherical counterparts of \hat{x},\hat{y},\hat{z}.

1. This is not a question from the book but i think if i can get the answer to this it will clear the idea i am confused about can i covert a cylindrical vector such as P(1 ar, 1a\theta) into cartesian after using the matrix i got Px = cos \theta - sin \theta Py = sin \theta + cos...