Axes Definition and 178 Threads

How could I change an equation to look the same as it did with "inverted" axes? I have graphed something in mathematica and when plotting I accidentally told it to plot the x and y axes backwards- as in x ranges from 1 to -1 from left to right and y ranges from 1 to -1 from bottom to top. Now...

Homework Statement A scalar function can be represented as a position on the x-y plane, or on the u-v plane, where u and v are axes rotated by θ from the x and y axes. Prove that the 2-dimensional \nabla^2 operator is invariant under a rotation of axes. ie, \frac{\partial^2 f}{\partial...

Homework Statement x1,x2) are the components of a 2 dimensional vector r when referred to cartesian axes along the directions i,j. derive the relations x1'= cosΘ x1+sinΘ x2 x2'=-sinΘ x1+cosΘ x2 for the components (x1',x2') or r referred to new axes i',j' obtained by a rotation of the axes...

Hi, I've been stuck on this for a few days now. I am trying to determine the X and Y axis of the general conic section equation: Q(x,y)=Ax^2 +Bxy+Cy^2 +Dx+ Ey+F =0 I have A, B, C, D, E, and F. I have already determined the center coordinates, but I have not found information on...

In analytical mechanics, we always need to solve the eigenvalue problem of moment of inertia tensor to find out the principal axes and principal moment of inertia. Well, I know that if we know the principal moment of inertia, the total rotating energy of the system could be written as...

Alrighty-then:smile:Homework Statement This is from a book called "Engineering by Design." It sucks. Really. It asks problems and doesn't provide sufficient information to answer them. Now that I have complained, here is the question: Explain with sketches why a combination of rotations...

Why is a space probe spinning around its own axes, when flying through space?

Homework Statement a 0.2 meter straight piece of wire has a current of 30 ampere flowing through it, pointing in the +z direction. the magnetic field presented in space is given by: B = 2B_0i + 4B_0j + 3B_0k what is the force on the wire? Homework Equations magnetic force on a...

principal axes for orthotropic material?? i am very much confused about the term 'Principal Axis'..my situation is I am not able to understand the following lines from a book '.....Since it is difficult to determine the three principal axis of a specific element to define the orthotropic...

[SOLVED] Moment of Inertia Problem: Perpendicular Axes THM Homework Statement First, the problem asked us to basically prove the Perp. Axes Thm and then use it to prove that the MoI of a thin, uniform square sheet with mass M and side L through ANY axis in its plane is equal to 1/2 M L^2...

Let a point be(x,y) If the coordinate axes are shifted in clockwise direction by an angle theeta,what are the coordinate of the new point(X,Y).

Particle 1 is moving on the x-axis with an acceleration of 5.45 m/s^2 in the positive x-direction. Particle 2 is moving on the y-axis with an acceleration of 7.56 m/s^2 in the negative y-direction. Both particles were at rest at the origin at t = 0 s. Find the speed of particle 1 with respect...

Homework Statement The plane defined by x + 2y + 3z = 12 and the point P(4,6,8) Find where the plane intersects the x,y and z axes Homework Equations The Attempt at a Solution I don't know where to start, I can vaugely remember that the variable t is brought into the equation, but...

The book was vague on this subject and as a result, everyone is in disagreement on this. All my friends think that the directions of the principal axes are the eigenvectors of the tensor of inertia wrt some Oxyz axes. I think that the directions of the principal axes are obtained by...

in my textbook says that a^2=p^2/(1-e^2)^2, and b^2=p^2/(1-e^2), are two axes of an ellipse, however there is no any proof as to how we can be sure that a and b are such axes. Where p is the focal parameter, and e is the eccentricity of the ellipse; a- is the big semi-axes, b- the small one.So i...

in my textbook says that a^2=p^2/(1-e^2)^2, and b^2=p^2/(1-e^2), are two axes of an ellipse, however there is no any proof as to how we can be sure that a and b are such axes. Where p is the focal parameter, and e is the eccentricity of the ellipse; a- is the big semi-axes, b- the small one.So...

Hi all, I've been stumped on this problem for over a month. Any guidance would alleviate my overwhelming frustration. Here is the original problem statement: Find the principal rates of deformation and principal axes for the flow given by: u = (x,y) and v = 0, satisfying the...

Homework Statement I have the field at the center of a charged ring on the x,y axes (top half has charge density of -lambda, bottom is +lambda lambda=la) to be E=(lay^)/(2pi epsR) (eps=epsilon) i can't find the potential for this, R=radius, Can anyone help? Homework Equations...

Pulley Question - Are the axes wrong?? Homework Statement Please see problem # 2 in the attached document. Homework Equations Newtons second Law The Attempt at a Solution See the two last pages of the attachment, I have attempted a complete solution but my answer is incorrect, I have...

I have a Sakai gyro that looks like this: http://img165.imageshack.us/img165/4556/sakainn4.gif Now I have to find the three main axes of the moment of inertia by considering symmetries. I put the two axes into the picture which I think I know. The first one would be the upright because...

when we teach classical space time diagrams we measure on the vertical line the dependent space coordinate whereas on the horizontal axis we measure the independent time coordinate in accordance with what we learn say in analytic geometry. in special relativity we reverse the situation...

Hey guys, This is my first post, and I spent a lot of time trying to figure this one out and I am totally stumped! Two of my classmates got different answers, and no matter how many ways i work this problem out, I still get the same answer. Also, forgive me if my mistake is really simple...

there are three axes when the angle made between each angle is 90deg. what would be the situation if this became 60deg. i mean how many axes would be there

I am having trouble rotating the axes to eliminate the xy-term. 8x^2+64xy+8y^2+12x+12y+9=0 I know Ax^2+Bxy+Cy^2+Dx+Ey+F=0 however, the professor is looking for an equation not an answer. Here are my choices and I am stumped: 40x^2 + 12 sq rt2 x + 12 sq rt 2 y + 9 = 0 40x^2 - 24y^2...

I've never understood how the aether was dispensed with. It is said that Maxwell's equations don't require it. If that is the case, then where do the x, y and z axes come from if not from an aether.

A flat rectangular plate of Mass M and sides a and 2a rotates with angular velocity w about an axle through two diagonal corners. The bearings supporting the plate are mounted just at the corners. Find the force on each bearing. I am not sure how to find force using Euler's equations since...

Find the are between the curve y=\sqrt{1-x} and the coordinate axes

I need help! I am practicing out of my book and this problem is killing me. Given the following equation, choose the best scale for the axes for x = 10, 20, and 30 y = 2x – 3 A) x-axis: from 0 to 80, intervals every 20; y-axis: from 0 to 40, intervals every 10. B)...