Transformation Definition and 1000 Threads

Homework Statement Muons are created in the upper atmosphere (at a height of 3000 m) and plummet downward toward a detector at ##v=0.980c##. The mean lifetime of a muon is ##t = 2.20~\mu s##. Find the mean lifetime of a muon measured by an observer on the ground. Find the distance that...

Homework Statement Ok I have a moving person (primed) going 50 m/s in the positive x direction, and I have someone stationary (unprimed) observing them. At t = 0, the moving person is at x(0) = 100m Write an equation for the object’s position as a function of time x(t) seen by the...

Homework Statement Obtain the Laplace transformation of the function defined by f(t) = 0 t<0 = t2e-at t>=0Homework Equations The Attempt at a Solution I'm a little unsure of what I'm doing here, so bear with me. L {t2e-at} = ∫inf0 t2e-at dt = ∫0inf t2e-(a+s)tdt How do I integrate...

I have two questions having to do with the Lorentz transformation for the time...some preamble first: The Lorentz transformation for time along the x-axis is t'=\frac{t-\frac{ux}{c^2}}{\sqrt{1-\frac{u^2}{c^2}}}, where u is the relative velocity of S'. Why is there a dependence on x...

1.what is lorentz transformations ? what are the uses of it ? 2.there are 2 galilean transformations equations .what are the uses of them ? are they useful to find the velocity of the objects at different reference frames or they have anyother applications/uses?

Homework Statement Hi guys, actually this isn't a homework question, but rather part of the working in a textbook on Linear Algebra. Homework Equations The Attempt at a Solution I'm not sure why it's U*li instead of U*il. Shouldn't you flip the order when you do a matrix...

Homework Statement Find Rae, Rbf, Rah, Rcg & Rbc. Homework Equations Am I going to use wye-delta transformation? The Attempt at a Solution I tried checking if I could use wye-delta transformation. There seems to be no parallel connections between the resistors. Please do help...

Hi, I was looking at a basic derivation of the lorentz transformation on youtube. I was wondering at what point do you incorporate the fact that speed of light is same in every reference frame because the guy only uses some algebra on a few equations that come from basic geometry and classical...

Homework Statement Find the Laplace transformation of the following function by using iterations of integration by parts: f(t) = tsin(t) Homework Equations The Attempt at a Solution I know how to do integration by parts (as learned in calculus) but have never seen a funtion...

I'm trying to understand the transformation relations for 2d stress and the book doesn't show the derivation of the 2d stress transformation relations from the directional cosines. The 2d stress transformation relations are found by using the transformation equation and the 2d directional...

Difficulty regarding notation for Lorentz transformation Please can somebody explain to me the relation between Δ^{σ}_{μ} and Δ_{σ}^{μ} as symbols representing a Lorentz transformation? Thanks.

Homework Statement If T is a linear transformation, proof that Tn is a linear transformation (with nEN). Homework Equations I know that T is a linear application if: T(u+v) = T(u) + T(v) T(au) = aT(u) The Attempt at a Solution Actually I don't know how to start using these two...

May you help me with finding the angle, and what is "line of sight"?(the final answer is 15°) Thank you in advance

What is the difference between orthogonal transformation and linear transformation?

I understand ##\vec A\rightarrow\vec A+\nabla \psi\;## [SIZE="4"]as ##\;\nabla \times \nabla \psi=0##\Rightarrow\;\nabla\times(\vec A+\nabla \psi)=\nabla\times\vec A But what is the reason for V\;\rightarrow\;V+\frac{\partial \psi}{\partial t} What is the condition of ##\psi## so...

Hello everyone, I've been thinking about energy transformations and an electrical generator came to my mind which basically transforms mechanical energy into electrical energy. What confused me as I was thinking about it is whether the electrical energy that results due to the rotation of the...

Ok, this should be an easy one but it's driving me nuts. When we take the Lorentz transformations and apply them to x2-c2t2 we get the exact same expression in another frame. I can do this math easily by letting c=1 and have seen others do it by letting c=1 but I have never seen anyone actually...

Can one explain the relativistic energy transformation formula: E = \gamma\ E', where the primed frame has a velocity v relative to the unprimed frame, in terms of relativistic time dilation and the quantum relation E=h\ f? I imagine a pair of observers, A and B, initially at rest, each...

Homework Statement Hi all. I am having trouble to understand the combination of transformation on a function: h(x)= a*f(b(x-c))+dHomework Equations The problem I am struggling with is the order of transformation; I do see that: f(x-c) is translation in the right since every event happen before...

Homework Statement The problem is tough to type out correctly. Pasting problem statement image http://postimg.org/image/a0r92a0wl/ http://postimg.org/image/a0r92a0wl/ The Attempt at a Solution I just need to know how to proceed with the problem. Not the answer. This is the scan...

There is something I'm struggling with and I can't seem to find the problem. We have the Z spinbase with: z = (1/sqrt(2))² <BRA|*(|s_z,+> + |s_z,->) which gives following z matrix: 1 0 0 1 and we have for X: |s_x, +> = 1/sqrt(2) |s_z,+> + |s_z,->) |s_x, -> = 1/sqrt(2)...

Homework Statement Find surface inside four boundary curves: xy = 4 , xy=8 , y=5x , y=15x using the transformation: u=xy , v=\frac{y}{x} Homework Equations I'm getting the new bounds to be: 4 < u < 8 , -15 < v < -5 OR 5 < v < 15 Jacobian is \frac{1}{2v}The Attempt at a...

I'm doing a research project currently and basically what I have is a camera measuring a probe. I have designed the camera to give the orientation of the probe using euler angles in the camera's frame of reference. This was working for most of my data, but now I need a 3-D visualization of what...

This is probably a stupid mistake I am making, but I can't figure it out. My apologies in advance... I am familiar with the text-book derivation of the Lorentz transformation (I don't have any problem with it). It starts out stating: x2+y2+z2-c2t2 = x'2 + y'2+z'2-c2t'2 meaning that a...

I want to transform from rectangular coordinates ( xyz) to (x",y",z") rectangular coordinates that is rotated at the origin as show in the attachment. Then I want to transform (x",y",z") rectangular coordinates into Spherical coordinates. Attach is the method I use, I want to verify I am doing...

I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are I_3 \pm dI_3 The problem is that i'd lke...

Given a specific metric, is there a easy way to transform it in Synchronous coordinates? For example having dsigma2 = (1+z)^2 dt^2 - ds^2 - s^2 dphi^2 - dz^2 , I was able to do some substitutions, but I had to stop at the differential equations presented in the attachement.

For a certain transformation T, it is known that T(x+y) = T(x) + T(y) It is required to determine whether this transformation is linear. Obviously it is not, since it need not satisfy the degree-1 homogeneity property of all linear maps. I'm just having trouble cooking up the...

Resource: Linear Algebra (4th Edition) -David C. Lay I understand that there are identities associated with transformations, but what I don't understand is when the transformation is rotated about the origin through an angle β. I believe β in this case is \frac{}{}\pi/2 \left[1,0\right]...

Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...

If X is a random variable distributed uniformly in [0, Y], where Y is geometric with mean alpha. i) Is this definition valid for uniform distribution ? ii) If it is valid, what is the pdf of the transformation Y-X?

Hello MHB, given a linear transformation F so that this is known $$\left\{ \begin{aligned} \phantom{1}F(1,0,0)=(1,2,3) \\ F(1,1,0)=(0,0,1)\\ F(1,1,1)=(12,3,4)\\ \end{aligned} \right.$$ Decide F progress: $$F(e_1)=(1,2,3)$$ $$F(e_2)=F(e_1)+F(e_2)-F(e_1)=(0,0,1)-(1,2,3)=(-1,-2,-2)$$...

Homework Statement I am a bit confused on why they can just randomly short the 4kΩ resistor, as you can see from the first pic to the second pic. THanks Homework Equations The Attempt at a Solution

Homework Statement Use source transformation to find the Thevenin equivalent circuit with respect to terminals, a, b. Homework Equations Voltage Division: (V in)*(R1/R1+R2) Thevenin / Norton / source transformation procedures RTh = RNo VTh = INo*RNo Polar...

The Schwarz-Christoffel mapping (a Riemann-mapping) from the unit disk (z-plane) to a twice-symmtric area (a cross, ζ-plane) $$ \zeta : \mathbf C \to \mathbf C $$ is given by: $$\frac{ \mathrm{d}\zeta }{ \mathrm{d} z} = \left( \frac{ ( z^2-b^2 ) ( z^2-\frac 1 {b^2} ) }{ ( z^2-a^2 ) (...

In a recent course on special relativity the lecturer derives the Lorentz transformation matrix for the four vector of position and time. Then, apparently without proof, the same matrix is used to transform the EM field tensor to the tensor for the new inertial frame. I am unclear whether it...

Hi Everyone, I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way: x = rcosθ Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...

Homework Statement Use source transformation on the voltage source and series-connected impedance for the circuit shown here to find the equivalent current source and parallel-connected impedance. Continue the simplification by combining the two parallel current sources into an equivalent...

Where T(p(x)) = (x+1)p'(x) - p(x) and p'(x) is derivative of p(x). a) Find the matrix of T with respect to the standard basis B={1,x,x^2} for P2. T(1) = (x+1) * 0 - 1 = -1 = -1 + 0x + 0x^2 T(x) = (x+1) * 1 - x = 1 = 1 + 0x + 0x^2 T(x^2) = (x+1) * 2x - x^2 = 2x + x^2 = 0 + 2x + x^2 So, the...

How do we go about finding the transformation that was used to go from one matrix to another ( provided of course that the two are linked by a transformation) in general if all we have is two matrices.

Hi. I'm reading about non-abelian theories and have thus far an understanding that a gauge invariant Lagrangian is something to strive for. I previously thought that the Yang-Mills gauge boson free field term ##-1/4 F^2 ## was gauge invariant, but now after realizing that the field strength...

Hi, I'm having trouble understanding the purpose of using two basis in a linear transformation. My lecturer explained that it was a way to find a linear transformation that satisfied either dimension, but I'm having trouble understanding how that relates to the method in finding this...

Hi All, I have a question about transformation matrices (sorry about the typo in the title). The background is that I've spent some time learning differential geometry in the context of continuum mechanics and general relativity, but I'm unable to connect some of the concepts. So I have this...

Dirac Equation as Example, Dirac Equation: \left(i\gamma^\mu \partial_\mu -m \right)\psi(x)=0 Can I write it in the following way? \left(i\gamma^0 \partial_0- i\gamma^j \partial_j -m \right)\psi^p(t,{\bf -x})=0

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...

This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...

Homework Statement My quantum mechanics text (in an appendix on linear algebra) states, "f the eigenvectors span the space... we are free to use them as a basis..." and then states: T|f1> = λ1f1 . . . T|fn> = λnfn My question is: is it not true that fewer than n vectors might...

Help please. I can't find what am I missing. The solution is in the attachment. Thanks in advance.

I've had to hit my books to help someone else. Ugh. Say we have the coordinate transformation \bf{x}' = \bf{x} + \epsilon \bf{q}, where \epsilon is constant. (And small if you like.) Then obviously d \bf{x}' = d \bf{x} + \epsilon d \bf{q}. How do we find \frac{d}{d \bf{x}'}? I'm missing...

I am starting to deal with optomechanical systems as part of my work, and am faced with what seems to be an uncomplicated problem, however I'm ashamed to admit that I am having great difficulty getting to grips with it. I'd like some pointers and/or advice as to how to go about solving these...