Transformations Definition and 823 Threads

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 ->...

a)So I'm reading over my notes and they say that under the Lorentz transformation L, \phi \rightarrow \phi' where \phi'(x)=\phi(x') where x'^\mu = (L^{-1})^\mu{}_\nu x^\nu I don't really understand why this is true. Why is it not just \phi'(x)= L \phi(x) Clearly this fails because the LHS is...

I asked my prof why the Lorentz transformations had to be linear (which my textbook assumed when deriving them), and he mentioned some stuff about homogeneity and ended with "it's advanced, just believe". Can anyone offer a simple explanation?

Homework Statement Suppose that A is a real symmetric n × n matrix. Show that if V is a subspace of R^n and that A(V) is contained in V , then A(V perp) is contained in V perp. Homework Equations A = A_T (A is equal to its transpose) The Attempt at a Solution I have no idea...

Homework Statement [PLAIN]http://img219.imageshack.us/img219/2950/linl.jpg Homework Equations The Attempt at a Solution Is this how I do part (iii)? From (ii) I get: M^{\mathcal C}_{\mathcal C} (\phi) = \begin{bmatrix} 1 & 3 & 2 \\ 1 & -3 & 0 \\ 0 & 0 & 2 \end{bmatrix}...

Homework Statement In the old West, a marshal riding on a train traveling 35.0 m/s sees a duel between two men standing on the Earth 55.0 m apart parallel to the train. The marshal's instruments indicate that in his reference frame the two men fire simultaneously. (a) Which of the two men, the...

In a lecture on special relativity online, the form x'=x\cosh{\omega}-ct\sinh{\omega} t'=-x\sinh{\omega}+ct\cosh{\omega} is used for the lorentz transformations, where the velocity is v=\frac{c\sinh{\omega}}{\cosh{\omega}}. However, I'm wondering, couldn't you also do...

Homework Statement Prove that if V is a finite-dimensional vector space, then the space of all linear transformations on V is finite-dimensional, and find its dimension. Homework Equations The Attempt at a Solution

I'm self studying some alg topology for next semester just working through chapter 0 and 1 of hatcher really. My question is: for any universal cover p of X there are two actions of pi_1(X, x0) on the fiber p^-1(x0) given by lifting loops at x0 and given by restricting deck transformations to...

Homework Statement Hello, We were supposed to fill in the missing products or reagents (I indicated which ones on the paper) but out of 40 points, I got 13. So now I'm a bit worried. I tried to redo it, could someone look it over? (see attached jpg) The Attempt at a Solution My...

Homework Statement Write down the transformation laws under general coordinate transformations for a tensor of type (0,1) and a tensor of type (2,1) respectively The Attempt at a Solution I seem to have two transformation formulas but they could in fact just be the same thing. I'll just do...

The group of four dimensional space time symmetries may be generalised to conformal transformations x \rightarrow x' defined by the requirement dx'^2 = \Omega(x)^2 dx^2 where dx^2 = g_{\mu \nu} dx^\mu dx^\nu (recall that Lorentz invariance requires \Omega=1). For an infinitesimal...

I am having trouble with this problem: Let T:V->W be a linear transformation. Prove that T is one-to-one if and only if dimension of V = dim(RangeT). I know that in order to be a linear transformation: 1) T(vector u + vector v) = T(vector u) + T(vector v) and 2) T(c*vector u) =...

Define B( \theta, \vec{n} ) \in SL( 2 , \mathbb{C} ) by B( \theta , \vec{n}) = \cosh { \frac{1}{2} \theta} + \vec{\sigma} \cdot \vec{n} \sinh{ \frac{1}{2} \theta} where \vec{n}^2 =1 Show that this corresponds to a Lorentz boost with velocity \vec{v}=\tanh{ \theta} \vec{n}. Show that ( 1 +...

I have a metric of the form ds^2 = (1-r^2)dt^2 -\frac{1}{1-r^2}dr^2-r^2 d\theta^2 - r^2 sin^2\theta d\phi^2 A singularity exists at r=\pm 1 . By calculating R^{abcd}R_{abcd} i found out that this singularity is a coordinate singularity. I found the geodesic equations for radial photons...

Homework Statement The attachment is the problem. Homework Equations The Attempt at a Solution I understand how to go about solving the laplace transformations but I have no idea how to start with the Heaviside functions for the 5t and the 30. What I got was 5t+30U6(t) but it turned...

Homework Statement Write down 3x3 matrices A, B, C such that when the vectors in R2 are expressed in homogeneous coordinates, the product ABC first translates vectors by (-1, 2), then reflects them about the line y=-x and finally scales them by 2. using your matrix ABC, determine the image...

hey, does anyone there know how the angular momentum (L=r x p) is transformed under Lorentz transformations?

How can one show that if det A = 1 and the 00th component of A > = 1 then A preserves the sign of the time component of time-like vectors? thanks!

I don't quite understand the idea that (as my book says) every linear transformation with domain Rn and codomain Rm is a matrix transofrmation... I mean i get the idea of what a linear transformation is (sorta like a function) but it gives the theorem: Let T: Rn -> Rm be linear. Then there is...

Homework Statement The Attempt at a Solution I think I first need to find T(e2)=? and T(e2)=? and then combine those into a matrix. I am having trouble starting to solve for T(e1) and T(e2) so far I have [1] = alpha [1] + beta [3] [0] [2]...

Homework Statement Consider the initial value problem: x'' + 2x' + 5x = δ(t - 1); with: x(0) = 0 and x'(0) = 0. Using Laplace transforms, solve the initial value problem for x(t). Homework Equations L[x''] = (s^2)*L[x] - s*x(0) - x'(0) L[x'] = s*L[x] - x(0) L[δ(t - 1)] = e^(-s)...

Homework Statement A light signal is sent from the origin of a system K at t = 0 to the point x = 1 m, y = 8 m, z = 13 m. a) At what time t is the signal received? b) Find ( x', y', z', t' ) for the receipt of the signal in a frame K' that is moving along the x-axis of K at a speed of 0.6c...

Homework Statement Consider a two-dimensional function φ = φ(x,t) that satisfies the relativistic wave equation given by: https://adgiiq.blu.livefilestore.com/y1pe5tdBVr0r62krIiWV_PQ42r1jrzQpWKz24xRgNe138phEqCNyZJKFXhBXqqL4YCvYeAsgVQtJJwovzjL0mKiNXyd6p1zHvkx/equation.jpg?psid=1...

Hi everybody I've got a problem related to canonical transformations that I can`t solve: Given the expression of the canonical transformation Q=3q\cdot\big[ \exp\big((p+q)^5\big)+1\big] +3p\cdot \big[\exp((p+q)^5)+1\big]+p P=p+q I have to calculate an associated canonical transformation...

Anyone help. I know I must be doing this wrong somehow Lightning hits both a tree and a pole. The spacetime coordinates for each is (x=0, t=10us) for the tree and (x=30000m, t=10us) for the pole relative to the ground. Therefore they occur simultaneously relative to the ground. A rocket comes...

I want to make sure of my understanding of coordinate transformations. First of all, is it true that if \[{x_i}\] is a coordinate system on a manifold, then \[{q_j} = {q_j}({x_i})\] is a coordinate transform from "x" space to "q" space? If so can "x" be a flat space and "q" a curved...

1. Problem Horizontal rod of length x traveling along the positive y-direction at velocity u. Determine the orientation of the rod in frame S', which is moving at velocity v in positive x-direction. 2. Homework Equations Lorentz Transformation for length contraction, x' =...

Hello, suppose one has a classical canonical transformation between two sets of canonical variables such that the new (primed) positions and momenta can be written as functions of the old (unprimed) ones. {\cal K}: x_i \to x_i^\prime(x); \quad p_i \to p_i^\prime(p) Using these relations one...

Hey I'm new here. Well we're currently doing Laplace in our Maths lectures. Now the Teacher has set us a project on Laplace and we need to find some applications of Laplace Transformations. Can anyone tell me some specific areas where Laplace is applied. I remember reading somewhere it's...

There's something about the lorentz transformations which is somewhat confusing to me, and that is how to treat the "x" coordinate. Supposing I have some spaceship which is moving from Earth to some other planet located at a distance "D" (from earth) with a velocity v. Now, the spacetime...

Homework Statement which of the following are linear transformations. a) L(x,y,z) = (0,0) b) L(x,y,z) = (1 ,2, -1) c) L(x,y,z) = (x^2 + y, y - z) The Attempt at a Solution I know that L is a linear transformation if L(u + v) = L(u) + L(v) and L(ku) = kL(u). I am not sure how to...

I read that the form of a galilean transformation on the point (t,x) is the following: constant velocity transform by velocity v: (t,x) ---> (t,x+vt) translation transform by (t0,x0): (t,x)--->(t+t0,x+x0) rotation transformation by rotation matrix R: (t,x)--->(t,Rx) and that it is based...

Homework Statement The system S' moves in relation to the system S with velocity \upsilon along the -x- axis. At the time when the beginnings of the coordinate system are in the same point, clocks in both system shows t=t'=0. Which coordinates will have a reference point during the motion in...

Homework Statement I have a question regarding how to compose 2 transformations, a rotation and a translation, of a linear algebra problem. Suppose we have a quadratic curve like the following one: (i) x^2 + y^4 - 6xy +2x -3y +6 = 0 We want to transform the above into its standard...

I've spent a large portion of my day trying to figure this out and I figured my best answer is likely to come from here. Forgive me if I'm wildly wrong about anything, I'm somewhat basic with physics, largely due to the fact that I'm 15 and my maths is limited to a GCSE level. My dilemma is...

Hello, I would like to check if my understanding of this linear algebra problem dealing with transformations is correct: Part (1) we have the following coordinates systems: \tilde{x} = \begin{pmatrix} x_1 \\ x_2 \\ 1 \end{pmatrix} and x = \begin{pmatrix} x_1 \\ x_2 \end{pmatrix}...

I am wondering about the order of operations concerning the Lorentz transformation of fields and the superposition of fields. I was given a problem: Two positively charged electrons start at the origin and then travel along the x-axis at a constant speed v in opposite directions. Calculate...

Hello, I had a question regarding unitary transformations. The most common definition I see for unitary transformations is defined as a transformation between Hilbert spaces that preserves inner products. I was wondering if all unitary transformations between Hilbert spaces (according to this...

I'm a teacher. I need to teach this subject to a group of smart 9th grade students that I am prepping to begin a "Green Physics" project. What are the energy transformations associated with a hydroelectic dam? I think I have it up to a certain point, and then I'm less than sure. Here's...

Iv just been reading a physics textbook and i feel iv completely missed something. It may help to draw a diagram and to read the thread slowly. Sorry if it is a little thick. My understanding of Special Relativity is that it allows two seemingly conflicting principles to co-exist, these being...

Hi all, I've been struggling with this for a couple of days now and am positing a question in the hope that someone can help me out. I have a global cartesian coordinate system X, Y, Z and a cube with it's centre at (0,0,0) and dimension 1. Hence it's corners are: (0.5, -0.5, 0.5), (-0.5...

Hi, I just have a quick question, I understand that (T\vec{u},T\vec{v})=(\vec{u},\vec{v}) defines a unitary transformation T , but how does one go from this relation to (T\vec{u},\vec{v})=(\vec{u},T^{-1}\vec{v}) as the other way to define a unitary transformation? Thanks

Homework Statement Theorem. The change of variables is reversible near (u0,v0) (with continuous partial derivatives for the reverse functions) if and only if the Jacobian of the transformation is nonzero at (u0,v0). 1. Consider the change of variables x=x(u,v)=uv and y=y(u,v)=u2-v2. (a)...

Homework Statement http://img338.imageshack.us/img338/9682/spaceships.gif V1, V2, U, alpha are given. The red spaceship is moving left in Velocity V1 (in the lab system) and a ball is thrown in angle alpha and speed U(in the red spaceship system). What is Alpha in the Blue system...

For the linear transformation, T: R^2\rightarrow R^2, T(x,y) = (x^2,y) find the preimage of.. f(x)= 2x+1 I have no trouble with these types of problems when it comes to vectors that aren't functions. Any help would be appreciated! Thanks! ~Matt

Below is a HW problem which I believe is correct. Can you guys take a look and advise? Which of the following are linear transformations A) L(x,y,z)= (0,0) B) L(x,y,z)= = (1,2,-1) C) L(x,y,z)= ( x^2 +y , y-z) To prove these relationships are linear transformations, they must satisfy...

Homework Statement describe the energy transformations required in the following Fax/Modem Radio And Television thanks

L: R^2=>R^2 is defined by L(x,y)= (x+2y), (2x-y) let S be the natural basis for R^2 and T=(-1,2), (2,0). T is another basis for R^2. Find the matrix representing L with respect to A) S B) S and T C) T and S D) T E) Compute L L(1,2) using the definition...

Homework Statement Find the power dissipated by the 8 ohm resistor. This was an example for source transformations. Homework Equations P=VI=V^2/r=I^2*R V=IR The Attempt at a Solution First I transformed the 1 amp current source and 20 ohm in parallel to a 20 V voltage...