Transformations Definition and 823 Threads

Hi, I've been breaking my head on the matrix form of the lorentz transformation between one set of coordinates in one inertial frame (t,x^1,x^2,x^3) and what those coordinates will be in another inertial frame (t',x'^2,x'^2,x'^3). Now I understand that if have a set of coordinates in one...

Hi guys, needing a bit of help understanding laplace transformations. Homework Statement 1. f(t) = (t-4)u(t-2) 2. g(t) = (2e^-4t)u(t-1) 3. h(t) = 5 cos(2t-1)u(t) Homework Equations Laplace transform table. The Attempt at a Solution So basically I am given the laplace...

I have a question about mappings that go from a vector space to the dual space, the notation is quite strange. A linear functional is just a linear map f : V → F. The dual space of V is the vector space L(V,F) = (V)*, i.e. the space of linear functionals, i.e. maps from V to F. L(V,F)=...

What are the differences in (scalar) field transformations: 1) \phi(x)\to \phi'(x) 2) \phi(x)\to \phi'(x') 3) \phi(x)\to \phi(x') How this transformations are connected to internal and external symmetries? For example, if we take spacetime global translations x^{\mu}\to...

what does it mean by "any \Lambda^{\alpha}_{\beta} that can be converted to the idendity \delta^{\alpha}_{\beta} by a continuous variation of parameters must be a proper lorentz transformation"?

Homework Statement Back in pre-calc, I learned that f(x) can be transformed in the ways of y = af(bx +c) + d But very often I come across nastier functions that aren't transformed by scalars, but instead let's say y = g(x) what does the transformation do to g(x)? 1. g(x) + x...

Hi, I have a silly question concerning the chain rule. Imagine I have a time and space transformation as follows, x^0 \rightarrow x^{'0} = x^0 + \xi^0, \ \ \ x^i \rightarrow x^{'i} = R^i_{\ j}(t)x^j + d^i (t) \ \ \ \ \ \ (1) where xi^0 is constant, R is an element of SO(3) and d is a vector...

I'm a bit lost on this part of my course (ODE's and complex analysis). We've only done about 2-3 of these (seemingly simple) problems where we're given the equation of a line or circle in the complex plane and are asked to find its image in the U-V plane with some transformation \omega, but I...

Hi guys, I'm currently struggling to show something my lecturer told us in class. We have that \Psi\left(x\right) \rightarrow S\left(L\right)\Psi\left(L^{-1}x\right) under a Lorentz transform defined L = exp\left(\frac{1}{2}\Omega_{ij}M^{ij}\right) with S\left(L\right) =...

Why do we carry out stress transformations? tnx

Identify the Hermite form of the following linear transformations and the basis for its kernel (x,y,z) = (x-y+2z,2x+y-z,-3x-6y+9z) So when finding basis for kernel we have to set equal to 0, giving: x-y+2z=0 (1) 2x+y-z=0 (2) -3x-6y+9z=0...

I am revising my graph transformations and I am curious: If we graph sin (2x) or sin (x/2) we are able to increase and reduce their cycles. Is there any transformation for other lines/graphs? My doubt is we can also do 2 sin (x), which is the stretch parallel to the y-axis as I am...

Hi all, (Also - if anybody could tell me how to get the latex to work on this page that'd be very handy!) While not technically homework this is a problem I've found I'm stuck on during my revision. Any help would be greatly appreciated. Homework Statement "By demanding that the covariant...

This isn't actually a homework problem, but a problem from a book, but as it's quite like a homework problem I thought this forum was probably the best place for it. Homework Statement Consider a system with one degree of freedom, described by the Hamiltonian formulation of classical...

Hi :smile: So: Let f (x) = 3x2 + 6x - 9 For the graph of f: a) Write down the coordinate of the vertex b) Write down the equation of the axis of symmetry c) Write down the the y intercept iv) Find both x intercepts My answers: a) For a I managed to find the x coordinate of the vertex by: x...

c^2 occurs frequently in special relativity: in the Lorentz transformations, in forumlas for the interval, relativistic energy, and others too. Is there an intuitive reason for the high occurence of c^2?

Homework Statement My question doesn't require numerical calculation. It is more about explanation. Here it is: what does it mean to say there are unique linear transformations? My textbook says "unique linear transformations can be defined by a few values, if the given domain vectors form...

Hello, Consider the following two situations. There is a train of mass M, going at V=10 m/s with respect to the train station. There is a mass m passenger on that train, who starts walking at v=1m/s parallel to the direction of the train motion. The kinetic energy of this system...

Can someone explain Laplace transformations! i don't understand ittttt. [edit] sorry. i hadnt even heard of laplace transformations until i found it in my assignment. basically i want to know how to use them so, some simple, well explained examples perhaps?

Let L:P1 >> P1 be a linear transformation for which we know that L(t + 1) = 2t + 3 and L(t - 1) = 3t -2 a) Find L(6t-4) I just want to check the way to calculate this question. Is L(6t - 4) equal to 6*3t - 4*2 = 18t - 8? if not, how to calculate it?

Homework Statement Let T : R2 -> R2 be the linear transformation defined by the formula T(x, y) = (2x + 3y,−x − y). Let S : R2 -> R2 be the linear transformation whose matrix is 3 −1 2 4 i. Write down the matrix of T. ii. Calculate the matrices of the linear transformations T o S...

The function of f is given by f(x) = 3x - 2, where x is part of a set of real numbers. Sketch the graph of f. Find a combination of geometrical transformations of which, when applied to the graph of f will give the graph of g(x) = 6x + 1 At a first glance I thought: Stretch by a scale factor...

Homework Statement Given A = \left(\begin{array}{ccc}1&-1&1\\0&1&1\end{array}\right) Why isn't Latex working for above array :( Define a transformation as T: \Re^{n} -> \Re^{m} T(\vec{x}) = A \vec{x} 1) a. What is n? b. What is m? 2) Find \vec{x} , if possible, given that...

I'm working my way through Jose and Saletan's mechanics text and I'm at the end of chapter 5 which introduces Hamiltonian dynamics. I've just finished reading about 'types' of generating functions. They work through an example (5.5) with the following transformation Q=\frac{m\omega q...

Hi, So in a general curved spacetime we have no preferred choice of modes and the Bogolubov transformations allow us to convert between the fields expanded in the various complete sets of modes. If we have one set of modes f_{i} and another g_i both normalized like normalized as...

Two observers A and B are in relative motion with a constant velocity[for example, along the x-x' direction].If A knows the the position of B accurately , the motion of B gets enormously uncertain[and vice verse] in his calculations/considerations.How is he going to derive the Lorentz...

Let us consider the B-E and F-D statics: {<}{n}_{i}}{>}{=}{\frac{1}{{exp}{(}{{\epsilon}_{i}{-}{\mu}{)}{/}{kT}}{\mp}{1}} Now we observe the formula from a boosted frame.The left side is a scalar and should not change in response to the Lorentz transformations.What about the right hand side?The...

Hi, My question is the following. In special relativity, the Lorentz transformations correspond to a physical situation in which two frames of reference move with uniform rectilinear motion one with respect to the other. In general relativity, given the physical situation in which one frame...

Homework Statement Let V be an n-dimensional vector space over R, and let S and T be linear transformations from V to V. (i) Show that im(S+T) \subseteq im(S) + im(T) (ii) Show that r(ST) \leq min(r(S),r(T)), and that n(ST) \leq n(S) + n(T) Homework Equations none that i can think...

Homework Statement A loop moves with velocity v along a charged wire. (The charged wire passes through the center of the loop.) In a reference frame where the charged wire is stationary and the loop is moving with v, what is the E field and B field at a point on the loop? In a reference frame...

Homework Statement if Sa: R2 -> R2 is a rotation by angle a counter-clockwise if Tb: R2 -> R2 is a reflection in the line that has angle b with + x-axis Are the below compositions rotations or reflections and what is the angle? a) Sa ○ Tb b) Ta ○ Tb Homework Equations I don't...

Homework Statement the mother graph is y = 2 ^ x Homework Equations y=2 ^ x The Attempt at a Solution so i know the graph is flipped upsidedown and the whole graph is moved up 6 spots so i can get y = -2 ^ x + 6 however the solutuion is y =-2 ^2x +6. i can't seem to figure...

Homework Statement If f,g are Riemann integrable on [a,b], then for c,d real numbers, (let I denote the integral from a to b) I (cf + dg) = c I (f) + d I (g) Homework Equations The Attempt at a Solution I have the proofs for c I(f) = I (cf) and I (f+g) = I (f)...

Can you please specify a reference to help me understand how QCD explains the fact that all particles observed in nature transforms under SU(3).

Homework Statement Find the equation of a sine function that has a vertical displacement 2 units down, a horizontal phase shift 60 degrees to the right, a period of 30 degrees, a reflection in the y-axis and an amplitude of 3. 2. The attempt at a solution Y = 3 sin (30x- 60) -2 I'm...

Homework Statement Event A occurs at xA = 500m. Event B occurs 5 microseconds later at xB = 1500m. With what speed must an observer move in the positive x direction so that the events occur at the same point in space in the observer's frame?Homework Equations Lorentz transformation...

How can you express the del operator after a change of variables? For example, if I want to use cylindrical coordinates for a fluids problem, what is the del operator in terms of the new coordinates? And how do you derive it for any other arbitrary coordinate transforms?

I wasn't sure if this counted as intro physics. Feel free to move if I have it in the wrong place. Homework Statement In class we learned some linear transformations where we have a stationary observer and another moving near the speed of light. Describing the reference frames: s' -> x'=u't'...

Homework Statement A3. Show that the Lorentz transformations on a spacetime 4-vector can be written as x'μ = (Lμν)*(χν) . Find the matrix L. Prove that (in matrix notation) Lτ gL = g where g is the Minkowski spacetime metric.Homework Equations Any help suggesting at least equations will be...

Homework Statement Not really a problem per se; more of an issue with some aspects of linear transformations. We've learned that a linear combination of linear transformations is defined as follows: (c_1T_1+c_2T_2)(\vec{x})=c_1T_1(\vec{x})+c_2T_2(\vec{x})\,\,\,\,\,\, \vec{x}\varepsilon...

Hello. When one is converting between coordinate systems, the Jacobian arises as a necessary consequence of the conversion. Does this occur with transformations between relativistic systems, and, if so, is this manifested through the prevalence of gamma in the transforms? Any guidance would...

1. R\circF\circR-1=S where F denotes the reflection in the x-axis where S is the reflection in the line y=x where R = R\pi/4 : R2 \rightarrow R2 3. An attempt I have found that the standard matrix for R = [cos\theta sin\theta]...

I'd like to start by mentioning that I have very little in the way of experience on the subject, so forgive me if my confusion is somewhat trivial.. My problem lies with understanding what the fundamental variables in the Lorentz Transformations actually represent. For example, it is to my...

I am struggling to understand spin transformations and have used Sakurai's method of |new basis> = U |old basis> to change basis vectors and hence should have Sz' = Udagger Sz U to transform the operator. I thought this should give Sz' = Sy in the workings (see attachment below) but it...

Homework Statement Let T \in L(V, W), where dim(V) = m and dim(W) = n. Let {v1, ..., vm} be a basis of V and {w1, ..., wn} a basis for W. Define the matrix A of T with respect to the pair of bases {vi} and {wj} to be the n-by-m matrix A = (aij), where T(v_{i}) =...

I was under the impression that a source transformation doesn't change a circuit at all, which I guess is an oversimplification. If you have a series RC circuit, with a DC voltage source, after the transients have died out, all voltage will be across the capacitor, and none across the...

Homework Statement A bus travels forward at a constant speed of 24 m/s down a straight highway. the driver puts on her sunglasses, and 3.5 s later, a passanger stiing 5 m behind her drops a pen. In the frame of reference of the earth, what is the distance seprating these events? Homework...

Homework Statement Let A: E \rightarrow F be a linear transformation between vector spaces (of any dimension) and let X be a subset of F with the following property (which is only a conditional): IF X \subseteq Im(A) THEN A is surjective. ... (*) Prove that X is a generating set for...

Homework Statement Hello. I came across a question that required me to solve for invariant points between a base trig function and the function after horizontal stretch. I can't remember the exact question right now, but I'm just wondering how I would go about solving it if I didn't know...

I've just read the statement "The Lorentz transformations have a representation on the fields" Can anyone explain the meaning of the word representation? I can't seem to get a satisfactory explanation anywhere and the notes don't go into much more detail on it.