Translation Definition and 236 Threads

In https://en.wikipedia.org/wiki/Galilean_transformation it is shown that translation is different from uniform motion. So, isn't translational motion another name for uniform motion?

I want to learn German to read those old classic papers written in German. I think the best way is to find a good, classic German book and compare it with its English translation. I believe in this way I can pick up German quickly. So, could anyone recommend some good German books in maths...

Okay so when there is time-translation symmetry because the metric components do not have any time- dependence, ##\partial_x^0## is a Killing vector. I'm just confused what this means explicitly, since a derivative doesn't make sense without acting on anything really? But by 'spotting the...

Homework Statement hi I have read a lot on homogenous coordinates and I feel like I now have a solid foundation. However none of the videos or books I have read give an explicit reason as to why translation with the extra dimension works(i.e. it does not result in scaling). Here 's what I...

Homework Statement There is a disk with mass 50 grams put on a slippy surface (no friction!). Its radius is 5 cm. Mass of the weight is 20 grams. At the beginning there is no motion. How far does the center of mass of the disk move in 10 seconds? (answer: 91 m) How many turns does the disk in...

Homework Statement All married couples have fights Homework Equations let x be a person and y be another person M(x,y): x is married to y F(x,y): x have fought y The Attempt at a Solution ∀x∃y(M(x, y) → F(x, y)): i read my translation as "For all x, there is some y such that if x is married...

If I have the operator, ##e^{a\partial_p}## acting on ##f(p)##, I know that $$e^{a\partial_p}f(p)=f(p+a)\,.$$ If I have ##e^{a\partial_p^2}f(p)##, this is just the Weierstrass transform of ##f(p)##. However, what happens if I have a general operator, ##e^{g(p)\partial_p}## or...

If we have log 3 (x+9) + 2 = y. It states that we have a HT 9 units left and 2 units up. But if we manipulate that too log 3 (x+9) = y - 2 And convert to Exp form. This gives me 3^(y-2) = x + 9 or 3^(y-2) - 9 = x This looks to me more like a HT 2 units right and a vt 9 units down. I don't...

Homework Statement A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its center of mass is a distance l from the edge...

Homework Statement Happy new year all. I was wondering if you can use matrices to translate and transform a function? So for example if I were to take the function $$f(x)=x^2+4x$$ and I want to the translate and transform the equation to $$2f(x+4)$$. Can this be done by matrices. I know how...

Please see attached. I am trying to show that ## T_{p} f (\tau + 1) = T_{p} f (\tau ) ## ##f(\tau) \in M_k ## and so can be written as a expansion as ##f(\tau)=\sum\limits^{\infty}_{0}a_{n}e^{2 \pi i n \tau } ## ##f(\tau + 1) = f(\tau) ## since ##e^{2\pi i n} = 1## Similarly ##f(p\tau + p) =...

Homework Statement I have the Jacobi theta series: ##\theta^{m}(\tau) = \sum\limits^{\infty}_{n=0} r_{m}(\tau) q^{n} ##, where ##q^{n} = e^{2\pi i n \tau} ## and I want to show that ##\theta^{m}(\tau + 1) = \theta^{m}(\tau) ## (dont think its needed but) where ##r_{m} = ## number of ways of...

**I am an extreme amateur when it comes to physics, so please forgive me if I use the wrong terminology or my description is incomplete** My washing machine always seems to get out of balance and "walk" across the room during the spin cycle, which led me to think up the following scenario...

Hi folks, I am interested in the historical original documents. Newtonian mechanics could be learned from--> Principia and Euler's Mechanica Lagrangian mechanics--> Analytical Mechanics Poisson--> I found his teatrise on mechanics where I expect to find out his "brackets", but I have not yet...

I am currently reading Goldstein's Classical mechanics and come on to this problem. Let q1,q2,...,qn be generalized coordinates of a holonomic system and T its kinetic energy. qk correspondes to a translation of the entire system and qj a rotation of the entire system around some axis, then...

Homework Statement For the first half of a straightly traveled path which is α=60° from some reference line, a body is moving with a velocity of v1=72 km/h. During the second half of a straightly traveled path, the body is moving with an angle of β=30° with a velocity of v2=36 km/h.What is the...

Homework Statement This isn't really a problem. I am just re-reading some section "Classical Mechanics" by John Taylor. I think this belongs in the math section, since my question is mainly about the del operator. There is just one fragment of one sentence that I want to make sure I am...

I don't understand what the eigenvalue of a translation operator means physically. The eigenvalues of other operators like momentum and hamiltonian give us the physically measurable values I suppose. Then what exactly do we obtain by the translation eigenvalues? I am new to the field of quantum...

Hi, As I know we now think that time translation is not a symmetry of spacetime because of the Big Bang, so we cannot say that our physical laws are applicable at every point in time. But then isn't the developing of the Big Bang theory against this asymmetry?

Two stars of equal mass M move with constant speed V in a circular orbital of radius R about their common center of mass .What is the net force on each star?the answer to this question was net force=GM^2/4R^2 .I want to ask that why net force not equal to zero although it is in translational...

given a dictionary \Sigma = \left \{f(),g(),R(,),c_0,c_1,c_2 \right \} and a sentence \phi over \Sigma, I need to find an algorithm to translate \phi to \psi over \Sigma' where \Sigma' = \left \{Q(,,,), = \right \} (Q is a 4-place relation symbol), so that \psi is valid iff \phi is valid. I...

Sorry, 30 years since college and I wasn't awake all the time. I'm trying to translate the symbology in the attached pics. Some of the super/subscripts are throwing me off in formulae 13, 14 and 15. Y and X = planar coordinates of points. n = number of points. σβ = standard error of angle...

Please see attached pic. I have received a handwritten document from a physicist. I am not familiar with the equations, therefore the symbols are difficult to figure out. I have done some searches. I know the first symbol is the "time second derivative" and another symbol is the "time...

I have this problem where I need to convert from mouse coordinates on the screen with relative coordinates on an object that can be arbitrarily translated, scaled, and rotated around another arbitrary position. I've already normalized all of the units to be the same (pixels) but the trig is...

While reading another thread on Stephen Hawking proposal on how information can escape a black hole, I came across the theme of "super translations." Please could someone explain what these are as Google provided no explanation

I think I'm having a really big block over a really small hangup, so forgive me. I'm on an internship and this is my first time working with rotations/change of basis in a real world scenario. I'm creating a calculator that gives torque in a door mechanism, after a given roll and pitch of the...

Howdy. It has become clear to me that translational motion is not taken into account in general relativity because it is subjective, and that rotational motion is taken into account in GR in places such as the Kerr Metric. What makes rotational motion so absolute? Couldn't an observer's...

Homework Statement I am working through a time independent perturbation problem and I am calculating the first order correction to the energy, and I am stuck operating the perturbation : v = i b (Exp[i g x]-Exp[-i g x]) on the ground state |0>. Homework Equations <0| v |0> = 1st order...

Is this a true phenomenon?? I just read 1 article, but i don't believe it Could DNA really be synthesized using The amino acid sequence?

Homework Statement I have quite a straightforward question on the taylor expansion however I will try to provide as much context to the problem as possible: ##T(a)## is unitary such that ##T(-a) = T(a)^{-1} = T(a)^{\dagger}## and operates on states in the position basis as ##T(a)|x\rangle =...

α I have been studying translation operators of the type T = exp ( -ipx0/ hbar) where p is the momentum operator which leads to T+xT = x+x0. I am ok with that but then I came across the following equation concerning raising and lowering operators exp(-alpha a+) a exp(alpha a+) = a + alpha. Is...

Homework Statement Let ##|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle## for infinitesimal ##\delta x##. Show that ##\langle x \rangle = \langle x \rangle + \delta x## and ##\langle p_x \rangle = \langle p_x\rangle.## Homework Equations ##\hat{T}(\delta x) =...

Homework Statement Put the sentence into symbols using the suggested notation. Dolphins and porpoises grin and frolic in the sea. (Dx = x is a dolphin; Px = x is a porpoise; Gx = x grins; Fx = x frolics in the sea) Homework Equations None. The Attempt at a Solution [/B] (\forall...

Homework Statement Given a rectangle R=[1,3] x [2,4], and the affin translation F : R^2 -> R^2 defined by F(x,y) = (1,3) + A*(x,y), where A is the 2x2 matrix (2 , 7 ; 3 , 1), what is the area of the affin transelation of the rectangle R? Homework EquationsThe Attempt at a Solution When I...

I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...

This is one of those "existential doubts" that most likely have a trivial solution which I can't see. Veltman says in the Diagrammatica book: Although the reasoning makes perfect sense for a Hilbert space spanned by momentum states, intuitively it doesn't make sense to me, because a...

Hello, I have one conceptual question. I have been working on Supersymmetry. Now, I understand that twice of supersymmetric transformation is equivalent to translation mathematically(naively). However, I don't quite understand why this should be the case conceptually. Supersymmetric...

Hi, I want to translate this equation R_{\hat{n}}(\alpha)\vec{x}=\hat{n}(\hat{n}\cdot\vec{x})+\cos\left(\alpha\right)(\hat{n}\times\vec{x})\times\hat{n}+\sin\left(\alpha\right)(\hat{n}\times\vec{x}) to index notation (forget about covariant and contravariant indices). My attempt...

I'm finishing a B.S. in math and have been getting a bit more into physics lately. I'm on track for a second major in either physics or Russian, but not super concerned about finishing - I'm applying to grad programs in pure math. I'm particularly interested in algebraic geometry, combinatorics...

Homework Statement Hi all, There is a question from the course book: Homework Equations S=k_B ln W The Attempt at a Solution My solution: So first of all, for each molecule, there are 2 motions: translational and rotational. For rotational I get: W_1 =\Omega \left ( \theta \right ) For...

Hey, I'm having some trouble understanding why the energy changes here between the blue and red paths (see attached image), it's representing state of an electron in a square lattice crystal. Like mathematically I can see it because obviously plug and chugging the different values k in E(k)...

Translate the sentence into an equation. The difference of a number times 8 and 5 is 3. Use the variable c for the unknown number. How do I write this as an equation?

Vectors and covectors transform differently with Jacobian Matrices inverse of each other. However, what is the general coordinate transformation is a simple translation of coordinates, the Jacobian Matrix will be trivially a delta and contains no information of how much the translation is. How...

Hi everyone, Let \psi (x) be a one dimension wave function. We suppose \langle p \rangle =q How can I compute the new \langle p \rangle when we set \psi _1 (x) := e^{\frac{ip_0x}{\hbar}}\psi (x) I want to comute it with the formula \langle p \rangle=-i \hbar \int \psi _1^*...

I need to prove that $$std(x+c) = std(x)$$ I have been trying to use the properties of the mean such as $$mean(x+c) = mean(x) + c$$ I am confused on the following property of the mean, is this statement correct? $$\sum\limits_{i=1}^{i=N}(x_i - mean(\{x\}))^2 = mean(\{x\}) \\$$ If that is...

I am working on this problem, they say if moments and products of inertia are computed with respect to the center of mass, the H(c)= -I(yz)ŵe(y) - I(xz)ŵe(x) + I(z)ŵe(z) how can I prove this?

Homework Statement A group of American physicist works on a project where planar lines are in the form X=tP+sQ, where P and Q are two fixed different points and s, t are varying reals satisfying s+t=1. They need to know formulae for the images of the line X=tP+sQ in the following three cases...

Suppose we have a test mass located at some point above the earth. It is allowed to free fall down toward the earth. It passes through a closed surface. Prior to entering the surface it has an initial momentum pi and initial kinetic energy kei. After leaving the closed surface it has...

Pretty please? I know there are people here that can read Japanese, I really would appreciate the help. Sorry it is rotated, I couldn't figure out how to get it changed. Thank you in advance!

Dear all, is there anybody knows how to set a 2 degree-of-freedom movement in ANSYS Maxwell 2D transient model? I have two fixed current-excited coils and a free magnet. The magnet should be able to move in a 2D space under the Lorentz forces. However, there are only translation and rotation...