Variation Definition and 540 Threads

Homework Statement Hi, Please see attached. I am trying to show the second equality , expressing all as a total derivative (I can then show that ##\delta S = ##) Homework Equations See above The Attempt at a Solution So the ## m ## term is pretty obvious, simply using the chain rule. It...

At the moment I'm working with the https://en.wikipedia.org/wiki/Schwinger's_quantum_action_principle']quantum[/PLAIN] action principle of J. Schwinger. For this I read several paper and books (like: Quantum kinematics and dynamics by J. Schwinger, Schwinger's Quantum action principle by K.A...

Homework Statement I am not sure whether the meaning of the equation ##(3)## which used for deriving momentum is as same as equation ##(4)##.I will make a detailed description below. The lagrangian function for a free particle is ##L=-mc^2\sqrt{1-\frac{v^2}{c^2}} \quad (1)## The action from...

Here the particle is performing circular motion due to the rotation of the earth. And for the circular motion it requires centripetal force then which force provides the necessary centripetal force. I think it is mgcos(lamda). Am i right?

Homework Statement In the notes , I don't understand why the shear stress is maximum at the edge ( circle part) . Homework EquationsThe Attempt at a Solution I think it's wrong . Refer to another diagram attached , i found that the shear stress varies parabolically across the vertical length...

Homework Statement y''-4y'+4y=(12e^2x)/(x^4) I am trying to solve this differential equation. I know you would use the variation of parameters method, and I am trouble with the wronskian. My solution manual doesn't actually use a wronskian so I can't verify my work Homework EquationsThe...

## L(x) = L(\phi(x), \partial_{u} \phi (x) ) = -1/2 (m^{2} \phi ^{2}(x) + \partial_{u} \phi(x) \partial^{u} \phi (x))## , the Lagrange density. ## S= \int d^{4}(x) L (x) ##, the action. ## \phi -> \phi + \delta \phi ## (just shortened the notation and dropped the x dependence) I have ##...

Hi folks, I am a bit confused with the extreme condition used in the calculus of variations: δ = 0 I don't understand this rule to find extreme solutions (maximum or minimum) If in normal differential calculus we have a function y = y(x) and represent it graphically, you see that at the...

Homework Statement Use the method of variation of parameters to find a particular solution Homework Equations https://flic.kr/p/NqhtyQ The Attempt at a Solution https://flic.kr/p/NicCbN [/B] Can some find my mistake? The answer is just suplosed to be - 2/3te^-t[/B]

What is the pressure experienced by any point at different locations inside a rotating tube filled with water? The axis of rotation is through the center of the tube.

Consider two atoms of platinum, A and B, in a sample of platinum. Atom A lives deep within the sample, and atom B lives at the tip of a sharp protuberance at the surface. My understanding is that electrons in the sample will accumulate within a surface defect such as the tip of a sharp needle...

I'm working through the discussion of calculus of variations in Taylor's Classical Mechanics today. There's a step where partial differentiation is involved that I don't understand. Given: $$S(\alpha)=\int_{x_1}^{x_2} f(y+\alpha\eta, y'+\alpha\eta', x)\,dx$$ The goal is to determine ##y(x)##...

http://www.utdallas.edu/~pervin/ENGR3300/Boaz.pdf see page 493 he said that first variation of I is δI = dI/dε * dε http://www.colorado.edu/ASEN/asen5227_offline/slides/292-334.pdf but this pdf said (see page 309) that first variation of I is δI = dI/dε * ε (y and I commute, α and ε...

Hello, I have a question. There is a classic problem in which a student who is at constant speed approach a bus which has begun to accelerate and is at a certain distance from the student; You need to figure out when it reaches the bus. The problem is easy to solve, if Xo is the distance...

The field strength of gravitational, electric and magnetic fields vary as the inverse square of the distance from the source. Is this because all of the above fields are generated by fermions and they behave identically regardless of the nature of the fields ? Do the above fermions have rest...

hi, When I read variation of metric, I bumped into a unfamiliar formulation for me. You can see the formula in my attachment. I can not understand where this comes from. Could you provide me with the proof of that formula? By the way, you can go to this link to look at from which the...

Homework Statement It is shown in Carrol, an Introduction to GR that the variatiom of Christoffel symbols are : https://scontent-sin1-1.xx.fbcdn.net/v/t34.0-12/13535871_1161725257182772_897443562_n.jpg?oh=df1a6d26aa0b199d4684b5f0785bee20&oe=576ECCCA But i have no idea how to derive that, any...

the volume of a sphere: V=(4/3)pi*r3 To me it looks like it is direct variation with a power function (V/r3=(4/3)*pi)but i don't think that's what they're looking for

Today I heard the claim that its wrong to use Stokes(more specificly divergence/Gauss) theorem when trying to get the Einstein equations from the Einstein-Hilbert action and the correct way is using the non-Abelian stokes theorem. I can't give any reference because it was in a talk. It was the...

Homework Statement So I'm deriving Lagrange's equations using Hamilton's principle which states that the motion of a dynamical system follows the path, consistent with any constraints, that minimise the time integral over the lagrangian L = T-U, where T is the kinetic energy and U is the...

Hello! I'm wondering if there's a general dependency/connection/correlation/function for changes in distance between an electromagnet (coil with iron core) and a magnet (Samarium Cobalt). Here's a picture to explain what I mean: If I move the coil closer to the magnet (smaller x) the force...

Kreyszig Advanced Engineering Mathematics shows the variation of parameter method for a system of first order ODE: \underline{y}' = \underline{A}(x)\underline{y} + \underline{g}(x) The particular solution is: \underline{y}_p = \underline{Y}(x)\underline{u}(x) where \underline{Y}(x) is the...

Hi, I recently did an experiment whereby we investigated the velocity distribution of air expelled from a round nozzle whose diameter, D, was 30mm. We have been asked to calculate the volume flow rate at distances of 2D, 6D and 10D along the centreline. We found the flow rates to INCREASE...

hello, My question will be quite naive for experts and reflects the fact that I'm new to the subject of varying the fine structure constant alpha and mainly need an introductory reference ... so if someone has a good one to advice ...thanks a lot i just don't understand the basics: how people...

Is it really possible for a system to decrease its velocity with no forces acting on it, just because the mass in it is "varying"? Consider for example a freight car and a hooper from which sand is released into the car. The freight car will decrease its initial velocity if there is no force...

Homework Statement For a given function ##g:[a,b]→ℝ, 0 < a < b##, compute its total variation \underset{[a,b]}{\mathrm{Var}} (g) where ##g(x) = \sin(x), x\in[a,b].## Homework EquationsThe Attempt at a Solution I know that between odd multiples of ##\frac{\pi}{2}##, ##\sin(x)## is monotone, so...

Hi Friends, I am trying to find variation in capacitance between two plates with applied body load. I defined an air box around the plates. Now I'm trying with electromechanics physics for applying body load and finding capacitance. I defined the two plates as linear elastic material. Applied...

I want to know the what is the effect of temperature on modulus of rubber, mathematical expression will be helpful

Hi, I've been working through Cornelius Lanczos book "The Variational Principles of Mechanics" and there's something I'm having difficulty understanding on page 168 of the Dover edition (which is attached). After introducing the Legendre transformation and transforming the Lagrangian equations...

Homework Statement Counting problems are a very tough subject to me, so if someone could give me tips, examples explaining what's really happening, that would be great. Homework Equations I know what permutations, variations, combinations, ... are. The problems involving only one of those...

Homework Statement Consider the functional ##S(a,b) = \int_0^∞ r(1-b)a' \, dr ## of two functions ##a(r)## and ##b(r)## (with ##a' = \frac{da}{dr}##). Find the ##a(r)## and ##b(r)## that extremize ##S##, with boundary conditions ##a(∞) = b(∞) = 1##. Homework EquationsThe Attempt at a Solution...

Hello, I am very much interested to how frequency of sound varies in water. Also, how the frequency varies with temperature and depth? What are the different formulas related to this? Secondly, how can we determine the best frequency of operation? I would be very thankful if anyone could answer...

I have tried to discover if the local time as well as the local space is varied by the passage of a gravitational wave. I have seen animations and discussion of the effects of gravitational wave on space and test particles but can't find a reference to the changes in the time component of...

Hi! I have some trobles while studying the lagrange mechanics chapter of Marion's Classical Mechanics. There are some variation techniques in that book, but I only studied calculus and elementary linear algebra in my freshman year. I can't understand how partial derivation and delta notation...

Hi, I've been given a list of heights and corresponding densities of air at these heights. I'm trying to find an expression for the variation of density with height. From the data, it looks like the density would be equal to some kind of logarithmic relationship? However, I'm not too sure how to...

i was trying to get a particular solution of a 3rd order ODE using the variation of parameters method the homogeneous solution is yh = c1 e-x + c2 ex + c3 e2x the particular solution is yp=y1u1+y2u2+y3u3 as u1=∫ (w1 g(x) /w) dx , u2=∫ (w2 g(x) /w) dx , u3=∫ (w3 g(x) /w) dx w =...

Homework Statement Let f is differentiable function on [0,1] and f^{'}(0)=1,f^{'}(1)=0. Prove that \exists c\in(0,1) : f^{'}(c)=f(c). Homework Equations -Mean Value Theorem The Attempt at a Solution The given statement is not true. Counter-example is f(x)=\frac{2}{\pi}\sin\frac{\pi}{2}x+10...

Homework Statement Why is potential energy variation between two points equals to the work of the opposite of conservative forces between these two points? Homework Equations If we call these forces $$\vec F_ext^C$$ \begin{equation} \Delta E_p=E_p(B)-E_p(A)=-\sum W_{A\rightarrow B}(\vec...

Homework Statement hello! so i am trying to figure out how to calculate the resultant velocities and directions(angles/vectors) that two perfectly elastic spheres might travel in if they were to be hit simultaneously by a third sphere at an angle. all the spheres are of equal mass, initial...

Hello, In the context of QFT, I do not understand the statement: ##\frac{\delta \phi(x)}{\delta \phi(y)}=\delta (x-y)## I understand the proof which arises from the definition of the functional derivative but I do not get its meaning. From what I see is generalizes ##\frac{\partial...

In the chapter 9-5 "The Linear Variation Method" p. 363 from the book: Basic Principles and Techniques of Molecular Quantum Mechanics by Ralph Christoffersen, the first thing he does is to minimize the energy, E = c†Hc/c†Sc, by requiring its derivative with respect to the...

Hello, I do not understand how to compute the infinitesimal variation of the field at fixed coordinates; under lorentz transformation . I am doing something wrong regarding the transformation of the ##x## coordinate. I am looking for: ##\Delta_a=\phi_a'(x)-\phi_a(x)##, variation appearing in...

Use the variation of parameters method to find a general solution of $x^{2}y''+xy'-9y=48x^{5}$ $m^{2}-9=0$ $(m+3)(m-3)=0$ $m=3,-3$ $y_{h}=c_{1}x^{-3}+c_{2}x^{3}$ $W=6/x$ Don't really know how to do wronskian with latex so i didnt include the steps. But i need help with the rest of this. i...

I need a formula to calculate permutation. For example I have a 5 numbers and I creating a 3 digit number from it. The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula. If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote...

Homework Statement : A cylinder is elongated by 2% of its original length. If Poisson's ratio of its material is 0.3. Calculate the percentage variation in volume.[/B]Homework Equations V = πr^2l η= 0.3= Δl/l/Δr/r[/B]The Attempt at a Solution I tried using calculus to differentiate V to find...

Homework Statement I'm trying to calculate the variation of the following term for the determinant of the metric in the polyakov action: $$h = det(h_{ab}) = \frac{1}{3!}\epsilon^{abc}\epsilon^{xyz}h_{ax}h_{by}h_{cz}$$ I know that there are some other ways to derive the variation of a metric...

Homework Statement Homework Equations F=ma The Attempt at a Solution As the diver's velocity increases, then force F due to air resistance would increase, so D is out. And C is out too, as air resistance would be equal to its weight at terminal velocity. The answer is B, but how do we know...

Homework Statement Hi all, I currently have a modified Einstein-Hilbert action, with extra terms coming from some vector field A_\mu = (A_0(t),0,0,0), given by \mathcal{L}_A = -\frac{1}{2} \nabla _\mu A_\nu \nabla ^\mu A ^\nu +\frac{1}{2} R_{\mu \nu} A^\mu A^\nu . The resulting field...

Homework Statement The figures showing the potential variation inside a PN junction normally shows the potential to be constant in the neutral P and N regions Homework Equations V=Q/4ΠΣr The Attempt at a Solution Since the potential due to the positive and negative charges should also exist...

Homework Statement 1. We are considering a step junction at equilibrium(no external voltage applied). 2. The potential variation is shown as negative potential at P region(which is shown as constant) and increasing through the transient region to become positive in the n region. Homework...