Derivation Definition and 1000 Threads

Homework Statement Problem 1: Derive the Euler-Lagrange equation for the function ##z=z(x,y)## that minimizes the functional $$J(z)=\int \int _\Omega F(x,y,z,z_x,z_y)dxdy$$ Problem 2: Derive the Euler-Lagrange equation for the function ##y=y(x)## that minimizes the functional...

I have seen the derivation of the kinetic energy equation using F=M*v' and E=F*x And I can see how this works, however if you try to do this without thinking about velocity, and only thinking about the rate of change of distance, and the rate of change of rate of change of distance, then the...

U = energy In the book: \frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2} mv^2 + \frac{1}{2} kx^2) then we have m \frac{d^{2}x}{dt^2} + kx = 0 because v = \frac{dx}{dt} however they get rid of \frac{dx}{dt} . They are ignoring the case where v = 0, because then m \frac{d^{2}x}{dt^2} + kx...

This is actually the problem in the textbook. I'm trying to derive the harmonic oscillator differential equation for this system, but It seems like it's very very challenging. could anyone help me out? Following is the question and figure from the textbook. Homework...

I've been working my way through Intro to Electrodynamics (Griffiths), and in Chapter 3, one of the derivations comes out to ∫sin(n\piy/a) sin(n'\piy/a) dy ={ 0 if n'\neqn a/2 if n'=n where the function is...

f:R->R is differentiable and f'(x)=[x^2/1+(x^2))] and f(0)=0. check whether 0<=f(x)<=x for all x belonging R. Thanks.

Introduction This is not a homework or coursework question (if it were it would be of the project type), and I am looking for hints not spoilers. Hi, I recently passed by kepler's laws again in a science class (this time Earth science), and am concurrently taking calculus in my math class...

Find the instantaneous velocity where r is the position vector as a function of time: r(t)=(3.0m/s^2)t\hat{x}+(4.0m/s)t\hat{y} I attempted to find the derivative of this to find instantaneous velocity, but the book's solution was different. I think the author of the book may have made a...

Homework Statement Consider the following equality: (\frac{∂S}{∂V})T = (\frac{∂P}{∂T})V If I rearrange the equality so that I write: (\frac{∂S}{∂P})? = (\frac{∂V}{∂T})? What variables will be constant in each side? I'm having some trouble in a few thermodynamics problems because...

http://imgur.com/SnHyP What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ? If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...

http://imgur.com/SnHyP What are the mathematical steps and assumptions to reach the conclusion that length(ab) ≈ dx + ∂u/∂x*dx ? If you consider the the squares of the gradients to be negligible, you still have a square root and multiplication by the constant "2". What other assumptions do...

I'm a little confused, in my fluid mechanics course we've covered many equations and they are all derived using an x-direction fluid flow. If I was to use these in a system in which fluid flowed in the y-direction would I have to re-derive them? Or would it be more of a case of using a...

Can someone tell me how I can derive Wien's law, i.e., \lambda_{max} T = constant where \lambda_{max} is the peak wavelength and T is the absolute temperature of the black body, using the equation, P=\frac{U^{*}}{3} where U^{*} is the energy density. Note: I'm not looking for...

i was reading about derivation of Euler's equations for rotational dynamics (john taylor, classical mechanics, chapter 10) when i got stuck on one of the reasonings essentially it refers to the moment of inertia tensor, since the tensor itself about a point is dependent on the position of the...

Homework Statement I am seeking a derivation of the formula for greatest detail or maximum resolution of an astronomical telescope, which is: Homework Equations M = fo/foe where: M: magnification fo: focal length of objective lens foe: distance of primary image from the eyepiece...

Hey guys, I was trying to reverse engineer Einstein's formula for energy, E=γmc^2 by re-engineering Newton's Law of motion, F=ma. I was talking with my physics prof about deriving energy from this because I got two different answers but it gets weird because the incorrectly derived formula...

Homework Statement http://postimage.org/image/j2ccrtjp1/ Here is a scan of my work. The problem is on the scan. Just trying to derive the velocity of the target in an elastic collision, as sketched in the image... Can't seem to find the problem for the life of me.

Equation attached. For those who can't see the image here it is in text form, k=(Gd^4)/(8D^3 n ) It is the equation for the stiffness of a spring in terms of its dimensions: G - shear constant d - wire diameter D - coil average diameter n - number of active coils (total coils -2 as...

I'm just getting started on relativity. I watched this a couple of day ago - But I didn't like the way Lorentz Transformation was derived (the assumption about the nature of the final transformations, to be more specific). I tried reading Einstein's original paper for a better derivation but...

I just have a question of "why/how?" I know that for instance \mathbf v=\omega \hat k \times \mathbf r where \mathbf v is my vector for velocity, \omega is my angular velocity and \mathbf r is my position vector from a point on the axis of rotation of a wheel to a point on the outer edge of the...

Homework Statement I'm taking a fluid mechanics class and I'm having an issue with acceleration and background knowledge. I know this is ridiculous, but I was hoping someone might be able to explain it for me. Homework Equations I definitely understand: ##a=\frac{d\vec{V}}{dt}## And I...

So I know about the lorentz factor and how it describes time dialition, mass increasing etc.. but I was wondering how it was derived in the first place?

Homework Statement Consider a cylindrical vessel with cross-sectional area 1m^2 Derive the particle flux (1/4n\bar{v})Homework Equations I have the solid angle: \Omega = 2π(1-cosθ) The Attempt at a Solution I'm assuming that the solid angle represents the full area that the particles can...

Homework Statement I was reading up on the Wave Function used in the Schrodinger Wave Equation. However one source said that ψ(x,t)=e^(-i/hbar*(px-Et)) Another source had this ψ(x,t)=e^(i/hbar*(px-Et)) Which one of these is true and could someone give a derivation for the correct...

Homework Statement I tried to reach the Bernoulli principle this way: Two pipes are connected, one has a cross-sectional area of S_{1} and speed of v_{1}; S_{2} and v_{2} for the other. The pipes are horizontal, the connecting wall between them at the crossing from one pipe to the other is...

Hi! I've got a problem with question 5 on this paper: http://www.freeexampapers.com/past_papers.php?l=Past_Papers%2FAEA%2FPhysics%2F2006/ Download AEA-PHYS-PP-MayJune-2006-AEA-Paper-1342.pdf. Starting from b) i), we got that: ε=Δ∅/Δt → W=εe Where W is denotes work, ε is...

Homework Statement Given the function f(x) defined as: (x^3-y^3)/(x^2+y^2) if (x,y)≠(0,0) 0 if (x,y)=(0,0) Find the parcial derivatives of the function at the point (0,0). Is the function f differentiable? Homework Equations The Attempt at a Solution d/dx [...

Hello guys, Check the attachment please. How is it what's written after "HENCE"? Where did 2*A^*<A> term go? the same thing for 2*B^*<B>??

In thermodynamics one of the maxwell relations is: \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V When I try to derive it from dU = TdS - PdV i get: T = \left( \frac{\partial U}{\partial S} \right)_V P = -\left( \frac{\partial...

Meaning of ct in Lorentz transformation - In Lorentz transformation matrix, the first column is defined as - ct, not t itself. Is it because ct satisfies the units of x, y, z? Or, simpler Lorentz transformation matrix will be derived? The idea of 'ct', instead of t, is quite abstract for me...

Homework Statement S=1+(a/r)-(b/r^3) Homework Equations need to find r=sqrt(3b/a) and S=1+ sqrt((4a^3)/(27b))) from a derivation of the above formula in #1. The Attempt at a Solution 0=(3b/r^4) - (a/r^2)

What is the derivation for E=hf and why did experimental observation of black bodies show that quantization of light was neccessary?

Homework Statement Let y=sin(x)^x. Find dy/dx My teacher said to use Natural long to solve this. she got, step 1:ln(y)=ln(sin(x)^x)=x ln(sin(x)) step 2:y(dy/dx)=1(ln(sin(x)+x(cos(x)/sin(x) Final answer:dy/dx=((sin(x))^x)[ln(sin(x))+x(cos x/sin x) I don't understand how she...

Confusion over derivation of angular momentum equation Hello, I'm a little confused over the relation between torque and angular momentum. When L=r×mv \frac{dL}{dt}=r×m\frac{dv}{dt}+mv×\frac{dr}{dt} According to Wikipedia, v=\frac{dr}{dt} mv×\frac{dr}{dt}=mv×v=0 So...

Hi, I have a specific question about the derivation of the relative velocity between two molecules A and B from the Maxwell Boltzmann distribution (which should equal square root of 2 times the average velocity). In equations, I have been evaluating this integral: \begin{eqnarray*}...

Deriving the basics of infinitesmal elasticity, I have a proof regarding the physical significance of the strain tensor E_{11} So we are considering a material line element parallel with the x_{1} axis being deformed. At a point in the proof we have du_{1} = u_{1}(x_{1}+dL_{0}, x_{2}...

Can someone derive for me the equation ωd=ωnsqrt(1-ζ2) Thanks

I'm having trouble understanding the derivation of the the position operator eigenfunction in Griffiths' book : How is it "nothing but the Dirac delta function"?? (which is not even a function). Couldn't g_{y}(x) simply be a function like (for any constant y) g_{y}(x) = 1 | x=y...

Beginning at 31:03 Dr. Susskind presents an intuitively very satisfying derivation of the Euler-La Grange equation(s). But, I'm not convinced it is rigorous. It seems his choice of variation is not the only possible choice for the neighborhood he selected. The reason this matters to me is...

So I am rereading David Atkinson's QFT book: http://books.google.co.il/books/about/Quantum_Field_Theory.html?id=vbAnQAAACAAJ&redir_esc=y And I am puzzled by what is written in pages 5-6 section 1.3 Special Theory of Relativity. He writes down the transformation between two inertial...

Higgs vacuum expectation value for the Standard Model: (ref. 1 pg. 14) v_h = \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}} Higgs mass equation for the Standard Model: (ref. 1 pg. 14) m_H = \sqrt{2 \lambda_h} v_h \lambda_h - Higgs self-coupling parameter. Integration via substitution: m_H =...

I was reading a paper and came across this equation: Fmagnetic=μ0(M<dot>∇)H Is this the correct expansion below? (I'm not too experienced with vectors operating on the gradient operator) Fmagnetic=μ0[(Mx ∂H/∂x)i + (My ∂H/∂y)j + (Mz ∂H/∂z)k] _____________ My reasoning partially comes from...

Hi, Got a problem with the following derivation: Coming from the Helmholtz equation one gets: \textbf{n}^2=\muc^{2}(\epsilon+i\frac{\sigma}{\omega}) which is of course something like: \textbf{n}=n+i\kappa My question is, how do you obtain the following relations...

Homework Statement Derive Vc, Pc and Tc from the Van der waals equation, then determine these values for Chlorine gas which as a=6.49 and b=.0562. Solve Algebraically without using Calculus. Given hints (verbatim): 1. First, convert V/n = ∇ in VDW equation and P->Pc and T ->Tc 2...

I was looking through a Taylor's Classical Mechanics chapter and I have a question about the derivation. So basically, it starts out with m\dot{v}_{y}=mg - bv_{y} and you find v_{ter} by letting m\dot{v}_{y}=0 where when you solve for v_{y} you will get v_{ter}. Now the book states how we...

Homework Statement The altitude of the space shuttle during the first 30 s of its ascent is described by the expression у = bt2, where the constant b has the value 2.9 m/s2. Using calculus, obtain an expression for the velocity and acceleration of the space shuttle during this period...

I have a simple question but I'm putting down the whole derivation as it is relevant. There is a point that I don't understand, or seems wrong to me. This is a derivation of Group Velocity followed by simplifying(approximating it) for long wavelength waves in shallow water. This appears in a...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

In my notes on waves (specifically water waves) there is a derivation of Group Velocity. They consider two waveforms with the same amplitude, that differ slightly in wavelength and frequency, which are then superimposed to give wave groups. kis wavenumber, \delta k is how much the wavenumbers...

First of all, my question isn't completely unrelated to a homework question. I know how to answer that question using definitions in the book and mechanically get to the end. But I wanted to start from basic principles and arrive at the same answer. This lead to a contradiction which sent me on...