Terms Definition and 1000 Threads

According to my CM text, Lagrangian Mechanics can be used to derive Newton's laws. We define the Lagrangian as L=T-V. Now, how do we know what T is? Is it defined to be 1/2mv^2? The only way I know how to derive that is using the work energy theorem which feels like 'cheating' since I am...

Homework Statement http://img88.imageshack.us/img88/1679/problemhup.png Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://img535.imageshack.us/img535/8075/solutionz.png That is how far i have got, using that sinh(x)=1/2(e^(x)-e^(-x)) I have to express h in...

Hello, i am reading on the Bohr Model. There are some parts i just do not understand. in classical mechanics, an object, such as an electron, revolving ina circle may assume an infinite number of values for its radius and velocity. Why is this? Therefore the angular momentum (L= mvr) (...

For multivariate normal distributions, Isserlis' theorem gives us moments in terms of cross-correlations, e.g., \operatorname{E}[\,x_1x_2x_3x_4\,] = \operatorname{E}[x_1x_2]\,\operatorname{E}[x_3x_4] + \operatorname{E}[x_1x_3]\,\operatorname{E}[x_2x_4] +...

Homework Statement If F(x,y)=0 find d^2y/dx^2 in terms of the partial derivatives of F(x,y). Homework Equations dy/dx= -Fx/Fy The Attempt at a Solution I tried to differentiate dy/dx with respect to x again, I thought I can get d^2y/dx^2 . But I couldn't find it. Actually I don't...

Homework Statement Say we have a given sum, S. I have to, as part of a more general problem in a program, find all possible distinct terms x1,x2,x3,x4 which when added, give that sum, and the ways they can be rearranged. Meaning i have to find all 4-tuples that adding one's members gives S...

Homework Statement I want to check that the QED lagrangian \mathcal{L}=-\frac{1}{4}F^{\alpha\beta}F_{\alpha\beta} + \bar\Psi(i\displaystyle{\not} D - m)\Psi where F^{\alpha\beta} = \partial^\alpha A^\beta - \partial^\beta A^\alpha, \ D^\mu = \partial^\mu - ieA^\mu is invariant under charge...

In layman's terms: what does the term "in layman's terms" mean? Please explain that to me. Everyone is using it and I don't get it. It bugs me so much I can't sleep.

So I'm always having troubles with memorizing the three-phase reaction terms, such as eutectic, eutectoid, peritectic and peritectoid. Are there any meanings of the prefix and suffix? Are there any tricks to memorizing the names and meanings (reactions) of these terms? Thanks a lot!

Homework Statement Find the mass and center of mass of the solid E with the given density function p. 38. E is bounded by the parabolic cylinder z = 1 - y^2 and the planes x + z = 1, x = 0, z = 0; p(x,y,z) = 4.Homework Equations The Attempt at a Solution I've been trying to find a solution to...

Hi I wonder if anyone could help me with this. I'm studying a crystal whose luminescence is excitonic in nature. Since the excitation density is high (with femtosecond laser pulses) exciton-exciton interactions have to be taken into account. The following kinetic equations are used to...

Find the acceleration vector in terms of u subscript r and u subscript \theta r = a(4-cos\theta) and d\theta/dt = 6 Im pretty sure to take the derivative: r' = a(4+sin\theta) r" = a(4+cos\theta) what should i do next?

Hi! As a part of a mathematical construction I used the rate of change of F(s) with s, i.e. dF/ds. F and s are smooth functions. The problem is that s(u,v,w) is a function of u, v & w and actually I need to find the rate of change of F with respect to u, v & w. The question is: what does...

Can someone please explain to me how exactly you write down a metric, say the FLRW metric in matrix form. Say we have the given metric here. ds^2 = dt^2 - R(t)^2 * [dw^2 + s^2 * (dθ^2 + sin^2(θ)dΦ^2)] Thank you.

Homework Statement Given \int_{0}^{k\pi} cos^{2m}(\theta) d\theta = A Express \int_{0}^{k\pi} cos^{2m}(\theta) cos(2\theta) in terms of A. Totally Stucked .. :XI've substituted cos^{2}\theta = \frac{1+cos(2\theta)}{2} Then i get 1/2 A + another chunck of integral. I've used...

Homework Statement find 2 power series solutions of the given diff eq about the ordinary point x = 0 y'' - xy = 0 Homework Equations y = (c_0)(y_1)[x] + (c_1)(y_2)[x] The Attempt at a Solution i can set it up to this (sorry idk out how to insert the subscripts with the summation symbols)...

A body falls into viscous liquid which causes the velocity to decrease at the rate proportional to the velocity. v=velocity(m/s) t=time(s) k= constant of proportionality The initial velocity of the body=30m/s k=0.3m/s^2 t=0.25s Solve for v in terms of t and k First step possible...

I've posted on here in relation to an aerospace analysis project I'm doing. I'm stuck on one part of the project where I need to develop the performance envelope of the turbojet engine. 3 of the 9 plots that are required are Thrust vs. Mach number. On each of those plots I'll about 7 different...

Homework Statement a.) What is the operational definition of an ampere? b.) What is the definition of an ampere in terms of a flow of electrons past a point in a wire? c.) What is the advantage of the operational definition over the definition in (b)? Homework Equations N/A...

Anybody here how could explain to me in the simplest terms triality? I know some very littel Lie and representation theory. As I understand there are vector and spinor representations for so(n). If n is even, there are two spin reps and one vec rep, if n is odd there is one spin rep and one...

I'm attempting to derive speed in terms of potential difference (voltage), can anyone let me know if there are any errors? http://www.texify.com/img/%5CLARGE%5C%21E_k%3D%5Cfrac%7B1%7D%7B2%7D%5Ctext%7Bmv%7D%5E2.gif...

Homework Statement Find the general solution of the given differential equation. Give the largest interval over which the general solution is defined. Determine whether there are any transient terms in the general solution. Homework Equations x(dy/dx) + 2y = 3 The Attempt at a...

Hello, Just a few questions about a couple of terms in and not in the SM Lagrangian. I'll talk in particular about these fields, and their representations in SU(3) x SU(2) x U(1) Q (3,2,1/6) (left-handed quarks, fermion) U (3,1,2/3) (right-handed up-quarks, fermion) \phi (1,2,-1/2) (higgs...

Where do the definitions of hyperbolic functions in terms of exponentials come from ?

I'm having trouble with integrating this. \int_1^8 \sqrt{9x^{4}+\frac{1}{2}+\frac{1}{144x^{4}}} dx I can get the problem down to \int_1^8 9x^{2}+\frac{1}{\sqrt{2}}+\frac{1}{144x^{2}}} dx , but I don't know how to integrate the last two terms in that integral. Am I doing something wrong?

Typically the action for E-M is F_{\mu\nu}F^{\mu \nu} where F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu since the equations of motion for A_{\mu} are the inhomogenous Maxwell equations. However, here comes my problem: If one expresses this action in terms of the electric and...

Suppose a_n defined in the following way: b_{2n}=a_{2n-1} b_{2n-1}=a_{2n} I know that \sum a_n is convergent. This how I proved that \sum b_n is also convergent. S_k=\sum_{n=1}^k b_n = \sum_{n=1}^k b_{2n} + \sum_{n=1}^k b_{2n-1} = \sum_{n=1}^k a_{2n-1} + \sum_{n=1}^k a_{2n} =...

find the first three non zero terms in the Taylor Series about z=0 of exp(z sin z) i have little idea how to even start on the question because it is exp to the power of z sin z and it just looks too complicated. i hav tried looking thru txtbooks for something similar but no similar question...

Homework Statement w(r,\theta)= u(rcos \theta ),rsin( \theta)) for some u(x,y) express \frac{ \partial w}{\partial r} and \frac{ \partial w}{ \partial \theta} in terms of \frac{ \partial u}{ \partial x} and \frac{ \partial u}{ \partial y} Homework Equations rewrite the...

What's the most persuasive argument for using the potential phi and A as independent deegres of freedom in the electromagnetic Lagrangian instead of the more physical field E and B? Why does the cannonical approach break down for E and B?

HI, I have solved the diffusion equation using the central difference scheme. Next, I would like to code this diffusion equation with a nonlinear term added to the equation. The full equation is as follows: dS/dt = Ds * d^2S/dx^2 - aS/b+S Since aS/b+S is a nonlinear term, I need to...

The Stefan-Boltzmann law is as follows: The energy radiated by a black body radiater per second per unit area is directly proportional to the fourth power of the absolute temperature. Equation: I = σT^4 Is it possible to explain this law by means of classical physics only? If so...

Dear all, i need help in finding out the terms below. Tried goggle it but fail to really understand them. Anyone can help? thanks! 1. Undercooling in welds 2. Quick solidification 3. Martensite, austenite, pearlite, ferrite phase for steels 4. Phase diagram for steels 5. Difference...

Representing a vector in terms of eigenkets in continuos basis(stuck here,guys help) I was reading Dirac and there is this formula which bothers me, |P>= \int{|\right{\xi'd}\rangle{d\xi'}} + \sum{|\right{\xi^{r}b}\rangle} Where |\right\xi'\rangle denotes the eigenket corresponding to the...

Homework Statement I am modelling the motion of a space probe and have some problems with obtaining velocity in terms of time v(t). I am given Q(z)=v2(z). Q(z) is a solution to ODE which I have solved with z being the independent variable. Homework Equations Q(z)= something really...

Homework Statement Let x1 > 9000, and xn+1 = )2009xn + 2010)/2011 for n >1 show that (xn) converges and find its limit Homework Equations Definition of a limit, Monotone Convergence Theorem. The Attempt at a Solution Since xn+1 is monotone for n>1 and bounded, then it...

So I am working in spherical coordinates and to find the gradient I have the eqn G-1d\phi where \phi is a scalar function Then I am supposed to compute in terms of {em} and {wm}. I am just confused what it means to compute in terms of? Do i have to convert the co and contra vectors...

Hello all. Again, thank you for the help so far. Forgive the lack of tex in this post, it somehow was creating errors no matter what I tried. My question this time involves understanding the F and D terms in SUSY theories. From what I understood, they were introduced as auxiliary fields (EOM...

Homework Statement State the definitions of greatest and least elements in terms of strict orderings. Homework Equations Let \leq be an ordering of A and < be a strict ordering on A, and let B \subseteq A. b \in B is the greatest element of B in the ordering \leq if, for every x \in...

I know someone who is doing biology and chemistry 11 and soon biology and chemistry 12, but has a hard time pronouncing all the terms (learning english) Is there a website out there that helps people pronounce all the terms in biology and Chemistry, in a grade 11/12 level? Thanks!

Alright, here is something that is driving me insane. I feel like I've looked through every stat mech book on the planet and not a one discusses this stuff properly. My difficulty is in the study of phase transitions when one applies Landau's approach of expanding the free energy about the...

Homework Statement For a finite isothermal sphere with a radius R and circular velocity v (remember, the rotation curve is constant), we derived the total mass and potential energy as M =v2R/G U = -GM2/R Express the potential energy U in terms of M and v. Use the virial theorem to find...

Hi, We all know that the finite difference formulae for the derivatives are given by: \frac{dy}{dx}_{i}=\frac{y_{i}-y_{i-1}}{\delta x} and \frac{d^{2}y}{dx^{2}}=\frac{y_{i-1}-2y_{i}+y_{i+1}}{\delta x^{2}} What would be the formulae for the boundary terms? when i=1? I think I can...

Homework Statement I need to have x on the LHS in terms of just y, h and t on the RHS:Homework Equations x = y + h(t2 - x2)sin(x)The Attempt at a Solution I really don't know where to begin. I'm pretty sure there'll need to be an arcsin somewhere. Is this even possible? Thanks in advance!

What is "action" in human terms? A friend, humanist by profession, asked what is "power"? Well, that was easy to explain in human terms. You do a certain amount of work, you use a certain amount of calories, you can do you work slowly, during one day, or you want to do it in one hour. Then you...

Does anyone know why in quantum field theory mass terms are quadratic in fields (not contaning derivatives)? Thanks!

Where could I find a webpage or guide on how to write unit vectors in terms of sin and cos? I looked through my textbook and tried searching google, but I can't find anything...I must be using the wrong terminology. edit: Delete me! I had one of those epiphany moments and figured it out...

Thant helped. thank you!

Homework Statement Using: particle velocity, beta particle momentum, p total energy, E Lorentz factor, gamma kinetic energy, KE Derive an equation for momentum as a function of kinetic energy. The functions have to depend either on the variable in the bracket, p(KE), or on a...

Hello, I am having some difficulty in understanding the terms in Bernoulli's equation. Bernoulli's equation is given as follows: P + 0.5(rho)(V^2) + (rho)gh = constant (along a streamline) The first term (P) is the Static Pressure. The second term (0.5(rho)(V^2)) is the Dynamic...