deriving Definition and 1000 Threads

Homework Statement Use Kepler's Third Law and a Taylor expansion to derive the following approximation for the orbital period of a satellite in low Earth orbit with a constant height h above the surface of the Earth. h << R_earth : P \approx P_{0}(1+3h/2R_{e}) Homework Equations Kepler's...

Expanding exp(hc / lambda*k_b * T) by Taylor series = 1 + hc /lambda*k_B * T +... But don't you take the derivative with respect to lambda? So I don't get how it would be this.

Hey all, (As I mentioned in my previous post) I am trying to derive the Hamiltonian for a aeroelastic system, where the dynamical equations of motion (determined by Newtonian Mechanics) are known. My process has been to 1. "guess" a form of the Lagrangian, check that it recreates the...

Homework Statement It's been a while since I've done derivatives. I'm working on a physics problem and can't seem to get the correct derivate for a function of the following form: f(x)= A [1+9x^2(x-4)^2]^1/2 A is a constant. The Attempt at a Solution I've tried various ways of...

Hi all, I am in a bit of a dilly of a pickle of a rhubarb of a jam with determining the Hamiltonian of a specific system. For background information it is an 2-DoF aero-elastic system where I am (temporarily) neglecting the aerodynamic lift and moment terms. Being an intrinsically...

Hi all, I'm following along the derivation of the field equations for f(R) gravity, and there's one step I don't understand entirely. There's just something in the math that's eluding me. So wiki has a pretty good explanation...

I've seen the derivation of Dirac Equation using Inhomogeneous Lorentz Group in L H Ryder's QFT book.Can anybody give some comprehensible descriptions of this method?

Hey. I've been having some trouble getting through Mohr's circle. The googles that I've found haven't been too useful. I've seen several questions of the same calibre and what I generally need is how to derive the magnitude/direction of the principal strains as well as the principle stresses...

1. An object of mass, M, is projected into the air with an initial vertical component of velocity, Vo. If the air resistance is proportional to the instantaneous velocity, with the constant of proportionality being, K, derive the equations for the displacement, velocity and acceleration as...

Hi there, i would like everyone to evaluate my working here, this is my attempt to wave equation / vibrating system using vector approach. please correct me if i had made some mistakes. Your help is much appreciated, Thanks, and have a nice day. :smile: Regards, Daniel.

Homework Statement Consider a standard i.i.d. Gaussian random vector \mathbf{X} = [X_1 \cdot \cdot \cdot X_n]^T and its squared magnitude ||\mathbf{X}||^2 = \sum_{i = 1}^nX_i^2. According to my textbook, to derive the density function of a chi-square random variable ||\mathbf{X}||^2 , one...

According to my textbook, to derive the chi-square density function, one should perform three steps. First we consider a standard i.i.d. Gaussian random vector \mathbf{X} = [X_1 \cdot \cdot \cdot X_n]^T and its squared magnitude ||\mathbf{X}||^2 = \sum_{i = 1}^nX_i^2. 1. For n = 1, show that...

hi, I have a very simple question. I am reading Bernard F. Schutz's A first course in general relativity. after completing the special relativity section I had a goal to sit down with paper and completely derive from square one the lorentz metric, four velocity and momentum, and finally come up...

Homework Statement See the attachment please. The Attempt at a Solution I know the v1 x delta (t) is for the rectangle, I don't see how the second part works? I don't understand why the t^2 and how a replaces the area formula i have written. Thanks for your help, its my...

Hey. I want to derive the conductivity of graphene. I'm looking for a formula of the sort: J = \frac{e}{\hbar} n \frac{dE}{dk} D(E) \Delta E where \frac{1}{\hbar} \frac{dE}{dk} is the electron velocity, D(E) = \frac{dN}{dE} is the density of states, \Delta E might be the applied voltage...

Hello, I read some fluidmechanics and there was something I didn't understand. The shear stress in a Newtonian fluid is tau=viscosity*dV/dy, (no need to be dy, but dx and dz also can do.) A shear component called tau(xx) came up, I have two questions about this component: 1. Shear is...

Could someone help me with this. In pipe flow show that the average velocity is half of the maximum velocity. I have it written in my notes that this is true, but not how to derive it.

Homework Statement Consider the Proca Lagrangian L=-\frac{1}{16\pi}F^2-\frac{1}{c}J_{\mu}A^{\mu}+\frac{M^2}{8\pi}A_{\mu}A^{\mu} in the Lorentz gauge \partial_{\mu}A^{\mu}=0 Find the equation of motion. Homework Equations F^2=F_{\mu\nu}F^{\mu\nu} The Attempt at a...

This formula (E = V/d) has been used to derive the value of capacitance...but how is this applicable?...this is for point charges and here we're dealing with plates. Any derivation to prove this is also applicable for plates?

OMG second time I'm opening a thread in the wrong forum FFS! Damn bookmarks! MODS move it please. Homework Statement Not a home work question, just something i cam across and need a clarification. Could One show me how to derive to the equation that X(cm)=int(X dm)/M int=the deformed S of the...

Hi Folks, I have a quick question about the Biot-Savart Law, I know what it is, but I don't know how to derive it. Could anyone give me either links or show me the derivation with origins. I have tried to google it but to no avail. Thanks in advance for all your help in advance Kipper

Homework Statement Hi, I am trying to write the sum and output of a full adder in terms of XOR logical functions using boolean logic and Karnaugh maps. I've got the expressions from the Karnaugh maps fine but I can't seem to rearrange them into the expected form shown at the end of my...

Homework Statement I must derive Torricelli's law. Homework Equations P+\rho gh +\frac{\rho v^2}{2} = \text{constant}. The Attempt at a Solution I chose the origin of the system as being on the surface of the liquid. I have that P_0 = P_1+ \frac{\rho v_1^2}{2}. But P_1=P_0+\rho...

Im aware that the generalised form of the Marcum Q function, which is Q_{M}(\alpha,\beta)=1/(\alpha)^{M-1}\int_{\beta}x^{M}.exp(-x^{2} +\alpha^{2})/2.I_{M-1}(\alphax)dx and the pdf of the amplitude in rice distribution is f_{r}(r)=r/\sigma^{2}exp( (-r^{2}-A^{2})/2\sigma^{2}...

Hi. I'm trying to derive a = (v^2)/r from the position of a particle moving in a circle. Since the equation for a particle moving in a circle is x(t) = r(isin(wt) + jcos(wt)) where w is constant. I took two derivatives to find it's acceleration. I got a(t) = -rw^2(icos(wt)+jsin(wt)). Now I'm...

Homework Statement Derive the equation used for calculating the deflection of a beam at some arbitrary point. Because I haven't seen anything like this on the web or in textbooks, I am asking for some feedback. Homework Equations v_{k} = \int\frac{\delta M(x)M(x)}{EI} dx The Attempt...

I'm being asked to derive the equation for the magnetic field produced by a variable gap magnet. I've been given a few clues, but thus far have been unable to actually complete the derivation. The final equation should be: B_{ext}=\frac{mg}{lR}\left(\frac{d}{i}\right) I'm told I need to...

Homework Statement Sort of stuck deriving the Klein-Gordon equation from Heisenberg equation of motion \dot{\varphi} = i [H, \varphi ] Homework Equations \dot{\varphi} = \frac{\partial\varphi}{\partial t} H = \int d^3x \mathcal{H} \Pi (x) = \dot{\varphi}(x) \mathcal{H} = \Pi...

Homework Statement Problem is this. I am tasked with deriving a formula or equations that I can then input into an excel format. I am to take an equipment base that has four sides with supports at each of the four corners. I am to find the load that each one will hold base upon the Center of...

I suppose this is also related to thrust vectors. I have a Y pipe with two exit nozzles. These exit nozzles are angled 43.75 degrees from the vertical and are at a radius of .1968m from the vertical. These nozzles have a deflector that can move from 0 degrees (fully open), to 90 degrees...

Homework Statement We know that T(2)=1, and T(n+1)=1+2T(n), i.e. T(3)=1+2*1=3, etc. Derive a formula for T(n) from above information. Prove the formula by mathematical induction. Homework Equations ?? I don't think there are any apart from the stuff from above. The Attempt at a...

Homework Statement Derive an expression for the radius of a satellite's orbit around Earth in terms of the period of revolution, the universal gravitation constant, and Earth's mass. Homework Equations The final equation should be: r = \sqrt[3]{\frac{T^{2}Gm_{E}}{4\prod^{2}}} The...

Homework Statement I want to show that: \arccos \,z= \left( -1 \right) ^{n+1} \arcsin \,z+\pi/2\, +n\pi Homework Equations There is a trigonometric identity that says \arccos \,z= \pi/2\, -\arcsin \,z The Attempt at a Solution So far, I have come up to this...

Hi all, I'm studying on the current transfer at quantum level and I have a point that is not so much clear. While reading the Fermi sphere from the book "Current at the nanoscale", I could not understand the expression: The number of electrons in the conductor, N, is the ratio of the...

I'm having a problem with that integration part. The average value of i^2 in one cycle = (sum of all i^2 in that period)/(that period). To derive (sum of all i^2 in that period) we use integration, but that gives the area, how can the area be a substitution for this?...they are different...

Homework Statement Consider 2 magnetic masses, m1 and m2; these 2 repel each other for a distance s with force f (relative to each other)...which applies from m1 to m2. Predict final velocity of m1 and m2. Assume final distance to be v1 and v2 Assume the 2 masses at rest initially...

Some confusions from some recent lectures; I asked the prof, but I still don't fully understand what is going on. We began with the action (tau is some worldline parameter, dots indicate tau derivatives; they are hard to see): S = \int d\tau \; \left\{ \dot x^{\mu} p_{\mu} - \frac12 e(\tau)...

Hi, first post here. I've been trying (out of personal interest, not homework) to re-derive http://www.springerlink.com/content/mm61h49j78656107/" relatively famous calculation on the ground state of Helium from 1929. And I'm stuck at one point. What Hylleraas did, was to parametricize the...

Derive formula #5 using any of the other formulas 1. Vav= d/t 2. Aav= V2-V2/t 3. d= (V1+V2/2) t 4. d= V1t + 1/2 a t squared 5. V2 squared = V1 squared + 2ad *note all the Vav, Aav, a and d have a vector sign ontop and d and t always have the triangle representing change in

I play an online shooter game with artillery that players can use. As best I can tell, the shell exits the artillery at 400m/s, I don't know if that's correct because units aren't listed in the code but it sounds logical. I know the distance to target as well, I only need to know what angle to...

The Problem: Using V2x=V1x+ax(deltat)t and (delta)x=V1x(delta)t + 1/2ax(delta)t^2 derive the formula V2x^2=V1x^2+2ax(delta)t Homework Equations 1st and 3rd x-component Kinematics Equations The Attempt at a Solution Ok, so I attempted to solve it, but it didn't work. I don't want...

There's a flaw in my logic, and I cannot find it. Ok, all you are allowed to use is Charles' Law (V/T = K) and Boyle's Law (PV = K) and you have to derive an equation relating pressure and temperature. V = kT V = k/P kT = k/P PT = 1 Therefore P1T1 = P2T2 But, this is the...

Homework Statement Derive the Following Equations: c = [(m_w*c_w + m_c*c_al) (T_e - T_i)] / m_s*(T_s - T_e) and L = (m_w*c_w + m_c*c_al) * (T_i - T_e) - m_I*c_w * [(T_e- T_m)/m_I] Homework Equations T_i - initial temp of water and calorimeter T_m - melting temp of ice T_e -...

Homework Statement Derive from Demoivre's theorem that cos2theta=(costheta)^2-(sintheta)^2 sin2theta=2sin theta costheta Homework Equations The Attempt at a Solution I really am clueless on this. I considered using (costheta +isintheta)^n, but don't know where to go with this idea.

Hi, everyone:) In my mechanics book a derivation is given for acceleration in rotating reference frames. However, there is one step I don't understand. First of all, it is derived that v=v'+\omega\times r' or \left( \frac{dr}{dt}\right) _{fixed}=\left( \frac{dr'}{dt}\right) _{rot}+\omega\times...

I need help with the electric field of a line of charge, a ring, semicircle, a line of charge at a point that bisects the line of charge, and a uniform disc. The teacher showed us how to derive those equations but he does it so fast that I didn't have time to copy them down. Even if I did I...

Maybe this counts as computational physics, or statistics I don't know where this topic belongs. Ok so I have this nice high quality Thermodynamic measurement data and I have to start the "data raping" for results. Let's call the series A(t), and B(t) and I have a few more. So for different...

Homework Statement Two of the MHD equations can be written as \vec{E} + \vec{v} \times \vec{B} = \eta \vec{J} \vec{\nabla} \times \vec{B} = \mu_0 \vec{J} where [itex]\eta[/tex] is the resistivity of the plasma. Derive an expression for the magnetic field at a very high resistivity...

In Wheeler and Taylor's 'Exploring Black Holes', on pages 3-12 and 3-13, the bookkeeper measure of radial velocity (i.e. radial velocity as measured from infinity) is derived. Basically the equation for 'Energy in Schwarzschild geometry' is established-...

I'm a PhD student (not in physics) working on a research problem where I need to use the Lagrangian/Hamiltonian approach for a problem. Suppose I have a particle/object that I can track the location/trajectory of; is it possible for me to derive or enumerate Hamilton's equations for that...