Eom Definition and 38 Threads

For (d), I am confused how ##a(t)## oscillates harmonically. The EOM is ##ml^2\ddot \phi + mRl\varphi \dot \phi\sin(\phi - \varphi t) = 0## Then using ##\phi - \varphi t = a(t)## ##l\ddot \phi + R\phi \varphi a(t) = 0## Where I used the small angle approximation after substituting in ##a(t)##...

I am trying to buy an EOM for a PDH lock with a large laser input power and I was told I should go for a free space EOM. I see that they come as resonant and non-resonant, but I can't seem to understand the advantage of a non-resonant one. The resonant one seems to do pretty much everything the...

Hi All, My goal is to relearn some control theory and implement a working inverted pendulum on a cart with an industrial linear motor. See video: Working through an example of an inverted pendulum on a cart posted here...

I'm having trouble following a proof of what happens when the Dirac Lagrangian is put into the Euler-Lagrange equation. This is the youtube video: and you can skip to 2:56 and pause to see all the math laid out. I understand the bird's eye results of the Dirac Lagrangian having an equation of...

I thought I'd start by writing the problem in a tensor formalism. I have identified with ##S## the Earth and ##S'## the rocket. Since the acceleration provided is in the rocket's frame of reference, I can write the following four-vector. $$ a'^\mu=(0, a, 0, 0) $$ Since we are interested in the...

It is the first time that I am faced with a complex field, I would not want to be wrong about how to solve this type of problem. Usually to solve the equations of motion I apply the Euler Lagrange equations. $$\partial_\mu\frac{\partial L}{\partial \phi/_\mu}-\frac{\partial L}{\partial \phi}=0$$...

The question :- My attempt :- The confusion that I am having is that to get the required form of the equation of motion, I had to approximate ##\theta## to be small to get ##x=l\theta## so that I could get the acceleration and the velocity. But, I had to leave the ##sin(\theta)## in the...

I have been going through my old books again, and found myself a little stuck. I am not entirely sure if this would be better in this one or diffy eq. The problem starts with having you find equation of motions when a= -bv, where b is constant and v = v(t) Using method of separable equations...

I set a small project for myself to design a controller for a rocket, which moves a mass around to shift the center of mass, in order to steer a rocket. The picture shows a simplified model of a rocket plus a movable mass. , shown is a rod for the rocket, and a mass for the controller. there...

##\int d^4 x \sqrt {g} ... ## if I am given an action like this , were the ##\sqrt{\pm g} ## , sign depending on the signature , is to keep the integral factor invariant, when finding an eom via variation of calculus, often one needs to integrate by parts. When you integrate by parts, with...

1. Homework Statement Question attached 2. The attempt at a solution Time-like killing vector is associated with energy. ## \frac{d}{ds} (\frac{\mu^2\dot{t}}{R^2})=0## Let me denote this conserved quantity by the constant ##E=\frac{\mu^\dot{t}}{R^2}## where ##\mu=\mu(z)## . similarly we...

Homework Statement Using the E-L equations to get the EoM from the action. Homework Equations I am using E-L equations in the form: ## \frac{\partial}{\partial_u} \frac{\partial L}{\partial_u \phi}-\frac{\partial L}{\partial \phi} ## where ##L ## is the Lagrangian The Attempt at a...

Homework Statement Attached: Homework Equations Euler-Lagrange equations to find the EoM The Attempt at a Solution [/B] Solution attached: I follow, up to where the sum over ##\mu## reduces to sum over ##\mu=i## only, why are there no ##\mu=0## terms? I don't understand at all. Many...

Homework Statement Find the equations of motion for the Lagrangian below: $$ L=\partial_\mu \phi^* \partial^\mu \phi - V( \phi,\phi^* ) $$ Where : $$ V( \phi,\phi^* )= m^2 \phi^* \phi + \lambda (\phi^* \phi)^2 $$Homework Equations Euler Lagrange equation: $$ \partial_\mu \dfrac {\partial L}...

Homework Statement Show that the classical path satisfying ##\bar{x}(t_a) = x_a##, ##\bar{x}(t_b) = x_b## and ##T = t_b-t_a## is $$\bar{x}(t) = x_b\frac{\sin\omega (t-t_a)}{\sin\omega T} + x_a\frac{\sin\omega (t_b-t)}{\sin\omega T}$$ Homework Equations The Lagrangian: ##L =...

Homework Statement Question attached. I am stuck on part d, but give my workings to all parts of the question below. Homework EquationsThe Attempt at a Solution [/B] a) EoM given by E-L equations: Gives ##-\partial_u\partial^u \phi + m^2 \phi - \frac{\lambda \phi^3}{3!} =0 ## b) ## L=T-...

Homework Statement Action attached: To find the EoM of ##\phi ## / ##\phi^* ## Homework Equations The Attempt at a Solution [/B] Without deriving from first principles, using E-L equations I have: ## \partial_{u}\frac{\partial L}{\partial_u \phi} - \frac{\partial L}{\partial \phi} =0 ##...

Hi there guys, Currently writing and comparing two separate Mathematica scripts which can be found here and also here. The first one I've slightly modified to suit my needs and the second one is meant to reproduce the same results. Both scripts are attempting to simulate the trajectory of a...

I know that in general plugging the EOM into the Lagrangian is tricky, but it should be perfectly valid if done correctly. Can someone help me see what I'm doing wrong here? I know I'm doing something dumb but I've been staring at it for too long Start with the E&M Lagrangian: L =...

Homework Statement An equation of motion for a pendulum: (-g/L)sinΦ = Φ(double dot) Homework Equations L = length g = gravity ω = angular velocity Φο = initial Φ The Attempt at a Solution The solution is Φ=Asinωt+Bcosωt solving for A and B by setting Φ and Φ(dot) equal to zero respectively...

## 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 ##...

Hello, I'm studying the setup of distributed Brillouin sensor (using fibre optics) and don't quite understand the purpose of EOM in the sensor. It says that "to generate both the pump and the probe waves from a single physical light source by using an electro-optical modulator (EOM)", but since...

I had seen a documentary about an algorithm that uses notions of evolution to deduce the equation of motion of a system by sampling a variable connected with the system. For example, they used the double pendulum case where they sampled the position of the free end of the pendulum and arrived...

I have a problem (this is not homework) Based on covariant Lagrangian ## \mathcal {L} = \frac {m}{2} \frac{dx^{\mu}}{ds} \frac {dx _ {\mu}}{ds} ## record the equations of motion in Hamiltonian form for a particle in the Schwarzschild metric (SM). Based on Legandre transformations...

I'm having difficulties understanding how I should calculate the angular velocities of a rigid body when the inertia tensor is given in body coordinates and has off diagonal elements. Let's assume I have an inertia tensor ## I = \begin{bmatrix} I_{xx} & -I_{xy} & -I_{xz} \\ -I_{yx} &...

Homework Statement Derive the equation of motion for the system in figure 6.4 using Lagrange's equations [/B] Homework Equations m1=.5m m2=m strings are massless and in constant tension Lagrange=T-V The Attempt at a Solution I currently have the kinetic energy as .5m1y'12 + .5m2y'22 I am...

Homework Statement Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ. The system is a pendulum consisting of a massless rod of length L with a mass m...

I'm going through Zwiebach Chapter 6 on relativistic strings to try to solve a similar problem. I got all the way to my equation of motion \begin{eqnarray*} \delta S & = & [ p' \delta \theta]_{z 0}^{z 1} + \int_{z 0}^{z 1} d z \left( p - \frac{\partial ( p')}{\partial z} \right) \delta...

I would like to ask something. How is the solution of EOM for the action (for FRW metric): S= \int d^{4}x \sqrt{-g} [ (\partial _{\mu} \phi)^{2} - V(\phi) ] give solution of: \ddot{\phi} + 3H \dot{\phi} + V'(\phi) =0 I don't in fact understand how the 2nd term appears... it...

I am currently working on a robotic manipulation problem and need to form a model for how an object responds. I start by writing up the equations of motion for the body, the motion is then constrained by an additional constraint equation. However, I am new to the notions of twists and wrenches...

Hi, I am given an interaction lagrangian piece as \mathcal{L}_1 = \frac{1}{2} g \phi \partial^\mu \phi \partial_\mu \phi Now normally when I have an interaction lagrangian piece I turn the field's into variations with respect to the source \delta_J, and take variations of the free partition...

Dear all, Could anyone please explain to me for a 3 level syste, coupled with 2 lasers, what is the equation describing the disspative term of the equation of motion of the density matrix? I am looking for a non-radiative decay, namely the overall population should conserved. I have found...

for a given spring/damper system the equation of motion is: [PLAIN]http://img600.imageshack.us/img600/2140/equation1.png where x is the displacement of a mass from a fixed point d is a damping constant L1 and L2 constant lengths k1 and k2 are 2 spring constants...

Homework Statement The specific Lagrangian for a cantilever beam is given by: \overline{L}=\frac{1}{2}m[\dot{u}^2(s,t)+\dot{v}^2(s,t)]-\frac{1}{2}EI[\psi ^{\prime}(s,t)]^2 where m,EI are mass and bending stifness, respectively. \dot{u},\dot{v} are velocities in u,v directions...

Hi all! I am working with a problem that for the life of me am having the hardest time with deriving the equation of motion. I have attached the sketch to give a better representation. The moment of inertia, J, is at the center of the spring. No friction between car and table and cables do...

Homework Statement Equations of motion are to be derived to describe the motion of a car(rear wheel drive) at rest which then accelerates to perform a wheelie. Basically, I need equations of motion that would help me determine the force that the rear wheels exert on the car in order to...

When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of \phi, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM...

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...