Equations of motion Definition and 210 Threads

We can write the Born-Infeld Lagrangian as: L_{BI}=1 - \sqrt{ 1+\frac{1}{2}F_{\mu\nu }F^{\mu\nu}-\frac{1}{16}\left(F_{\mu\nu}\widetilde{F}^{\mu\nu} \right)^{2}} with G^{\mu\nu}=\frac{\partial L}{\partial F_{\mu\nu}} how can we show that in empty space the equations of motion take the form...

Some time in the 1980s when I first started studying relativistic gravity, for ease of comparison with Newtonian and Special Relativity gravity I worked through pages of geodesic equations for a general isotropic coordinate system with spherical symmetry, converting everything to terms relating...

Homework Statement The functions are given: ##r(t)=pe^{kt}## ##\theta (t)=kt## ##v(r)=\sqrt2kr## ##a(t)=2k^2r## Find the radius of the curvature of the trajectory in the function of ##r## Homework Equations $$R=\frac{(\dot x^2 + \dot y^2)^{3/2}}{(\dot x\ddot y - \ddot x\dot y)}$$ There is also...

Homework Statement [/B] Homework Equations The Attempt at a Solution [/B]

Homework Statement A pendulum with a mass m hanging on a elastic bug rigid massless rod which may swing in the xy-plane. The pivot point is the origin of the coordinate system. The force acting on the pendulum is the sum of force of an elastic central force directed towards the origin, and...

1. Homework Statement A particle of mass m is attached to the end of a light spring of equilibrium length a, whose other end is fixed, so that the spring is free to rotate in a horizontal plane. The tension in the spring is k times its extension. Initially the system is at rest and the...

Hello, I'm trying to develop a pendulum to test protective equipment so I want to work out the length I'll need to generate a desired velocity and the necessary mass I'll need for a specific moment of inertia. I know there are multiple ways to solve for linear velocity with equating Ek and Ep...

My textbook is describing a 3-body situation where there are two large masses rotating around their barycentre, and a third much smaller mass experiencing gravitational forces from the two larger masses. If the frame of reference is the one in which the barycentre is at rest, then it is not...

Homework Statement (a) Calculate the Conserved currents $$K_{\mu \nu \alpha} $$ associated with the global lorentz transformation and express them in terms of energy momentum tensor. (b) Evaluate the currents for $$L=\frac{1}{2}\phi (\Box +m^2)\phi$$. Check that these currents satisfy...

Homework Statement While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.91 m/s. The stone subsequently falls to the ground, which is 16.5 m below the point where the stone leaves your hand. At what speed does the stone impact the ground? How...

The equation of motion of a pendulum with a support oscillating horizontally sinusoidally with angular frequency ##\omega## is given by (5.116). (See attached.) I get a different answer by considering the Euler-Lagrange equation in ##x## and then eliminating ##\ddot{x}## in (5.115): Referring...

Hi everyone, I am trying to calculate the equation of motion of a charged particle in the field of a monopole. The magnetic field of a monopole of strength g is given by: \textbf{B} = g \frac{\textbf{r}}{r^3} And the Lagrangian by: \mathcal{L} = \frac{m\dot{\textbf{r}}^2}{2} +...

Homework Statement The Lagrangian density for a massive vector field ##C_{\mu}## is given by ##\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\frac{1}{2}m^{2}C_{\mu}C^{\mu}## where ##F_{\mu\nu}=\partial_{\mu}C_{\nu}-\partial_{\nu}C_{\mu}##. Derive the equations of motion and show that when ##m...

So I have the lagrangian density ## L = -\frac{1}{2} W^{\mu \nu}_i W_{\mu \nu}^i## where ##W^{\mu \nu}_i = \partial ^\mu W^\nu_i - \partial ^\nu W^\mu_i + \epsilon_i^{jk}W^\mu_j W^\nu_k## and I want to find the equations of motion. I have gotten to the stage using the EL equations...

Hello to everybody, i have been programming an n-bodies integrator in MATLAB, in an earth-centric ECI perturbations framework. The main objective is to 'write down' in a procedure an interesting part of phisics, and secondly (at the very end of it) to get a complete integrator for meteor orbits...

Homework Statement Find the analogous electrical circuit for the following mass spring damper system. Homework EquationsThe Attempt at a Solution I am rusty with writing equations of motion. I wanted to see if someone could check my work. Looking at the diagram, there are three equations...

Quick question, I'm preparing to work on supergravity. For completeness I was deriving the equations of motion for the Bosonic sector of maximal sugra. The Action principle is ##S=\int \star R -\frac{1}{2}\star F_4\wedge F_4 + \frac{1}{6} F_4\wedge F_4\wedge A_3## with ##F_4 = dA_3##. The...

Homework Statement Homework Equations ## 2as = v^2-u^2 ## ## v = 0 ... \text{at maximum height}## ## \therefore s = \frac{-(u)^2}{2a} \\ a = -g \\ \therefore s = \frac{-(u)^2}{-2g} = \frac{(u)^2}{2g} ## Please explain using only the Three equations of motion and not anything related to...

Homework Statement Sketch the trajectory over the time interval 0 ≤ t ≤ 10 of the particle whose parametric equations of motion are given by X= t−3sint . And y = 4 − 3cost find the value of x,y,t Remember that you should be in Radian mode! Answer Do you isolate the t first and plug it in...

Hi, Can you help me in collecting equations of motion that are unsolvable with elementary methods (especially with high school maths)? One that I found is when I release a body attached to an ideal spring that can freely rotate around an axis. The reason why I need them is because I would like...

Homework Statement there are a lot of mathametical and graphical derivations of the three laws of motion but i have been trying to derive the second equation of motion from the first one but i always end hopeless. please help Homework Equations 1st equation v[f] = v + at 2nd...

I understand that the coordinate system (CS) for a distant observer Od is different than that for an observer Of who is falling radially toward the event horizon of a non-rotating black hole (BH). Using the Schwarzschild metric, I would like to understand the transformation equations that...

Homework Statement Give governing equations for the system about its static equilibrium, assuming small vibrations System consists of two springs located under 45 degrees to the vertical (both have same k-value) in undisturbed situation. Lower ends of the springs are attached to each other...

Homework Statement My teacher keeps saying we can't have negative times because they don't exist and when I do these questions I get negatives and can't understand them at all, can someone help me? 1. How long does it take to slow a car from 10m/s to rest at a rate of -1.75m/s^2? 2.How long...

Homework Statement A particle moves on the surface of an inverted cone. The Lagrangian is given by Show that there is a solution of the equations of motion where and take constant values and respectively Homework Equations The equations of motion and are (1) (2) So can be...

So this is about a modelling project I'm doing. If you have an object that was being towed in water and the towing force is suddenly removed. There is a force F=1/2(density of fluid)(C constant)(A)V^2 that acts on the object. I am trying to find the distance X it will take for the object to...

Homework Statement I am just wondering what effect a torsional spring, with constant K, would have on the equations (1) to (5), under the section "Force analysis and system equations". The torsional spring is located where the pendulum and cart are connected...

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} &...

I have a moving body with constant linear and rotational acceleration. Given a starting condition (position, orientation, linear and angular velocities), how can I combine the equations of motion to give a position and orientation a given time on?

Homework Statement http://postimg.org/image/9fw7awqov/ The question is to write the Laplace transformed equations of motion for the system Homework EquationsThe Attempt at a Solution I am confused about a couple of things: why is an angle is not defined for the rotation of J2. Does it means J2...

Hi everybody! I'm struggling with a physics problem I though I had solved, but as it is turning out recently, I probably hadn't. The problem might actually be pretty easy, just me being unable to solve properly. All of you are familiar with inverted pendulum. Now, imagine an inverted pendulum...

Usually, equations of motion (with constant acceleration) are written in terms of values of position/velocity at time ##t=0##. Take for example: $$x = x_0 + v_0t + \frac{1}{2} a t^2$$ Where ##x_0## and ##v_0## are the values (at ##t=0##) of position and velocity respectively. What if we're...

Recently I created a structural vibrations simulation and would like to hear some feedback or suggestions.

Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...

Hi guys! I have a question on applying constraint on Linkage systems. Assumed that there is a two dimensional one-bar linkage, one end can only rotate and one end is free (Such as the figure above, please neglect the damper-spring system if you want). This link can rotate only 180 degrees, not...

When can we use the three equations of motion? Also, Is it necessary for the body we are considering to be a point object?

Homework Statement If the engine of a car provides an acceleration of 2ms-2 to start it from rest, assuming the mass to be roughly 1000kg, calculate the time after which the car comes to rest if the engine is turned off after 15 seconds and the frictional force is 15N) Homework Equations v=u +...

Hey guys, I'm wondering if I can get some help with a question in my homework. Here's the question: A workman on the scaffolding outside one of the physics classrooms drops a wrench. A pupil decides to time how long it takes for it to pass the classroom window. It was found that it took...

Hey gang, I'm re-working my way through gauge theory, and I've what may be a silly question. Promotion of global to local symmetries in order to 'reveal' gauge fields (i.e. local phase invariance + Dirac equation -> EM gauge field) is, as far as i can tell, always done on the Lagrangian...

[SIZE="4"]Definition/Summary Hamilton's equations of motion is a very general equation of a system evolving deterministically in phase space. [SIZE="4"]Equations \left( {\begin{array}{*{20}{c}} {\dot q}\\ {\dot p} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 0&1\\ { -...

Hi, my professor asked me to proove the equations of motion of a problem. The equations that I need to find are in page 2 of the file https://docs.google.com/file/d/0BxOdCfkh6FqpUlY5TktpbDZTc2M/edit , equations 7 and 8. But, I'm having trouble with the exercise. I uploaded my attemps...

Hello, I have seen some pretty esoteric questions get answered pretty clearly on here so I figured I would give it a shot. I am trying to verify a derivation using Lagrange's EOM for a dynamic system and I have run into a snag with one of the terms. $$ \frac{d}{dt}(\frac{\partial...

This is a very basic question. We know for a particle moving under constant acceleration we can use both the equations x = \frac{v + v_0}{2}t and x = v_0t + \frac{1}{2}at^2 If we want to find t form each of these equations, the first one gives only one value but the second one gives two...

Homework Statement A bus is traveling steadily at 30 m/s along a straight road passes a stationary car which, 5s later, begins to move with a uniform acceleration of 2 m/s^2 in the same direction as the bus. (i) how long does it take the car to acquire the same speed as the bus? (ii)...

Hi, I'm trying to find the first integral of motion for this set of PDE. I'm not really that familiar with this method of solving PDE. I'd really appreciated if someone could help me. The problem seems quite complicated but then again the paper I've got it from says it's a straigthforward...

Homework Statement A particle of mass m moves freely in space in the x direction. (a) Derive equations of motion for the following operator expectations: <x(t)>, <p(t)> , <X^2(t)>,<P^2(t)> Homework Equations The Attempt at a Solution baah I don't even know... I guess we'll...

Homework Statement The first block with mass m_1 slides without friction on a wedge which has an incline of angle \alpha. The wedged shaped block has a mass m_2 . The second block is also allowed to slide on a flat frictionless line. Find Lagrange's equations of motion. Homework...

Homework Statement Please see the attached picture for the problem description. Now, I have a solution using the Lagrange method, (it should coincide with Newton's second law, I believe?) I just have a hard time getting my equations of motion to match. Homework Equations ∑Fext - M dv/dt =...

Homework Statement To try and relate the three ways of calculating motion, let's say you have a particle of some mass, completely at rest, then is acted on by some force, where F equals a constant, C, times time. (C*t). I want to find the equations of motion using Lagrangrian, but also Newton...

Equations of Motion, help... Homework Statement I'm attempting to draw a 'free body diagram' of 2 pulley's connected by a belt (open configuration), and hence derive the 'equations of motion'. The issue I'm having is in regard to, the 'tight' & 'slack' sides & wheather they should be...