Equation of motion Definition and 255 Threads

Let's say I have the equation: ##\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn## It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ##{\theta}(t)## and y(t) are equations of t. J and Jn are just...

Dear fellow relativiters, I never fully got how to get from the field equations of Einstein's R_{ \mu \nu} - \frac{1}{2} g_{ \mu \nu} R= -\frac{8 \pi G}{c^4} T_{ \mu \nu} to a special metric, let's say the FRW metric ds^2 = c^2 dt^2 - a(t)^2 \cdot (\frac{dx^2}{1-kx^2} + x^2...

Homework Statement Problem figure The rigid body assemblage shown in the figure above, has a force P(t) acting upon it (varying with time). Pick a generalized coordinate such that a single degree of freedom equation of motion can be written. There is a black, massless, rigid bar. Call this...

Homework Statement the forces will be like this m⋅dv/dt=-m⋅g-k⋅v I need to find the velocity equation and the place equation, thereby meaning the integral of the velocity equation. for the condition t,v=0,v_0 The Attempt at a Solution i have found this...

Hello, I've thought about it a few times and this question interests me. If a brane (M2 in my case) in euclidean signature preserves some supersymmetry, does it automatically solve the equation of motion? In order to be more precise here is what I mean: Take 11D SUGRA with an AdS_4xS^7...

Homework Statement Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at speed 2v, while the second was traveling at speed v at an angle phi south of east. After the collision, the two-car system travels at speed v_final at an angle...

Homework Statement I need to derive an equation of motion for the system modeled in this java app: http://web.whittier.edu/physweb/lagan/250/ejs_ehu_oscillations_cylinders.jar I was told to treat the weight force as if it was acting only at the center of mass of the rod, and that normal...

Homework Statement i have uploaded my question. please check out the attached .pdf file. Homework Equations The Attempt at a Solution

Attached is the formula for the equation of motion for a system of coupled oscillators. Could someone please tell me what the variables and indices refer to here? Thanks! :)

Hello, I have worked out some force diagrams for forced oscillations and ended up with the solution as : mx_double_dot+rx_dot+kx=Pcos(Ωt) I am now asked to work out the amplitude. I know all of the variables except frequency(Ω). What equations can I use to find that? Thanks.

What are the Newton's equations of motion of a single particle (using cartesian, cylindrical, and spherical coordinates)? I know the first: F=ma (Along x, y, z) But the in other coordinates?

Hi All, I’m implementing a code to solve the equation of motion using the 4-step Adams-Bashforth method. Here’s my section of code that does this: a=F/m; upnew= up + delta *( (55/24)*a - (59/24)*am1 +(37/24)*am2 - (3/8)*am3 )...

hi let me says you have an arbitrary rigid body and a force F acts on this body at some point A, which is not the center of mass that is called C. how do you get the equation of motion? my idea was to separate out translation and rotation: maybe the whole body moves by F=ma and...

How can I find the equation of motion of a system with the Hamiltonian in matrix form?

I am new to General Relativity and confused by the geodesic equation and MiSaTaQuWa equation. Most of the book saying that the geodesic equation is the motion of a particle in curved-spacetime. However, I read somewhere about this MiSaTaQuWa equation of motion. What is the difference between...

Homework Statement A bead of mass m slides without friction along a wire which has the shape of a parabola y=Ax² with axis vertical in the Earth's gravitational field g. a)Find the Lagrangian, taking as generalized coordinate the horizontal displacement x. b)Write down the Lagrange's equation...

Homework Statement Examine the equation x¨ + β(x^2 − 1)x˙ + x = 0 Explain qualitatively the motion in three cases: |x| < 1, |x| > 1, and |x| = 1. In each case, do you expect the motion to be bounded our unbounded? Define the energy of the system as E ≡ 1/2 (x^2 + v^2). Show that the...

Homework Statement Hi there, I have been trying to use the Kalman filter to predict the location of some missing data with an 4D volume. I have coded it and got it to work but only because of the substational amount of literature which is availlable on the subject. What I am really confused...

Homework Statement A system is connected as follows, going vertically downwards: (ceiling)-(spring with constant k)-(mass 1)- spring with constant k)-(mass 2) Let x be the displacement from the equilibrium position of mass 1, and let y be the displacement from the equilibrium position of...

Homework Statement What is the equation of motion of canoe stroke in canoeing sport Homework Equations F=ma Momentum=mV The Attempt at a Solution My P - DT = MT (dVcrew/dt + dVboat/dt) the Book response, P - DT = (m dVboat/dt ) + MT (dVcrew/dt + dVboat/dt)...

Homework Statement I teach myself classical mechanics from David Tong http://www.damtp.cam.ac.uk/user/tong/dynamics.html From the homework set I should verify that the Lagrangian L=\frac{1}{12}m^{2}\dot{x}^{4}+m\dot{x}^{2}V-V^{2} Yields the same equations as the mere...

I'm going through Landau/Lifgarbagez's book II of theoretical physics. In it they have a derivation of the equation of motion from the principle of least action, however I don't understand one step. Homework Statement Derive the equation of motion: \frac{d^2x^i}{ds^2}+\Gamma^i_{kj}...

In classical mechanics, the acceleration \vec{a}_A of a particle A relative to a reference frame S (non-rotating) fixed to a particle S, is given by the following equation: \vec{a}_A = \frac{\vec{F}_A}{m_A} - \frac{\vec{F}_S}{m_S} where \vec{F}_A is the net force acting on particle A, m_A is...

Hi all, Homework Statement My problem is a pretty basic one, in a exercise a rigid rod of mass M is rotating around a horizontal pivot point i one end. The rod has the length L. I now need to derive the equation of motion using the Lagrangian formalism. My question is: Can i view the...

I'm most of the way through this problem. I've already found the lagrangian equations of motion as a second order differential equation. I'm just stuck at the end... Homework Statement Derive a first order differential equation for the motion of a hoop in a bigger hoop. Homework Equations...

s = ut + (1/2)at2 if s = 0, a = -2u / t so since acceleration is change in velocity over time, so change in velocity = -2u why is the change in velocity given as -2u?

hey guys, I have a question regarding how to get the potential energy for this. I can get the correct answer, but the solutions do a step that makes absolutely no sense to me, so hopefully someone leads me in the right direction :smile: Homework Statement Using energy method, derive the...

Homework Statement A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion m\ddot{z} = -m\gamma\dot{z} + F(t) to find v(t) = \dot{z}(t) for the initial velocity \dot{z}(0) = v_0 Hint: what is the time derivative of...

Homework Statement A particle with a mass of 0.5 kg is attached to a horizontal spring with a force constant of 50 N/m. At the moment t = 0, the particle has a maximum speed of 20 m/s and is moving to the left. (a) Determine the particle's equation of motion. (b) Where in the motion is the...

Homework Statement I have to set up a differential equation of motion for a particle undergoing projectile motion, for which I know the initial position and velocity vectors Homework Equations The kinematics equations. The Attempt at a Solution Well I can easily take a(t) = -gj...

1. The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5 seconds The Attempt at a Solution Im getting confused on whether the above equation is for velocity or distance. I know the derivative of distance is velocity and that the derivative of velocity is...

?How to derive the equation of motion F=ma, given this info Homework Statement http://img861.imageshack.us/img861/1557/2009b5a.gif Homework Equations The Attempt at a Solution Is my attempted solution correct? [PLAIN][PLAIN]http://img42.imageshack.us/img42/2465/2009b5asol.gif

1. Write the equation of motion for the pendulum for different lengths. Use the motion at its greatest extension when t=0 and find the phase shift. I am supposed to find the equation of motion (x=xmax cos(\omegat+\phi) where xmax is the amplitude, \omega is the angular frequency, and \phi is...

Hi What is the difference between Lagrange's equation of motion and the Euler-Lagrange equations? Don't they both yield the path which minimizes the action S? Niles.

Homework Statement The brakes on a car are applied when traveling at 55km/h and it comes to rest uniformly in a distance of 50m. The mass of the car is 800 kg . Calculate the braking force and the time for the car to come to rest. Homework Equations F=ma v=u+at t=s/v=50*3.6/55=3.27s...

Homework Statement A free-falling sky-diver of mass M jumps from an aeroplane and beforen he opens his parachute experiences air resistance which is proportional to the square of the magnitude of his velocity. a) Show that the equation of motion for the sky-diver can be written as dv/dt = -g...

Attached Pdf is a free boday diagram of a vibratory roller without of balance vibratory mechanism. I need to determine the drum displacement (Xd), frame displacement (Xf) and the phase lags (Teta f and Teta d). where do i need to start from and what softwares can i use?

i have a question but no mark scheme so i can't see where I am going wrong. a mass, m, is dropped with speed zero from point O at time t=0 after time t it has traveled x. the body is subject to acceleration due to gravity and drag -mkv. (A) write the equation of motion: ok so i know...

http://www.damtp.cam.ac.uk/user/tong/string/string.pdf In these notes, I am trying to derive the equation of motion (1.21) corresponding to the Nambu-Goto action: \partial_\alpha ( \sqrt{ - \text{det} \gamma} \gamma^{\alpha \beta} \partial_\beta X^\mu ) =0 I have found and proved all...

I have this density operator \rho(t) = \sum_a |\psi_a(t)\rangle P_a \langle\psi_a(t)| and I am supposed to be showing that "the equation of motion satisfies i\hbar\frac{\partial\rho(t)}{\partial t} = [H,\rho(t)]. I'm not making much progress though, this is all the info I'm given. I'm thinking...

I have this question that gives me a density matrix \rho (t) = \Sigma_a |\Psi_a(t)\rangle P_a \langle \Psi_a(t)| and all I am told is that it is just for some "quantum system" and that Pa is the probability of the system being in the state |\Psi_a(t)\rangle I am asked to first show that...

Hey Everyone, I basically need a crash course on kinematics as I am trying to model this in simulink. I am given an intial set of position, velocity, ECI to Body Quaternion and suppose to convert into rotational rate and linear acceleration. Can anyone explain what i need to do? I tried...

1. A rigid straight uniform bar of mass m and length l is attached by a frictionless hinge at one end to a fixed wall so that it can move in a vertical plane. At a distance a from the hinge it is supported by a spring of stiffness constant k, as shown in the figure Ignoring gravitational...

Thanks. This next one is a bit confusing, not so much the first part, its the second, i think i got it wright, i just don't know how to put it on peper to present it to the tutor. b) A car is being driven along a straight and level road at a steady speed of 25 ms-1 when the driver...

Homework Statement 2N classical, real, scalar fields \phi_i (x^{\nu}) \psi_i (x^{\nu}) ,where i=1,...,N I have to find the equations of motions for \phi_i (x^{\nu}) \psi_i (x^{\nu}) Lagrange density is given by L= \sum_{i=1}^N (\frac{1}{2}(\partial_{\mu} \phi_i \partial^{\mu}...

Homework Statement I am trying to get an equation of motion for the following (seemingly simple) setup. You place on a rod on a pivot. The rod's centre of mass is precisely over the pivot. Think of balancing a ruler horizontally on your finger. Gravity, of course acts downward. The...

I studied physics a long time ago and somebody just asked me this question. After trying for a while I couldn't work it out. The situation is this: there's a chain of length $l$ on a table, of which a portion, of length $x_0$, is hanging out (enough so that when you stop holding it down, the...

Homework Statement Anyone know how to write a equation of motion for a mdof system like this: http://img100.imageshack.us/img100/1678/mdofsystem.jpg If u could explain step by step how to do it, would be great. Thnaks

Homework Statement A flexible rope of length 1.0 m slides from a frictionless table top. The rope is initially released from rest with 30 cm hanging over the edge of the table. Find the time at which the left end of the rope reaches the edge of the table. Homework Equations The...

Hi everyone. I'm new here, and I would like some help understanding the equation of motion. It's a simple high school homework question, so I think you guys should be able to help me out here. I'm not sure if I'll be able to properly fit the question into the template, because I know how to...