Equation of motion Definition and 255 Threads

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?

Homework Statement Given the Lagrangian ##\mathcal{L} = \frac{1}{2}(\partial_{\mu}\Phi)^{2}+\frac{1}{2}\Phi^{2}-\frac{1}{2}\Phi^{3}+\frac{\alpha}{8}\Phi^{4}##, where ##\Phi=\Phi(x)##, find the equation of motion of the system. Assume that the field ##\Phi## is spherically symmetric, i.e...

Homework Statement A body of unit mass, whose position is x(t) is subject to a velocity-dependent force of the form F=a(dx/dt)-b(dx/dt)^2 where a and b are positive constants and the positive x direction is to the right. a) Write down the equation of motion b) If the motion is initially to the...

Homework Statement Find the equation of motion of a chain of atoms in 1D with alternating magnetic dipoles At stationary equilibrium the atoms of mass m are separated by d , all displacements are small compared to d Homework Equations U=μBx=2μ2(μ0/4π)(1/x^3) F(x)=-dU/dx The Attempt at a...

1. Problem Statement Assume there is an rigid object with mass m in 2D space, an impulse J = FΔt is applied at time t1 at the particle Pimp and Pimp is on the exterior boundary of the object. The impulse cause a free plane motion of the object and the object is only affected by the force of the...

Hello Physics Forums! Supposing that we have an action that says: $$L=\frac{1}{2}R-g_{C\bar{D}}\partial_{\mu}z^C\partial^{\mu}\bar{z}^D+\frac{1}{4} + \frac{1}{4}ImM_{IJ}F^I_{\mu\nu}\cdot F^{J\mu\nu} +\frac{1}{4}ReM_{IJ}F^I_{\mu\nu}\cdot \tilde{F}^{J\mu\nu}$$ where...

Hi all, I started a level 3 btech in mech engineering and today was my first physics class. All went well apart from the tricky question at the end of class. I thought it was a good idea to ask the question "how much harder can this be from last year". Turns out for me not being brilliant at...

Hi, I have read this paper “Dynamic equations of motion for a 3-bar tensegrity based mobile robot” (1) and this one “Dynamic Simulation of Six-strut Tensegrity Robot Rolling”. 1) http://digital.csic.es/bitstream/10261/30336/1/Dynamic%20equations.pdf I am trying to implement a tensegrity...

Homework Statement A particle of mass m moves in two dimensions under the following potential energy function: V(##\vec{r}##) = ½ k (x2 + 4y2) Find the resulting motion, given the initial condition at t=0: x = a, y = 0, x' = 0, y' = vo Homework Equations F = ma = -dV/dr The Attempt at a...

I am trying to solve the differential equation that will give me the equation of motion of a point charge under the influence of another point charge's electric field. Say point charge A is free to move, and it currently a distance D away from point charge B. Point charge B is fixed in space...

Homework Statement H=\sum^N_{i=1}(\frac{p_i^2}{2m}+\frac{1}{2}(x_{i+1}-x_i)^2+(1-\cos(2\pi x_i)) Homework Equations Hamilton equation of motion I suppose ##\dot{q}=\frac{\partial H}{\partial p}## ##\dot{p}=-\frac{\partial H}{\partial q}##[/B]The Attempt at a Solution If particles are...

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...

Homework Statement what is equation of motion for pendulum?pendulum is made of pointmass, which mass is m, is fixed to thread ,which length is l? Oscillation aplitude is θ.Other side of thread is fixed in (0;0;0)point. at time t=0 t=0;y=0 ;z=0 ;φ=θ Homework Equations...

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...

Homework Statement Find the equations of motion for both r and \theta of Homework Equations My problem is taking the derivative wrt time of and \dfrac{\partial\mathcal{L}}{\partial\dot{r}}=m \dot{r} \left( 1 + \left( \dfrac{\partial H}{\partial r}\right)^2 \right) The Attempt at a...

Hi! I have the following problem with some old lecture notes I recently had a look on. I have two different fermions (1 and 2) with masses m1 and m2 and the following Lagrangian (where the mass term for fermion 2 is dropped, because we are only interested in the dynamics of fermion 1) of the...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >[/color] So this is the problem Here is the question: A 32lb weight strecthes a spring 2ft.The weight is released from rest at the equilibrium position. beginning at t=0, a force equal to f(t)= sint...

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...

Homework Statement A small ball with mass M attached to a uniform rod of mass m and length l pivoted at point o and attached to two springs with spring constant k1 and k2 at distance d1 and d2 from point o as shown in Fig 2. The system oscillates around the horizontal line. Assume the system...

Hi, I'm completely stuck with problem 3a). I have no idea of how to start. Anyone have any clue?http://speedy.sh/9JkCf/handin1-4.pdf

In a recent thread, I referred to what I thought was a well-known very simple way of describing how objects move in a gravitational field, in terms of the rate of change of their coordinate momentum in isotropic coordinates. It seems that this result is not widely known (and I can't see a...

Homework Statement Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, vx=0, vy=1. My trouble is figuring out my function. Homework Equations d2r / dt2 = -r/r3 The Attempt at a Solution What I have been doing...

Homework Statement If v(x)=ax-2, then what is its force in terms of x. What is its motion as a function of time when x=a? Homework EquationsThe Attempt at a Solution

Homework Statement Homework Equations f_spring = k(x_near - x_far) The Attempt at a Solution a. FBD: The force goes through the nodes, and the sum of the forces must be 0 because the nodes are massless. Therefore, kx_1 = x(t) So x_1(t) = x(t)/k b. FBD: For this system, the parallel...

Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution... Homework Statement The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be...

I was wondering how to derive hamilton's equation (in the form of poisson brackets) from Heisenberg's equation of motion

I have a question about this classical invariance problem I'm working on. I'm almost done, and I understand the theory I think, so my question may seem a bit more math-oriented (it's been a few years since crunching equations). I have found that under a gauge transformation for a single particle...

1. Here is the sketch: http://i.stack.imgur.com/0s1is.jpg The sketch is supposed to be side-view of the path of the object. The following values are known: - r - radius of the circle that describes the path AB of the object - a - angle that characterizes the part of a circle that...

I would expect that the Heisenberg equation of motion for the Dirac field would yield the Dirac equation. Indeed, these lecture notes claim it as a fact in eq 7.7 but without proof. My trouble is that I know the anti-commutation rules for the Dirac field but I don't know how to calculate the...

Homework Statement Hello everybody, i have got the following task to solve. Given the following potential: U_{LJ}(\vec{r}) = D \Big[ \big( \frac{R}{r}\big)^{12} - 2* \big(\frac{R}{r} \big)^{6} \Big] where r means the length of \vec{r} Give an equation of motion explicitly of the...

I was studying the equations of free fall and of launch when I realize that those equations are spetial case of a object in motion through of a gravitational field. So exist some general equation that describe the motion (the trajetory*) of the object through of the field (using initial values...

Hello, I need help understanding how to apply the formula for converting a Lagrangian to an equation of motion in this following specific application. On page 4 of Zee's QTF in a Nutshell, he gives a Lagrangian (equation 1). In the following sentence he gives the corresponding equation...

I have a system with one generalized coordinate, x. In the potential energy part of the lagrangian, I have some constants multiplied by the absolute value of x. That is the only x dependence the lagrangian has, so when I take the partial derivative of the lagrangian with respect to x (to get the...

Guys, My calculus is really rusty and I need help solving this equation using a time derivative (denoted with a dot) in order to get the relativistic equation of motion for the Universe The equation is: adot^2 = Λc^2a^2/3 where adot is the time derivative of the scale factor, lambda...

hi, all. I am trying to derive the equation of motion of a mass spring system without using the energy method but I am wrong somewhere and I can't find it, can you help me find where I am wrong. Equation of motion of a simple mass spring system is indeed mx''+kx=0 but here I am thinking that...

Homework Statement Assume that the center of mass of the Earth moves with approximately constant velocity with respect to the fixed stars, and that \mathbf{\omega}, the angular velocity of the earth, is constant. Rederive the terrestrial equations of motion...

Homework Statement A particle of mass m is in a harmonic oscillator potential with spring constant k. An observable quantity is given in the Schrodinger picture by the operator: Z = a^{\dagger}a a^{\dagger} a a) Determine the equation of motion of the operator in the Heisenberg...

Homework Statement Find the maximal ground reaction force for the limiting case where the speed at initial contact is equal 0 (Vo=0) expressing it as a mulitple of the body weight (mg) ω = √k/m Homework Equations Y1(t) = A sinωt + B cos ωt + g/ω^2 The Attempt at a Solution I...

Homework Statement A 10 kg block is displaced 20 mm and released. If damping coefficient is 100 N.s/m, how many cycles will be executed before amplitude is reduced to 1 mm or below? The stiffness of the spring is k=20000 N/m. Homework Equations The Attempt at a Solution I...

Homework Statement [/b] The attempt at a solution[/b] I have done the first bit but don't know how to show that phi(r,t) is a solution to the equation of motion.

I'm trying to integrate the equations of motion for a object. F + mg = ma where F is the drag force, g gravity, a is acceleration, etc... I'm trying to do it numerically and I'm confused about one thing: Since this is a 2nd order vector differential equation, should it be equivalent...

Homework Statement The nonlinear, inherently unstable inverted pendulum is shown in Figure 1.15. The goal is to maintain the pendulum angle θ(t) = 0 by using a feedback controller with a sensor (encoder or poten- tiometer) for θ(t) and an actuator to produce an input force f (t). The...

Homework Statement A system is composed of two blocks of mass ##m_1## and ##m_2## connected by a massless spring with spring constant k. The blocks slide on a frictionless plane. The unstretched length of the spring is ##l##. Initially ##m_2## is held so that the spring is compressed to...

1. Homework Statement : Find the equation of motion for the system below (see the attached files) https://www.physicsforums.com/attachment.php?attachmentid=58905&stc=1&d=1369155073 Solve the problem with the state vector approach. Choose realistic values on k1,k2,c1,M and F Homework Equations...

Homework Statement How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge e and mass m, with 4-momentum p^a and electromagnetic field tensor F_{ab} of a constant magetic field \vec B perpendicular to the plane of motion...

Background for the question: In standard GR the equation of motion of a (classical) particle is a geodesic. A geodesic is a curve along which the tangent vector is parallel transported. If the tangent vector is denoted by V this condition is \nabla_V V=0 In components this is...

I'm trying to get the position vector of the offset mass relative to the inertial frame of reference. Do I account for the fact that the disk has rolled a little bit with respect to the inertial frame of reference? With that, I have r,vector = d n1 + R n2 + R/2 er = R*theta n1 + R n2 + R/2 er...

A 900N force acts on a 5kg box in horizontal direction initially at rest. When V=6m/s the force stops. Through what distance was the block pushed. I said this: F=ma v=x/t ---> t=x/v (1) a=v/t (2) combine (1) and (2) a=v^2/x So x=v^2/a That is the same as angular...

Hello everybody, this is my first time posting here, so if I make any errors, correct me please. :) Homework Statement We have a body of mass 2 kg and it starts to move with constant velocity 5 m/s along a straight line. After 2 seconds a force that decreases with square of the distance starts...

Homework Statement From a height of 18 meters above ground, an object is thrown vertically upwards at a speed of 30m/s. Find the equation where height h depends on time t. Find the maximum height of the object. Homework Equations h=h0+v0t-(gt^2)/2 The Attempt at a Solution The equation of...