Equations of motion Definition and 234 Threads

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...

In Hamiltonian formulation there is an expression df / dt = { f , H } + ∂f / ∂t where f is function of q, p and t. While expressing Hamiltons equations of motion in terms of Poisson Bracket, i.e if the function f = q of p then its partial time derivative ∂f / ∂t becomes zero.. Please explain why?

The head of a snake can accelerate at 50 m/s2when it strikes. The snake’s head starts from rest and accelerates constantly until it strikes a victim that is 0.5 m away. a) How fast is the snake’s head moving when it hits the victim? b) How long does it take the snake’s head to get to the...

In the special relativity the conservation of energy and momentum is represented by the equation: ##\partial_{\mu}T^{\mu\nu}=0##, where ##T^{\mu\nu}## - stress-energy tensor. In the case of perfect fluid ##T^{\mu\nu}=(\rho+p/c^2)u_{\mu}u_{\nu}-pg^{\mu\nu}## this equations leads to...

I seem to be getting into a bit of a mess with my signs when using Newton's second law in classical mechanics. Here's an example (I am fine with completing the question, it's just when I look at alternative ways of setting up axes and solving it, things change): Homework Statement A ball of...

This isn't really a specific homework question, but since it comes up so often I thought to post it here. Maybe it will help others as well! So, you have the case of two masses, connected by springs. If it's the classic case of two carts attached in series to a wall on one side, with mass m1...

Hey guys, Imma type this up in word so its nice and clear! http://imageshack.com/a/img32/2013/3q8s.jpg

I hope this fits this section. This doesn't all fit into the title, but this comes from a homework on conformal field theory, and I am slightly stumped on it. I just can't seem to get anything sensible out of it at the end, but it may be because I've just done something wrong (even though I've...

1. I'm not quite sure how the laplacian acts on this integral 2. \frac{\delta S}{\delta A_{\mu}}=\int\frac{\delta}{\delta A_{\mu}}(\frac{1}{4}F_{\rho\sigma}\frac{\triangle}{M^{2}}F^{\rho\sigma}) 3. I know I have to split the integral into three integrals for x y and z, but I'm not sure if a) I...

This is perhaps a stupid question, but are the field equations, for example, for QED useful for anything? By field equations (equations of motion) I mean the equations, which are obtained by inserting the Lagrangian into the Euler-Lagrange equation. In the case of QED, one gets a Dirac-like...

Homework Statement A particle is projected vertically upwards at 30 m/s. Calculate (a) how long it takes to reach its maximum height, (b) the two times at which it is 40 m above the point of projection, (c) the two times at which it is moving at 15 m/s.[b]2. Homework Equations [/b final...

Homework Statement OK, we've been asked to derive the equations of motion in spherical coordinates. According to the assignment, we should end up with this: $$ \bf \vec{v} \rm = \frac{d \bf \vec{r} \rm}{dt} = \dot{r} \bf \hat{r} \rm + r \dot{\theta}\hat{\boldsymbol \theta} \rm + r...

I'm studying for our comprehensive exam . I just need to clarify something. So the equation of motion for lagrangian dynamics is \frac{d}{dt}\frac{\partial L}{\partial\dot{q}_{i}} = \frac{\partial L}{\partial {q}_{i}} However, in my notes there are example which uses the principle of virtual...

Hi, I am having a little bit of conceptual trouble with this problem and would appreciate your help. The problem setup is given in the figure. Let's say we have a slender uniform rigid arm(mass m, length l) in space, with a coordinate system B attached to the left end of the arm as shown. C is...

I'm terrible at calculus and am trying an exercise to hopefully help me understand it better. I want to derive the equations of acceleration, velocity and position of a car with known power and mass. As the car's speed increases, the acceleration will decrease. force = mass/acceleration...

Suppose we have a star and a planet with radius vectors r1 and r2 respectively in a fixed inertial coordinate frame. Relative position of planet from sun is r = r2 - r1 Why is the gravitational pull felt by the planet equals to F = Gm1m2 / r^2 * ( -r/r ) ? Therefore, F= Gm1m2/r^3...

In Landau's Mechanics it states "If all co-ordinates and velocities are simultaneously specified, it is know from experience that the state of the system is completely determined and that its subsequent motion can, in principle, be calculated. Mathematically, this means that, if all the...

Homework Statement Two particles move near the surface of the Earth with u. acc 10 m/s^2 towards the ground . At the initial moment , the particles were located at one point in space and moved with velocities 3m/s and 4 m/s in opposite directions . Find the distance between the particles...

Homework Statement A brick is dropped from a hot air balloon which is ascending at 5ms^-1. The height of the balloon above the ground at the time of release of the brick was 30m. a. Determine the time that it took the brick to hit the ground. b. At what height was the balloon above the...

I'm working on a project for myself in regards to atmospheric reentry. I've come across some equations that describe the reentry trajectory. I decided to derive the equations using the diagram shown in the attached picture. Are these correct? The reason why I'm asking is that I'm getting small...

Hello, This is my first post on this forum, so please excuse me if I am not clear enough. I have recently been fascinated about chaos and decided to learn about the equations of motion in a double pendulum. I am in high school and have been so interested about chaos and its equations of motion...

Hi, I am trying to create displacement time series graphs of a double bar pendulum using Matlab. Am I correct in assuming that if I use the ode45 solver to integrate the equations below I can plot displacement time series graphs? Are these the correct coupled first order ODEs to use...

For a Lagrangian L(x^k,\dot{x}^k) which is homogeneous in the \dot{x}^k in the first degree, the usual Hamiltonian vanishes identically. Instead an alternative conjugate momenta is defined as y_j=L\frac{\partial L}{\partial \dot{x}^j} which can then be inverted to give the velocities as a...

Homework Statement I seem to be having trouble setting up my equations and not getting the correct answer to some of these problems. Ex 1: Determine the acceleration of block A when the system is released. The coefficient of friction and the weight of each block are indicated in the...

1. The distance from two airports is 1286 km by air. Plane A leaves the first airport at 10:00a heading north toward the second airport, another plane leaves from the second airport at 11:00a heading south towards the destination plane A originally departed from. Plane A travels at 720km/h, and...

Homework Statement http://sphotos-d.ak.fbcdn.net/hphotos-ak-ash3/526007_3920535257917_1525052730_n.jpg Write down the differential equations of motion. (Step by step if you can)2. The attempt at a solution x"+(f/m)x'+3(k/m)x=0 or x"+σx'+ω^2x=0 where σ=f/m and ω=sqrt(3k/m) Thanks in advance.

Having a bit of trouble with this question, if anyone could help? For the following questions we assume the Hamiltonian to be of the generic form H(r, p) = T(p) + V (r) = p2/2m+ V(r) where T(p) and V (r) denote kinetic and potential energies, respectively. Find Hamilton's equations of motion...

Hi, I'm trying to clear up a confusing point in the book by José and Saletan, concerning equivalent Lagrangians (in the sense that they give you the same dynamics). It is clear that if L_1 - L_2 = \frac{d\phi ( q,t )}{dt}, then L_1 and L_2 will have the same equations of motion. However...

Homework Statement A collar of mass m slides without friction along a circular track of radius R as shown in THE ATTACHMENT. Attached to the collar is a linear spring with spring constant K and unstretched length zero. The spring is attached at the fixed point A located a distance 2R from...

This seems like such a simple question that I fully expect its solution to be embarrassingly easy, but try as I might I can't get the answer. Consider some system which can be described by N generalized coordinates q_1,...,q_N and a Lagrangian L(q_i,\dot{q}_i,t). (I'll just use q_i as a stand...

First year grad student here, I've taken two terms QFT. I'm studying some effective field theories, and one of the techniques I've seen used for writting down the effective lagrangian is identifying some fields or components of fields that are "small" and removing them from the lagrangian by...

Homework Statement See attachment "problem" Homework Equations Euler's laws of motion (moment equations), work and energy equations The Attempt at a Solution See attachment "work" I did the work for (1) and (2). I end up with two equations: the first is the tension T, the second...

Homework Statement I struggle to write equations of motion for spherical magnetic pendulum. The forces acting on the pendulum are: gravity, tension in the rope, and 4 repelling forces Here is the picture for the problem: first attachment (I didn’t add forces to not mess it up) There are...

In both my Maths and Physics exams they give these equations of motion: v = u + at v2 = u2 + 2as s = ut + (1/2)at2 s = (u+v/2)t However the following equation is never included (even though it can simplify some problems significantly) s = vt - (1/2)at2 Why is this deliberately...

Hi, Qualitatively: I am trying to decipher a method I've found in the literature, namely Whitham's method. It is a technique used to averaged out "fast variations" in the Lagrangian to then deduce governing equations for the system. I am trying to quantitatively deduce how accurate Whitham's...

Homework Statement Suppose that the force acting on a particle is factorable into the following forms. (a) F (x,t) = f(x)g(t) (b) F (v, t) = f(v)g(t) (c) F (x, v) = f(x) g(v) For which of these cases are the equations of motion integrable Homework Equations F = md2x / dt2...

Disregard. I done figured it out.Homework Statement Find equations of motion for the metric: ds^2 = dr^2 + r^2 d\phi^2Homework Equations L = g_{ab} \dot{x}^a \dot{x}^b \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{x}^a} \right) = \frac{\partial L}{\partial x^a} The Attempt at a...

Homework Statement So my main issue is with regards to when you integrate Newton's second law twice to get the position of a particle with respect to time. Why does everyone say that the first constant of your integration is initial velocity and second constant is initial position. Is...

I was just playing about at home with some hamiltonians to see how well I could analyse them without having to solve the equations of motion, I can't think of 3 constants of motion in this particular case so I'm guessing that they aren't integerable anyway. My little system had U(r) = x\ y^2 +...

Hey, in general relativity, essentially I am asking how any metric (I.e. schwarzschild metric) was found. are the metrics derived or are they extrapolated from the correct lagrange equations of motion? If there is a derivation available, please provide a link. thanks

1. The problem This is two questions from my assignment - the second of which I'm stuck on. It's about a loudspeaker. Question one looks at a simple loudspeaker. Question two introduces a bass reflex enclosure to the system. Here's question 1...

Homework Statement Hi, I'm trying to work out the following equation that I have made for myself, based on the following information: An object of mass m is traveling from a point r_0. The object has two forces acting on it, both of which are inversely proportional to the square of the...

Homework Statement I am reposting an edited version of this problem from a previous post of mine, due to it not being entirely relevant to that post, and also the question was asked after the thread had been replied to, so looks like an answered question. I also aim to give more detail here...

I know that it works with adding a total time derivative and multiplying the Lagrangian by a constant. are these the only things that can be done to a Lagrangian such that the equations of motion have the same solutions q(t). Thanks!

So, I'm reading Wald, and in it he talks about how the divergence-free nature of the stress-energy tensor implies "a lot" of knowledge about how matter moves in a curved space time. I'm wondering, how much is "a lot"? Can we obtain the full equations of motion from this? Wald gives the example...

Homework Statement A speed skater crosses the start line of a straight 200m downhiull course with speed of 30m per second. She accellerated uniformly all the way down taking 5 sec to cover the course - what is her speed at the finish line? I know this should be simple, but just can't get the...