Equations of motion Definition and 210 Threads

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

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...

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...

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...

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...

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...

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

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...

Homework Statement Find equations of motion (eom) of a particle moving in a D-dimensional flat space with the following Lagrangian L = (1/2)mv2i - k/ra, r = root(x2i), m,k,a are constantsHomework Equations The Attempt at a Solution The equations of motion are given by d/dt(∂L/∂vi) - ∂L/∂xi...

Homework Statement "A ball is tossed upwards with speed V_0. Air resistance is -mkv^2 and there's gravity too. Find the the time it takes the ball to reach the maximum height. Do not solve the equation of motion exactly. Use the perturbation method on the equation of motion. Solve the equation...

Hi, I am learning trigonometric graphs and transformations as I am learning my SHM equations and I have a doubt: Firstly, I have a hard time defining angular frequency and that might be one of the sources of my problem. Can anyone help me with that? Is it simply how many full, 2pi rotations it...

Hi :smile: I am a bit lost with the equations for velocity: I don't know Calculus yet, so my teacher just gave me the equation: -wx0cos(wt) (w being omega) He then said: v0 = wx0 and therefore, concluded: -v0cos(wt) and then for when the displacement is maximum at time = 0: v0cos(wt) Is...

Homework Statement Exactly the same problem as https://www.physicsforums.com/showthread.php?p=3335113#post3335113 but instead of a cylinder, the surface is a cone.Homework Equations Same as previous thread. The Attempt at a Solution I used cylindrical coordinates (r, \phi , z). By intuition I...

Homework Statement I must determine the conserved quantities+the equations of motion (of the trajectory in fact) of a particle over the surface of a cylinder.Homework Equations Lagrangian and Euler-Lagrange's equations.The Attempt at a Solution I've found the Lagrangian of the particle to be...

Hi there, Physics lovers! I've got some questions for you! Denoting by (1) ds^{2}=g_{\mu\nu}dx^{\mu}dx^{\nu}=c^{2}d\tau^{2} the interval (and \tau the proper time) and using the signature (+---), we have that the equations of motion for a free particle are: (2)...

Homework Statement From Mandl and Shaw (exercise 4.5): Deduce the equations of motion for the fields: \psi_L(x)\equiv{1 \over 2} (1-\gamma_5)\psi(x) \psi_R(x)\equiv{1 \over 2} (1+\gamma_5)\psi(x) for non-vanishing mass, and show that they decouple in the limit m=0. Hence show that the...

I was just thinking about equation of motion: s=x_0+ut+1/2at^2 where u is initial velocity diff w.r.t.t to find velocity at a given time : ds/dt=u+at My question is, why was it so simple to differentiate w.r.t.t, as "u" is a function of "t" and "a" is a function of...

I am trying to input these 2 equations of motion for a double acting pendulum into mathematica in hopes of solving for θ2, θ2', and θ2''. I am fairly new to the program and I am having trouble inputting the equations. I am swinging a prosthetic leg like a pendulum and I am trying to predict what...

Hi! I have to solve the nonlinear equations of motion in the article (16) (17) (18). I Trasform the system in a system of first order differential equations but i don't have the initial conditions. Is it possible to solve it with the ode45 MATLAB function?

Homework Statement Hi, I need to proof the covariance of the equations of motion under an infinitesimal symmetry transformation. Homework Equations Equations of motion: E_i = \left(\frac{\partial L}{\partial \chi^i}\right) - \partial_{\mu} \left(\frac{\partial L}{\partial \chi^i_{\mu}}\right)...

Homework Statement A thin disc if mass m, centre of mass offset from centre by h (horizontally right in diagram), and radius r rests on a rough horizonal surface. It is originally at rest and then released. No slip occurs between disc and horizontal surface. Write the equations of motions of...

Homework Statement A slope angled 36* to the horizontal has a hoop cylindrical shell going down it, which has radius 3cm and mass 100g. 1) Write down an equation of motion for the angular acceleration. 2) Will the linear acceleration change if the hoop is changed to a cylinder (i.e...