Equations of motion Definition and 234 Threads

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...

Homework Statement A particle is moving freely in the x direction. Find the initially allowed (i.e. at t=0) values of \langle x^2 \rangle and \langle p^2 \rangle, and find equations of motion for \Delta x and \Delta p, Homework Equations \frac{d}{dt}\langle A\rangle =...

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've been doing a Q where particles undergo circular/near-circular motion in an electric field. The electric field varies as 1/r. With the first particle, they set it off tangentially to the field lines, so it undergoes circular motion. With the second particle, they set it off at a...

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...

Hi there, I originally posted this in the SR, GR section so sorry for the re-post. Can anyone point me in the direction of any papers that explicitly derive the equations of motion in f(T) gravity. I have seen the wikipedia derivation in f(R) gravity but can't find anything for f(T) where...

Homework Statement An air track glider is placed on a linear air-track which is slightly tilted. It is given a velocity of 1.5 metres per second up the track. If its acceleration is 2 metres per second squared down the track, find the time at which it is 1m below its starting point...

A car with an initial velocity of 60m/s slows down with deceleration of -8m/s^2. How far will it have traveled after 10 seconds?

Homework Statement I was tasked with finding the equations of motion for an the airplane model pictured below. Mass 1 and Mass 3 represent the wings. K1 and K2 are linear springs that represent the stiffness of the wings. M2 is the fuselage and M4 is the landing gear. K3 is the linear...

Homework Statement To derive the equations of motion for a compound pendulum. Pendulum parameters are: mass M, mass moment of inertia= Ixx,Iyy,Izz,Ixy,Iyz,Izx, Euler angles theta, phi & psi and their time-derivatives theta_dot, phi_dot, & psi_dot, and coordinates of center-of-mass (x,y,z)...

Equations of motion! the conditions pleasezz What are the conditions that enable the equations of motion to be used except from the fact that acceleration must be uniform ?

Hi guys, I have a question about finding a lagrangian formulation of a theory. If I have a system for which I know the equations of motion but not the form of the lagrangian, is it possible to find the lagrangian that will give me those equations of motion? Is there a systematic way of doing...

Homework Statement A motorcyclist starts from rest at a point O and travels in a straight line. His velocity after t seconds is vms^-2, for 0 =< t =< T, where v = 7.2t - 0.45t^2. The motorcyclist's accelaration is zero when t = T. Find the value of T. Homework Equations --- The...

Let's say that L=((1/2)m*v^2-V(x))*f(t), or something similar. What are the equations of motion? For time independent it should be: (d/dt) (dL/dx_dot)=dL/dx . Using this I get m\ddot{x}+m f_dot/f x_dot+dV/dx=0. Is this right? I keep thinking about the derivation of the equations and it...

Homework Statement Hi Guys, I am hopeful someone here may be able to help with this but if people think this should be on a different forum please let me know and I'll move it. I am writing a computer game and I am currently working on the computer controlled player. The player is a...

[b]1. Frame made up of 3 rigid bars linked to each other and the ground by rotational springs, k, a viscous damper, c which connects opposite corners of the frame. Subject to base lateral motion (s(t)), and the two vertical bars rotate by an amount theta(t). Assuming small displacements...

1. The Cheetah is the fastest land animal in the world. It can Accelerate from rest to 20m/s in 2 second, and has a top speed of 30 m/s. it can only maintain its top speed for 450 metres before it has to stop and rest. in contrast an antelope runs at a top speed of 22 m/s for much longer...

Homework Statement Example 3.13 : Example 3.1 Homework Equations v=u+at S=ut+1/2at2 v2-u2=2aS The Attempt at a Solution I know the solution is in front of me, that's ok but I have a confusion regarding negative & positive signs. In both the examples something is moving vertically upwards...

Homework Statement Question 1 on the following page: http://www.maths.tcd.ie/~frolovs/Mechanics/PS10.pdf It's the second part I'm stuck on ('Explain why the equations of motion do not...') Homework Equations The Attempt at a Solution I first found equations for x_1 'dot' and...

Spring Mass Damper Solution of a Motorcycle Suspension I am trying to create a model of a motorcycle suspension to figure how road bump forces get transferred to the bike. I have created a free body diagram of the system and also attached a pdf. If you need the original powerpoint in case...

Contradiction in the equations of motion...??! I' ve found a strange contradiction between the fist and second equations of motion. First we start with the second equation: s = ut + 1/2at2 We factor 't' out, whoch gives us: s = t(u + 1/2at) We divide both sides by 't', and on...

Can anyone help? I have to derive eq of motion of a compound pendulum with 3 rotational dof. I know how to do it, for simple pendulum (using Lagrangian's).

Homework Statement Consider a massless supersymmetric particle (or superparticle) propagating in D-dimensional Minkowski space-time. It is described by D bosonic fields X^{\mu}(\tau) and D Majorana fermions \psi^{\mu}(\tau). The action is S_{0}=\int d\tau \left(\frac{1}{2}\dot{X}^\mu...

Homework Statement An electron enters a zone of uniform magnetic field \vec B = 0,4T{\rm{ }}\hat j with velocity {\vec V_0} = {10^5}m/s{\rm{ }}\hat i. Find the differential equations that govern its motion through the field, and solve them to find the equations of motion. What happens to its...

A car traveling at 40km/h has it's speed reduced to 10km/h in 2.0s. Assuming that the same deceleration would be in effect, find how far the car will travel in coming to rest from a speed of 60km/h?

Hi, This is on my electrodynamics homework and I haven't been able to get anywhere with it. Here it is: The Hamiltonian of a particle of mass m, charge q, position r, momentum p, in an external field defined by a vector potential A(r,t) and scalar potential \phi(r,t) is given below...

Homework Statement A hoop of mass m and radius R rolls without slipping down an inclined plane of mass M, which makes an angle \alpha with the horizontal. Find the Lagrange equations and the integrals of the motion if the plane can slide without friction along a horizontal surface. Homework...

Homework Statement I'm confused. Some websites say it is dL/dx = d/dt dL/dv, whereas others say it is the equations of acceleration, velocity and displacement derived from this, which would require integration, yes? Homework Equations The Attempt at a Solution

I saw this problem posted on the internet somewhere and am intrigued how to solve it. The problem is a fox chasing a hen with the following conditions: 1) The fox's starts at position x=0, y=10m (0,10) 2) The hen start's at position (0.0) 3) The fox runs at velocity 4m/s in a direction...

It's been at least 5 or 6 years since I've done any form of calculus so I'm very rusty :( I'm trying to determine the time it takes to achieve constant velocity of a motor I'm trying to spec out/replace. Here's what I've got: We have a motor initially at rest which is driving a platform and...

There was a recent exam question and i was wondering how to find out the answer. Q. A basketball player throws a ball with an initial velocity of 6.5m/s at an angle of 50 degrees to the horizontal. The ball is 2.3m above the ground when released. The ball travels a horizontal distance of 2.9m...

Homework Statement I need something like the equations of motion, but accounting for drag as given by the http://en.wikipedia.org/wiki/Drag_equation" . Particularly for: Homework Equations & v && = v_0+at \qquad & s && = s_0 + v_0t + \tfrac12 at^2 \qquad The...

Hi, I hope someone can help me with this question, I originally posted this question in the homework help forumbut no one seems to be able to help me with it. I think my problem is more math related - I don't really know where to start. I have been a given a matrix containing aircraft...

Hi, I hope someone can help me with this question, although its aeronautical engineering, I think I have more of a maths related problem - I don't really know where to start. I have been a given a matrix containing aircraft equations of motion (see attached picture). Also shown is an equation...

Homework Statement A simple car with 4 wheels for use in a computer game. Front wheels turn only. Derive the equations of motion for the car. Car is controlled by setting its speed s, and steering angle phi. The forward Euler method is used to compute the forward kinematics. At time t...

Homework Statement Hi, I'm trying to compute the equations of motion for a car as shown in the attached image. α = steering angle θ = orientation of the car relative to the world coordinate system Say you're given the linear velocity v and the steering angle α. How do you compute...

Can anyone help me familiarize myself with the Kinematic Equations of Motion? I need to know them for this summer institute. Thanks, Randeezy

Homework Statement This is for a math based physics class. I need the equation ofa pendulum and of a spring. Homework Equations Spring: x=Asin(wt-phi)+B Pendulum: theta=theta0cos(wt+phi) or theta=theta0cos(sqrt(g/l)sin(theta)) The Attempt at a Solution I don't know which of...

Hi, I am trying to use DSolve in Mathematica 6.0.1.0, in order to find equations of motion (x[t], y[t]) from second-order differential equations. I have looked through much documentation, and attempted numerous codes to figure this out, but get many errors or the same answer every time. This...