Equations of motion Definition and 210 Threads

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...

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...

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 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...

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...

I'm working on a simple simulation for an inverted pendulum mounted on a cart. I derived the equations of motion using Lagrangian dynamics, but I want to go back and add viscous damping terms to the linear motion of the cart, as well as the angular motion of the pendulum. I also want to add a...

Homework Statement Ball A is released from rest at height h1 at the same time that a second ball B is thrown upward from a distance h2 above the ground. If the balls pass one another at a height h3 determine the speed at which ball B was thrown upward. Given: h1 = 40 ft h2 = 5 ft h3 = 20 ft g...

Homework Statement The "reaction time" of the average automobile driver is about 0.700 . (The reaction time is the interval between the perception of a signal to stop and the application of the brakes.) If an automobile can slow down with an acceleration of 12.0 , compute the total distance...

Homework Statement A particle of mass m is attracted to a force center with the force center with the force of magnitude k/r2 . Use plane polar coordinates and find Hamilton’s equations of motion. Homework Equations (L)agrangian = T-U , U=-\intF dr The Attempt at a Solution I...

Here is my problem: I am new to physics all together, NEVER a physics course at all. I am in a Calculus Based physics class, placed there due to the A's I made last semester in calculus (and for other scheduling conflicts) The problems involving the equations of motion are giving me trouble...

Hello, I have a little project I'm playing with that involves calculating a series of forces and summing them to define the motion of an object (in this case, a walking pedestrian). The force equation is modeled on time-dependent vectors and scalars and is solved using Gear's...

ok so I've got the three components of the inertia tensor (A,A,C) and I've derived expression for, using matrices, the angular velocities w1,w2,w3 (these expressions can be found online if you don't already know them). anywho, what i need to do next is use the fact that torque = rate of change...

These are the EOMs for a 4D space-time that has a plane singularity at x=0. They are simpler than most, but as I've confessed before, I need help with even the simplest DE's. This is not a home-work question. x\frac{d^2\tau}{dt^2} - \frac{d\tau}{dt}\frac{dx}{dt} = 0 x^3\frac{d^2x}{dt^2} +...

[SOLVED] Application of the equations of motion with constant acceleration Homework Statement A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 4.0 m/s. Two seconds later the bicyclist hops on his bike and accelerates at 2.2 m/s^2 until he...

I am looking over an old problem about a cart that has a pendulum on it, and you are supposed to find the equations of motion. The pendulum is made from a mass and a wire. Because wire can only support tensile loads, the tension has to be directed along the direction of the wire. Any force not...

Hi, I am just wondering how you would approach this problem: Using the definitions below, derive an equation for velocity as a function of acceleration and time (v=f(a,t)). Assume initial velocity is Vo. The answer to this problem is v=v0+a(t2-t1). My question is how would you arrive to...

Problem Consider the spin precession problem in the Heisenberg picture. Using the Hamiltonian H=-\omega S_{z} where \omega=\frac{eB}{mc} write the Heisenberg equations of motion for the time dependent operators S_{x}(t), S_{y}(t), and S_{z}(t). Solve them to obtain \vec{S} as a function...

Hello, I am currently trying to simulate an object that can rotate around an axis bouncing on a piece of yarn. I have as equations of motion for the object: I d²Theta/dt² = Gravity_Torque + Yarn_Torque With the gravity torque alone this system is perfectly conserving energy: the...

Homework Statement Solve the following to the proper number of significant figures: a) A loaded truck has mass (2.12 X 10^4 +/- 6 X 10^2) kg and when empty, it has a mass of (1.72 X 10^4 +/- 5 X 10^2) kg. What is the relative uncertainty of the mass of the gravel dumped from the truck...

Quick "Equations of Motion" questions (2). Rxn time; deceleration 1. A meteorite strikes on October 9, 1992, a 27-pound meteorite struck a car in Peekskill, NY, leaving a dent 22 cm deep in the trunk. If the meteorite struck the car with a speed of 130 m/s, what was the magnitude of its...

Hello ! I'm reading Landau/Lifchitz's mechanics book. At equation (2.8), the author explains that when I add a time derivative of any function of time and coordinates f(q,t) to the lagrangian, the equations of motion are unchanged. I understand the mathematical development leading to S'...

Here's a quick one: If the generalized force F is not zero, does the equation dH/dq = -pdot become dH/dq = F- pdot ?

Homework Statement Hi All, The question That I am stuck on is: A packing crate has a nass 100kg is allowed to slide down on a ramp until it hit the ground. The friction resistance to motion is 240N. The length of the ramp is 10 m and thehieght of the crate from the ground just before...

Only reason I'm posting here is that i'll get more views than in the cosmology thread, I'm afraid.. (Basically, I'm working through a couple of different models and after some work I'm a bit stuck: http://trond.hjorteland.com/thesis/node21.html I'm basically trying to integrate equation 3.33...

i'm learning how to integrate equations of motion but can't get very far solving anything because i can't figure out how to integrate fxns of the type dx/Sqrt[E-U(x)] . The only solutions my lecturer gives me to these questions are using mathematica but i need to do them in tests so i need to...

The problem is to determine the equation of motion for a point particle on which both the gravitational force and a friction force of magnitude |\vec{F}_fr| = k|\vec{v}| act and to show that when the particle starts at rest, its velocity cannot exceed mg/k. I have attached my calculations but...

Can someone please explain what you are supposed to do when you are only give two or three of the things (eg displacement or time) when you need four, how are you supposed to work it out then? :bugeye: it seems to be very confusing! :confused: I am really confused and need help! Thanks :smile:

If for the "geodesic" equation of motion we have the compact form: \nabla _ u u =0 usign the "Covariant derivative"... as a generalization of Newton equation with F=0 (no force or potential) \frac{du}{ds}=0 where "u" is the 4-dimensional momentum... My question is if we can put the...