Equations of motion Definition and 234 Threads

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...

I'm practicing some differential forms stuff and got a bit stuck on something. I'd type it out but the action is very long so it's easier if I just link to where I'm getting it from, this paper http://gesalerico.ft.uam.es/tesis/pablo_camara.pdf Equation (4.20) (pdf page 51) is the IIA action...

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...

Dear All, Currently I'm working out a formula for Destroyers in the online game BattleGround Europe to be able to blast inland towns with their deck guns. To do this I've had to use the equations of motion. I could use some help on dechipering the final part of the clue. Points to note are...

dE*dE/(dt*dt) -dE*dE(k*L*L/m)/(dx*dx)=0 m-mass L-distance beetween mass point

Equations of Motion Help! I have been working on this for awile and still can't figure it out. What equation would I use to solve this problem? Here is the problem: On a ride called the Detonator at Worlds of Fun in Kansas City, passengers accelerate straight downward from zero to 45 mi/h...

Two physics students conduct the following experiment from a very high bridge. Thao drops a 1.5kg shot put from a vertical height of 60m while at exactly the same time Benjamin throws a 100g mass with an initial downwards velocity of 10 m/s from a point 10m above Thao. At what time will the...

Departing from the Navier-Stokes equations for an incompressible flow (with \rho and \mu=\rho \nu constant): \frac{Du_i}{Dt}=\frac{\partial u_i}{\partial t}+u_j \frac{\partial u_i}{\partial x_j} = -\frac{1}{\rho} \frac{\partial p}{\partial x_i} +\nu \frac{\partial^2 u_i}{\partial x_j^2}...

If I got v=u+at i get, \int v = \int (u+at) dt which is s=ut+\frac {1}{2} at^2 + C how do i explain away the integration constant in this derivation?

The question: A 2-kg point mass is welded on the interior of a 2-kg thin ring at point P. The ring has a radius R = 160 mm and rolls on the surface without slipping. (a) Draw a free body diagram for the ring and point mass. Develop the equations of motion for the system. (b)...

I'm studying Lagrangian Dynamics using a Schaum's Outline. This book seems to assume that the student can easily set up the Differential Equations of motion, but I can't seem to get the hang of it. The book does not give any actual methods or examples for setting up these Differential...

DEAR MEMBERS, I AM LEARNING THE EQUATIONS FOR MOTION, AND WE ARE TAUGHT 'SUVAT' BUT I DON'T QUITE UNDERSTAND WHY I NEED ALL 4 OF THEM AND WHAT EACH IS USED FOR ? FOR EXAMPLE : V^2 = U^2 + 2AS WHERE DOES THE SQUARE COME FROM ? PLEASE HELP ME. FROM ROGER :cry:

Ok, so I am dealing with a critically damped oscillator in which the natural frequency(w) of the oscillator is equal to the coefficient of friction (y). I am given the force mfe^t and told to find a solution for x, where x'' +2yx' +w^2 =fe^t. How do I go about doing this? The solution...