Homework Statement
A particle of mass m is constrained to move on the inner surface of a cone os semiangle alpha under the action of gravity. metion generalized co-ordinates and setup lagrangian and equation of motion.
Homework Equations
The Attempt at a Solution
Might there be a similarity between Dyson's equation and Heisenberg equation? (It's just a feeling, nothing based on arguments.) Both describe how a system (density matrix or Green's function) behaves in time. Both require knowledge of the intial system at time t=0 and the potential acting on...
Problem Outline: I'm trying to determine how to keep the distance between 2 cars on a (3D) roller coaster ride. Currently the front car moves away from the back car.
My current implementation uses a second order differential equation to model the acceleration of the cars at time t. The...
Lagrange equation of motion
(from Marion 7-7)
A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find...
I do not understand how people construct a suitable action which after variation will give the correct equation of motion. For example, the Einstein Hilbert action: S=integration[R d^4x] gives the equation of motion when varied with respect to [g_mu nu]. But no book I had read so far tells me...
Homework Statement
The equation of motion of a mass m relative to a rotating coordinate system is
m\frac{d^{2}r}{dt^2} = \vec{F} - m\vec{\omega} \times (\vec{\omega} \times \vec{r}) - 2m(\vec{\omega} \times \frac{d\vec{r}}{dt}) - m(\frac{d\vec{\omega}}{dt} \times \vec{r})
Consider the case F =...
Homework Statement
A particle is dropped from rest, at the surface, into a tank containing oil
The acceleration of the particle in the oil is a = g – kv
where g is the gravitational acceleration and –kv being denoted by
the resistance put on the particle by the oil.
Solve for x as a...
I have recently been working on a project regarding black holes and the spaghettification aspect of it interests me quite a bit. So, I have set out to try to derive some mathematical descriptions of the geometry of the object being spaghettify.
I have spent a few hours (uncessfully) trying to...
For a particle of mass m moving in a potential V(r) = -b/r^2 where the constant b>0 obtain the equation r = r(\phi} of the trajectory for the particular states of motion with total energy E = 0 and angular momenta such that \frac{L^2}{2m} < b
SKetch the trajectory and discuss the motion for...
Please , I need to set up the equation for two springs.
The first one is attached to a ceiling and has a constant k. The second one is attached at the tail of the first one and has a spring constant k'.
If a mass m is attached to the second spring, How can I set up the equation for the system?
a car starts from rest and acclerates down a straight track of length L= 1600m with a constant accleration. If the time it takes for the car to travel the final d= 100 m of the track (from 1500m to 1600m) is T=0.125s, then the acceleration of the car is... the answer is 80.7 m/s^2
this isn't...
a uniform thin rod of length L and mass m is pivoted at one end the point is attached to the top of a car accelerating at a rate A.
a) what is the equilibrium angle between the rod and the top of the car?
b) suppose that the rod is displaced a small angle phi from the equilibrium derive the...
A drag racer experiences air resistance equal to -cv². Assuming the racer is designed for maximum acceleration, I am to find v[t] and v[x]. If I can just get the equation of motion I'll be set.
I think it is F = ma - μmg - cv² = m dv/dt. According to the answer, the book thinks it is F = -...
A smooth wire is bent into the form of a helix the equations of which, in cylindrical coordinates, are z=a*beta and r=b , in which a and b are constants. The origin is a center of attractive force, , which varies directly as the distance, r. By means of Lagrange’s equations find the motion...
Assume a masssless pulley and a frictionless surfce constraining two equal masses. Let x be the extension of the spring from mits relaxed length. I have to derive the equations of motion by Lagrangian methods, and solve for x as a function of time with the boundary conditions x=0, x'=0, and t=0...