we can express theta as a product of the angular velocity and time thus plugging this in space of theta in the above equations we can express r hat and theta hat as a function of time. But i am having problems in integrating them and again converting them back to the terms of r hat and theta hat...
Let's say we got one particle in x direction only and we got some motion x(t) which we figured it out through Lagrangian.
In Noether's theorem for coordinate transformation symmetry, we start with the following:
x(t)' = x(t) +εf(t) (ε - some number) - I denoted new path with x(t)'
I'm...
The mathematical representation of the net external force on a system(obtained from Newton's second law) is ##\vec F_{net} = \frac {d\vec P}{dt}##, which is the rate of change of linear momentum of the system. If we substitute ##\vec P = m\vec v## into the formula for force and differentiate, we...
Hi :) This is a problem from David Tong's Classical Dynamics course, found here: http://www.damtp.cam.ac.uk/user/tong/dynamics.html. In particular it is problem 6ii in the first problem sheet.
Firstly we can see the lagrangian is ##L = \frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2) -...
I've already found the potential and force that produce the given orbit. my results were:
##V=-\frac{al^2}{mr^3}##
##\vec{F}=-\frac{-3al^2}{mr^4}\hat{r}##
Now, I've been trying to find the period using the equation
##t=\sqrt{\frac{m}{2}}\int_{r_0}^{r}\frac{dr'}{\sqrt{E-V_{eff}}}##
Using...
Hello forum, i want to make a samulation of a body. The body will be moved horisontal on y,x axis. I want on my simulation the body to change direction many times(for example i want to go for 10sec right and then left end right...). My question is does i need more than one differential equation...
There's an undergraduate physics course at my uni that covers these topics and the course description is: Mathematical descriptions for classical physics: oscillations, mechanical waves, electromagnetic waves, physical optics and thermodynamics. Are there any good studying materials/textbooks I...
Let's say we have a system of two point particles that can interact with each other by forces that are position and velocity dependent. The forces might or might not be derivable from a generalized potential.
Assuming Isotropy of space and homogeneity of space and time, what are the constraints...
Greetings.
So... let us consider a particle moving in the yz plane, coming from the infinite towards a region were a gravitational potential is appreciable. The Lagrangian of the system is
\mathcal{L} = \frac{1}{2}\mu (\dot{r}^2+r^2{\dot \phi}^2) + \frac{G\,m\,M}{r}
where \mu is the reduced...
1.Problem statement
Prove the average external force of a system of particles N starting from rest and ending at rest is zero.Homework Equations
If the system moves periodically prove the av. external force is zero in a period
The Attempt at a Solution
I don't quite understand what i am asked...
two saipens one known as Alpha who is on the left and the other on right Beta are present, Alpha first presses down on a bar and Beta has to use all of its strength to lift Alpha's hand a distance h a distance, in this scenario the fulcrum is placed close to Beta, now in the next scenario it is...
Hi, as a side project I am making a solar system simulator in Python, but I am getting extreme inaccuracies.
As the image shows - I am comparing the simulation to data obtained from NASA's Horizon.
I have written a a basic Verlet integrator in the Python class posten below:
import numpy as...
If a smooth sphere with radius a is fixed on a plane, and a particle is projected horizontally at the highest point outside/on of the sphere with speed (4ag/5)^0.5, I know that the particle will lose contact with the sphere when it makes an angle of theta with the upward vertical, where theta is...