Clasccal mechanics Definition and 14 Threads

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...

Why it's easier to push the door from the furthest distance From the pivot point?

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...