# What is Clasccal mechanics: Definition and 14 Discussions

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1. ### Unit vectors that change as a function of time

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...
2. ### I Noether’s theorem -- Question about symmetry coordinate transformation

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...
3. ### I Meaning of the terms in the formula of the net external force

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...
4. ### Using Lagrangian to show a particle has a circular orbit

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) -...
5. ### Finding the period of an orbit ##r=a(1+\cos\theta)##

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...
6. ### Classical mechanics -- Equations for simulating the motion of a body

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...
7. ### Classical Textbook for light, heat, waves

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...
8. ### I Galilean Invariance and constraints on Forces.

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...
9. ### Conservation of angular momentum in scattering processes

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...
10. ### Prove the average external force is Zero

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...
11. ### Lever, bar, and mechanics why does this happen?

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...
12. T

### B Why it's easier to push the door from the furthest distance

Why it's easier to push the door from the furthest distance From the pivot point?
13. ### I Solar system simulation errors

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...
14. ### I Launching a particle at the highest point inside a sphere

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...