Tagged Questions
4
votes
1answer
185 views
Constants of motion vs. integrals of motion
Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
0
votes
1answer
101 views
Non-relativistic Kepler orbits
Consider the Newtonian gravitational potential at a distance of Sun:
$$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$
I write the classical Lagrangian in spherical coordinates for a planet with mass ...
3
votes
1answer
477 views
Conservation of linear and angular momentum
Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
0
votes
2answers
155 views
Having Trouble With The Principle Of Conservation Of Momentum For a Multiparticle System
I'am reading John Taylor's Classical Mechanics chapter 1 page 20 where he proves the principle of conservation of momentum which states "If the net external force $F^{ext}$ on an $N$-particle system ...
1
vote
1answer
163 views
How to determine n equidistant vectors from point P in three dimensions
As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces.
For the first part of the assignment, the particle has mass $m$, ...
5
votes
2answers
364 views
What's the importance of Noether's theorem in Physics
The Noether's theorem that I want to mention is the following: Noether's theorem.
I know the importance of Noether's contribution to modern algebra. Can anyone write about Noether's theorem in ...
2
votes
2answers
308 views
How do you find conserved quantities for linear second order ODEs?
I have a differential equation of the form
$ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $
where $f$ and $g$ are known functions of time.
Is there a systematic (or otherwise) way of ...
4
votes
4answers
500 views
What does it mean, when one says that system has N constants of motion?
For example for an isolated system the energy $E$ is conserved. But then any function of energy, (like $E^2,\sin E,\frac{ln|E|}{E^{42}}$ e.t.c.)
is conserved too. Therefore one can make up infinitely ...
1
vote
0answers
557 views
Do symmetries increase the number of conserved quantities? [closed]
Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential ...
