3
votes
1answer
124 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
1
vote
1answer
83 views

Confusion with curl of Lorentz magnetic force

Since the magnetic force is a no work force, $dW=\vec F\cdot d\vec r=0$ for $\vec F(\vec r)=q(\vec v(\vec r) \times \vec B(\vec r))$, therefore $\oint \vec F \cdot d\vec r=0$ by Stoke's theorem. ...
1
vote
0answers
88 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
1
vote
2answers
251 views

Emmy Noether's theorem in simpler terms

I'd like to understand Noether's theorem and its contents as to what it implies in a bit simpler terms. I am familiar with mathematics unto Calculus 1,2,3 and some linear algebra and group theory. I ...
1
vote
1answer
170 views

Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
0
votes
0answers
84 views

Rocket hovers- and then what?

If we have a rocket, using conservation of momentum we derived in my classical mechanics course $$m\dot{v}=-\dot{m}v_{ex}+F^{EXT}$$ $m$ is the total mass of the rocket and fuel still on the rocket ...
4
votes
1answer
122 views

Is it possible to project a problem of mechanics in a lower dimensionality?

I had the intuition that, in classical mechanics, when the trajectory of a body is known, then analysis of its motion can be done in the linear space of that trajectory, if all forces are projected on ...
1
vote
2answers
383 views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
1
vote
3answers
481 views

Is it possible to deduce the conservation of angular momentum from the conservation of energy?

Is it possible to deduce the law of conservation of angular momentum from the law of conservation of energy? If possible, by what sense the conservation of angular momentum has the status of law, if ...
3
votes
1answer
163 views

Two components of angular momentum conserved $\Rightarrow $ All three components are conserved?

I was wondering whether it is correct to say that if two components of the angular momentum are conserved, then all three Cartesian coordinates of the angular momentum are conserved? I would regard ...
10
votes
1answer
135 views

Is there a trajectory which is not a solution of the equation of motion but satisfies all conservation laws?

I'm wondering whether conservation laws are sufficient to imply equations of motions. Specifically: 1) In classical mechanics of point particles, are conservation of energy, conservation of momentum ...
15
votes
6answers
675 views

Is there a momentum for charge?

Since mass and charge behave similarly, so, just like center of mass, I define a point center of charge, that is defined by $$\vec r_{qm} = \frac {\sum{q_i \vec r_i}} {\sum{q_i}}$$ where $\vec r_i$ ...
6
votes
1answer
1k 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 ...
6
votes
1answer
379 views

Can a deformable object “swim” in curved space-time? [duplicate]

Possible Duplicate: Swimming in Spacetime - apparent conserved quantity violation It is well known that a deformable object can perform a finite rotation in space by performing deformations ...
0
votes
1answer
125 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 ...
5
votes
3answers
798 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
203 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
278 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
642 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
420 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 ...
5
votes
4answers
635 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
629 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 ...