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5 votes
2 answers
628 views

Confusion about Noether's Theorem

In classical mechanics, a transformation $q \rightarrow q + \delta q$ is a symmetry if the resultant change in the Lagrangian is a total derivative, $$ \delta L = \frac{dF}{dt}.$$ If we derive the ...
Bilge K. Aksebzeci's user avatar
4 votes
5 answers
2k views

Can energy conservation equation be seen as equation of motion?

After all, energy conservation equation is a differential equation that can be solved to find the motion, but this is never done. It is alway considered equation of motion only the time derivative of ...
user avatar
0 votes
1 answer
2k views

Lagrangian of a charged particle in a magnetic field (specific problem)

I have to determine the Lagrangian and the angular velocity $\omega = \dot\theta$, in cylindrical coordinates $(r, \theta, z)$, of a electron with mass $m$ and charge $-e$, wich is experiencing a ...
Leonardo Loreti's user avatar
1 vote
1 answer
183 views

Equations of motion describing a great circle

I'd like to argue that equations of motions of the form $$\ddot \varphi = 0 \quad \text{and} \quad \ddot\theta = \sin\theta\cos\theta\dot\varphi^2$$ describe a great circle. I think the standard ...
Sito's user avatar
  • 1,235
2 votes
2 answers
444 views

Rotation as an example of symmetry in classical mechanics

I modified the question because it was confused. On my book there is this mathematical definition of symmetry transformation: "The equations of motion have a symmetry, if the solutions of the ...
SimoBartz's user avatar
  • 1,978
0 votes
1 answer
1k views

Equations of motion of a cylinder on a horizontal plane

How would I go about deriving the equations of motion for the motion of the centre of mass of the cylinder in this system: The cylinder has mass $M$ and radius $R$ and the small mass $m$ is being ...
Jannik Pitt's user avatar
  • 1,052
0 votes
1 answer
533 views

What does it mean to find an equation of motion, given vector functions that describe both the object's position and velocity?

I don't really understand how to approach a problem that asks to find the equation of motion. Intuitively, I would guess that an "equation of motion" is an equation where the particle's position is ...
whatwhatwhat's user avatar
  • 1,179
42 votes
7 answers
11k views

Is there a proof from the first principle that the Lagrangian $L = T - V$?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are used. ...
Chin Yeh's user avatar
  • 771
10 votes
3 answers
2k views

Is there any case in physics where the equations of motion depend on high time derivatives of the position?

For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order ...
Andrey S's user avatar
  • 1,066