All Questions
Tagged with equations-of-motion classical-mechanics
9 questions
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. ...
- 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 ...
- 1,066
5
votes
2
answers
630
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 ...
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 ...
user291161
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 ...
- 1,978
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 ...
- 1,235
0
votes
1
answer
2k
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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 ...
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 ...
- 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 ...
- 1,179