All Questions
36
questions
1
vote
0
answers
38
views
Weird sign in EOM: Centripetal vs. centrifugal term [duplicate]
Something goes wrong when I was deriving the equation of motion in Kepler's probelm, as below,
Angular momentum conservation $L = Mr^2\dot{\theta}^2$.
And Lagrangian is $L = \frac{1}{2}M(\dot{r}^2 + ...
- 425
0
votes
1
answer
141
views
Correct Lagrangian for classical central force problem?
Wikipedia gives the following Lagrangian for central force problem:
$$\mathcal{L}=\frac12 m \dot{\mathbf{r}}^2-V(r)$$
where $m$ is the mass of a smaller body orbiting around a stationary larger body. ...
- 103
0
votes
0
answers
80
views
Substituting the conservation of angular momentum into the Binet formula results in contradiction [duplicate]
Background Information
The lagrangian of a particle in a central force field $V(r)$ is
$$
L=\frac12m(\dot r^2+r^2\dot\theta^2+r^2\sin^2\theta\dot\varphi^2)-V(r).
$$
The particle must move in a plane, ...
- 675
0
votes
1
answer
149
views
Problem 6.3 from David Morin (classical mechanics) [closed]
I get the lagrangian for the system as
$$
\begin{align}
\mathscr{L} = \frac{m}{2}(\dot{x}^2 + l^2\dot{\theta}^2 + 2l\dot{x}\dot{\theta}\cos \theta) + mgl\cos\theta
\end{align}
$$
Where $\theta$ is the ...
- 23
0
votes
2
answers
176
views
Lagrangian of inverted physical pendulum with oscillating base
An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
1
vote
1
answer
148
views
Lagrangian formalism for non-inertial reference frames
I was solving the exercise where the massless ring with radius $R$ is rotating around axis (shown in the picture) with angular velocity $\omega$. On the ring is a point-object with mass $m$ which ...
3
votes
2
answers
121
views
Why are you allowed to omit the $V^2$ term in the non-inertial frame?
I'm trying to find trying to find the Lagrangian and Hamiltonian for a particle in a non-inertial frame, but when I try to do so, I always get a quadratic term, which textbooks like Landau & ...
- 57
0
votes
1
answer
419
views
Kinetic Energy of pendulum with moving support
I am trying to calculate the kinetic energy of a pendulum with moving support. I have come across two ways that could be used to calculate the kinetic energy, and although I know that the first of ...
- 29
0
votes
2
answers
520
views
Decomposing Lagrangian into CM and relative parts with presence of uniform gravitational field
Most problems concerning two-body motion (using Lagrangian methods) often only consider the motion of two particles subject to no external forces. However, the Lagrangian should be decomposable into ...
- 343
0
votes
1
answer
102
views
Special relativity v.s. "homogeneous time" within an inertial reference frame
I am asking a conceptual question.
As we learned from classical mechanics, say Lagrangian formulation, as stated in Chap 7.9 of Classical Dynamics book by Thornton-Marion (5th Ed) p.260:
in our ...
- 4,336
2
votes
3
answers
2k
views
Lagrange Equations for Non-Inertial Frame of Reference
I am trying to expand my limited knowledge of Lagrange's equations for evaluating motion. Regarding the Lagrangian in a rotating coordinate system, the text Mechanics by Symon states "...we use ...
- 9,381
0
votes
3
answers
193
views
Having trouble taking derivative of a cross product when finding Lagrangian to find force equation for rotating non-inertial frame
I've been working on a problem for my classical mechanics 2 course and I am stuck on a little math problem. Basically, I am trying to prove this equation of motion with a Lagrangian:
$$m\ddot{r} = F + ...
- 17
3
votes
1
answer
1k
views
Why is total kinetic energy always equal to the sum of rotational and translational kinetic energies?
My derivation is as follows.
The total KE, $T_r$ for a rigid object purely rotating about an axis with angular velocity $\bf{ω}$ and with the $i$th particle rotating with velocity $ \textbf{v}_{(rot)...
user86425
4
votes
4
answers
542
views
Is the numerical value of the Lagrangian conserved, when moving between inertial reference frames?
I am doing a course on Lagrangian mechanics and the instructor mentioned that the numerical value of the Lagrangian is conserved when I shift between two inertial reference frames, even though their ...
- 593
1
vote
0
answers
376
views
Rewriting the Lagrangian in terms of the constant(s) of motion doesn't work. Why? (spherical pendulum) [duplicate]
I am trying to solve for the equations of motion to simulate a spherical pendulum. I decided to use the spherical coordinates. The Lagrange equation is,
$$
L=T-V=\frac{1}{2}m\left(l\dot\theta\right)^2+...
- 317