All Questions
14 questions from the last 7 days
3
votes
1
answer
439
views
Can the gravitational force of a black hole "lock" a particle in an unstable equilibrium?
In classical mechanics, it is possible to have points of stable, unstable, and neutral equilibrium depending on the gradient of the potential field. Near a black hole, the gravitational potential ...
- 41
4
votes
2
answers
346
views
Is there a classical Lagrangian system with essentially no cyclic coordinates?
Here is what I mean:
In Lagrangian mechanics, we have the equation
$$
\frac{\mathrm{d}}{\mathrm d t} \frac{\partial L}{\partial \dot q_i} = \frac{\partial L}{\partial q_i},\quad i = 1,2, \cdots, n.
$$
...
- 121
3
votes
1
answer
118
views
Covariant derivative acting on Dirac delta function
Pardon my naive computational question. In my calculations, I encounter the following expression:
\begin{equation} \label{eq1}
\frac{\delta}{\delta g^{\gamma \epsilon}(z)} \left( g_{\mu \alpha}(x) \...
- 85
2
votes
1
answer
56
views
Why does the application of a magnetic field lead to non-thermodynamic equilibrium effects
There is a two-dimensional container filled with $N$ gas atoms, each with an electric charge $q$ and mass $m$. A magnetic field is gradually applied to this system in the direction perpendicular to ...
- 79
0
votes
1
answer
59
views
Why are independent variables treated differently in kinetic energy calculations across problems?
In two different problems involving Lagrangian mechanics, I am confused about how independent variables are treated in the kinetic energy calculations. Specifically, in one case, an independent ...
- 101
0
votes
1
answer
54
views
How to show that angular velocity in 3D space is indeed a vector by using Feynman' method?
After reading this chapter of Feynman Lectures oh Physics: https://www.feynmanlectures.caltech.edu/I_20.html, inspired by Feynman's method in showing that torque is a vector, I decided to show that ...
- 421
0
votes
2
answers
36
views
What happens if a ball collides with a wall that provides a perfect rebound and the wall disappears after half the contact time?
I would like to pose a question that currently sparks my curiosity, and I would appreciate your help in answering it.
Imagine a ball colliding with a wall that provides a perfect rebound for the ball. ...
- 11
1
vote
1
answer
29
views
From material derivatives to partial derivatives in the wave equation
Consider the Cauchy momentum equation:
$$\rho \frac{d^2 \mathbf{u}}{d t^2} = \nabla \cdot \boldsymbol{\sigma} + \rho \mathbf{f}$$
where $\rho(\mathbf{x},t)$ is the density, $\mathbf{u}(\mathbf{x},t)$ ...
- 225
0
votes
0
answers
28
views
Why can't infinitesimal canonical transformations be used to represent infinitesimal boosts?
Consider the following differential form:
\begin{equation}
\textbf{d}F=Q\textbf{d}P+p\textbf{d}q+(K-H)\textbf{d}t
\end{equation}
The generating function for the canonical transformation is given ...
- 79
1
vote
1
answer
44
views
Why do we include both local and temporal acceleration in fluid mechanics but only consider temporal acceleration in solid-body mechanics?
I am a beginner in physics, and I was studying fluid mechanics, specifically Newton's second law, when I was surprised to find that the expression for acceleration was composed of both local and ...
- 11
-1
votes
2
answers
36
views
Why must the total time derivative only be a linear function of velocity? [duplicate]
I'm hung up on page 7 of Landau & Lifshitz Course on Mechanics. They claim,
$$L(v'^2) = L(v^2)+\frac{\partial L}{\partial v^2}2\textbf v\cdot \epsilon \tag{p.7}$$
The second term on the right of ...
1
vote
1
answer
16
views
Can the concept of angular velocity be uniquely defined for a deforming rigid body in non-uniform motion?
In rigid body mechanics, angular velocity is well-defined when the body maintains its rigidity. However, consider the case of a body that is deforming due to external forces while simultaneously ...
- 41
0
votes
0
answers
11
views
Semi-Holonomic Constrains Forces Derivation Using D'Alembert's Principle
The other day I was in a lecture of Analytical Mechanics about D'Alembert's Principle, and specifically about semi-holonomic constrains forces.
At the lecture, my professor stated that the constraint ...
- 21
1
vote
0
answers
32
views
How much does classical mechanics depend on the choice of symplectic form?
TlDr; a different choice of symplectic structure on a phase-space $\mathcal{M}$ affects the Hamiltonian mechanics insofar as it could affect what the canonical coordinates are, but is this the only ...
- 230