All Questions
10,536 questions
0
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5
answers
101
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A theoretical experiment about gravity and propulsion
An observer travels in a spherical ship drifting through space. The observer cannot 'see' anything outside the ship.
At some time, the ship approaches a massive object P and describes an hyperbolic ...
0
votes
0
answers
65
views
Weak Equality & Strong Equality?
I have been trying to understand the meaning of these concepts: Weak $(\approx)$ and Strong $(=)$ Equality in the Dirac-Bergmann Algorithm for Hamiltonian Constrained Systems. I have already read ...
2
votes
1
answer
192
views
How does an electron move around the nucleus according to classical mechanics?
If an electron moves around a nucleus in an elliptical path, is the moment of inertia of the electron with respect to the nucleus a constant w.r.t time?
I think that both the electron and nucleus must ...
4
votes
1
answer
262
views
Why can generalized forces be derived from generalized potentials? Doesn't this confuse their relation to kinetic energy?
In Wolfgang Nolting's 'Analytical Mechanics', the concept of 'generalized potential' is discussed:
For non-conservative systems, but with holonomic constraints, instead of that, the starting point ...
1
vote
1
answer
71
views
Meaning of colon symbol $:$ in optics
When I was reading some early days nonlinear optics paper/textbooks (particularly between 1960-1985), I often see expressions such as:
$\chi^{(2)}:\textbf{E}\textbf{E}$
or
$\nabla\textbf{E}:\partial \...
38
votes
13
answers
13k
views
If water is nearly as incompressible as ground, why don't divers get injured when they plunge into it?
I have read that water (or any other liquid) cannot be compressed like gases and it is nearly as elastic as solid. So why isn’t the impact of diving into water equivalent to that of diving on hard ...
3
votes
1
answer
359
views
Fredric Schuller's lecture notes for Classical Mechanics
In 2014, Dr. Friedric Sculler taught a course in German at FAU on classical mechanics. In one of the classes, he mentions sharing his detailed notes with the class which are in English.
The link for ...
-2
votes
1
answer
113
views
Advanced math courses for theoretical physics students [closed]
Theoretical physics studies concerning statistical mechanics, dynamical systems and analytical classical mechanics all require working knowledge of mathematical concepts and theories (e.g. manifolds, ...
0
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0
answers
39
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Differences in Landau/Lifshitz Volume 1 editions
I can't seem to find any relevant information about the sections that are altered between editions of Landau/Lifshitz, specifically the first volume.
I'm a big sucker for nice books (collector!), and ...
3
votes
5
answers
960
views
What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
0
votes
2
answers
68
views
Statistical mechanics of a deterministic system
I have a classical gas in a box with adiabatic walls so it's isolated from its environment, and at $t=0$ I (magically) record the exact microstate of all the particles. Since this is classical, the ...
0
votes
0
answers
53
views
Diffusion with an external force
Suppose I have particles diffusing and additionally there is an external force $F(x)$ or potential energy $U(x)$. For example, let's say I had food coloring diffusing in an approximately 1D tube of ...
0
votes
1
answer
53
views
Why is linear charge density $dq/dl$ and not $q/l$?
If linear charge density is charge per unit length then shouldn't it be $q/l$. Why is it $dq/dl$ instead? Wouldn't that mean it is only being calculated for a small element and not the whole length?
2
votes
2
answers
95
views
Covariant derivative of a Wilson line
Does the covariant derivative of a Wilson line given by $$W[A; z_0, z] = {\cal P}e^{-i\int^z_{z_0} dz ~A^af_{abc}}$$
vanish, i.e. $$D_zW[A; z_0, z] = 0~?$$
1
vote
0
answers
188
views
Linear Triatomic Molecule
I am self-studying classical mechanics from the 3rd edition of Goldstein's Classical Mechanics. Right now, I'm working on Chapter 6, Problem 5, in which we are asked to consider a linear triatomic ...
0
votes
1
answer
50
views
What is an anti-vortex? [duplicate]
May be it's a stupid question, since the concept of anti-vortex should be as old as vortex itself. But strangely I found no proper definition or mathematical explanation of anti-vortex, neither in any ...
0
votes
0
answers
50
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Validity of Bertrand's theorem for a self-interacting system
We know that in classical mechanics, a particle of mass $m$ orbiting in a given central-force potential $V$ will satisfy the following eom:
$$\frac{d(m\dot{r})}{dt}-mr\dot{\theta}^2+\frac{\partial V}{\...
0
votes
0
answers
33
views
Lagrangian in systems with damping
The top comment of this post (Difficulties while trying to apply the Lagrangian approach to a problem with damping) mentions the importance of multiplying the standard lagrangian with $e^{\omega t}$ ...
3
votes
4
answers
491
views
The Ehrenfest Paradox and the Wall of Death
In another question evaluating the reality of length contraction, the circular motion was involved and some answers argued that centrifugal force would negate any possible length contraction. A famous ...
0
votes
0
answers
41
views
Linear response theory for dry friction at steady state
In this paper, Brownian motion with dry friction has been studied rigorously. The formulae for the propagator and the steady state are given. Since it is not reversible, the steady state should be a ...
0
votes
3
answers
56
views
Why is the friction force for a block on an inclined plane regarded as going through the COM?
I have been looking at some of my old A level books with example answers to questions regarding acceleration of a block on non-smooth inclined plane. But they all show the friction force as if it is ...
1
vote
0
answers
62
views
Adjoint of the covariant derivative of a field?
Let's call $D$ the covariant derivative, $T$ the transposition of a field and $*$ its complex conjugate, so $T*$ is the "adjoint".
Is: $$(D_{\mu}\Phi)^{T*} (D_{\mu}\Phi)=D^{\mu}\Phi^*D_{\mu}\...
0
votes
0
answers
53
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Why does Lagrangian mechanics state Nature is Extremal, And How? [duplicate]
I was recently learning about the calculus of variations and came across the euler lagrangian formula. $$L_y - \frac{d}{dx}L_{y'} = 0$$
Where $L$ is the Lagrangian
While learning how to use it from a ...
0
votes
1
answer
149
views
Why does perturbation theory work so well?
In perturbation theory, we introduce a small perturbation to the system. This perturbation is usually a small parameter that slightly modifies the Hamiltonian or the equations of motion.
We assume ...
0
votes
2
answers
54
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The No Slip/Slip Condition for Rotating/Rotating and Translating Bodies
Consider a sphere of radius $r$ that is rolling on a rough surface, where its translational velocity $v$ is equal to $\omega r$, where $w$ is the angular velocity of its rotation. In this case, I ...
1
vote
0
answers
46
views
Physical interpretation of Lorentz and Fano resonance
I'm currently studying about lorentz oscillation and fano resonance (ref: https://doi.org/10.1088%2F0031-8949%2F74%2F2%2F020).
According to the lorentz model, also known as driven damped oscillated ...
1
vote
3
answers
82
views
How much time does it take for an object to fall from space? [closed]
Let's say there's an object of mass $m$ in space, $h$ meters away from the surface of the Earth. $h$ is large enough that $g$ cannot be assumed to be constant. The acceleration varies according to ...
-2
votes
3
answers
130
views
When computing the Euler–Lagrange equations, why do we assume the coordinates do not depend on time?
I've just started to learn lagrangians through this video and I'm a bit confused. The setup has that $L = T-V$. With $T=\tfrac{1}{2}mv^2$ and $V=mgx$. So, $L= \tfrac{1}{2}m(dx/dt)^2-mgx$. This is all ...
-2
votes
2
answers
89
views
Are there any experiments that examine Hamilton's Principle directly?
Or can it be examined?
I 'd glad if you can share some ideas about "principles" in general.
1
vote
3
answers
73
views
Conceptual doubt related to motion of two blocks on an incline
I was solving the following question:
In the arrangement shown in the figure all surfaces are smooth. Select the correct alternative(s)
(A) for any value of θ acceleration of A and B are equal
(B) ...
0
votes
1
answer
84
views
Odd notation $\stackrel{\leftarrow}{\nabla}$ for a gradient
I've tried working out the Heisenberg EOM for the 4-current operator. Two very beautiful articles (DOI: 10.1103/PhysRevA.84.042107, DOI: 10.1103/PhysRevA.90.012508) present this result, but I have not ...
14
votes
7
answers
2k
views
Does a vehicle turning on a banked road need to turn its wheels?
A vehicle drives in a circle on a track at constant speed at with radius of curvature $\rho$. The vehicle's acceleration is $$a = \upsilon' T + \kappa (\upsilon)^2 N \\ = \kappa (\upsilon)^2 N.$$
The ...
6
votes
3
answers
2k
views
Something fishy with canonical momentum fixed at boundary in classical action
There's something fishy that I don't get clearly with the action principle of classical mechanics, and the endpoints that need to be fixed (boundary conditions). Please, take note that I'm not ...
6
votes
2
answers
115
views
Why does my curry "bounce back" after stirring?
I recently cooked a big pot of curry, consisting largely of coconut milk, a bit of chicken stock and some vegetables. You can probably imagine that it was somewhat thick in consistency. The cooking ...
1
vote
3
answers
84
views
Do we consider a spring to be a constraint in classical mechanics. If yes/no why so?
I was brushing up on my DOF concepts before moving on to Lagrangian mechanics. One of my professors told me that a spring is not considered a constraint but his explanation was not satisfactory in my ...
-1
votes
1
answer
58
views
Logarithmic Spiral motion of a particle [closed]
Is this motion a central force motion when beta=omega.The particle is moving in the logarithmic spiral
-3
votes
1
answer
120
views
Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
0
votes
1
answer
44
views
How does one prove that the position of COM of a particle system is independent of position of origin of coordinate system? [closed]
Say you have 2 mass particles m1 and m2 about some cartesian coordinate system whose origin is at position A , while another at position B .
How would one prove that the position of COM of the ...
2
votes
2
answers
178
views
QFT introduction: From point mechanics to the continuum
In any introductory quantum field theory course, one gets introduced with the modification of the classical Lagrangian and the conjugate momentum to the field theory lagrangian (density) and conjugate ...
2
votes
1
answer
77
views
Preservation of exact equations of motion in time-dependent perturbation theory for the Hamilton-Jacobi equations
From the Hamilton-Jacobi formalism the solution for the unperturbed hamiltonian $H_0$ has a generating function $S(q,\alpha,t)$ such that
$$K_0 = H_0(q, \frac{\partial S}{\partial q},t) + \frac{\...
0
votes
0
answers
19
views
Partial differentiation assumption in development of equation of motion for Lagrangian [duplicate]
In the book "Quantum Field Theory Demystified", David McMahon derives the equation of motion for the Lagrangian:
$$
L=\frac{1}{2}(\{\partial{_u\phi})^2-m^2\phi^2\}
$$
where $ \phi $ is the ...
0
votes
0
answers
37
views
How to transform generalised (polar) coordinates into cartesian coordinates?
I have a set of observations $D=(q(t_i), p(t_i))$ for $i=1,...,n_{data}$, where $q(t_i), p(t_i) \in R^n$. It is known that the $(q(t_i), p(t_i))$ represent angles and angular momenta of a mechanical ...
0
votes
3
answers
192
views
Does A Pivot Exert A Force
On a frictionless horizontal table, a uniform stick is pivoted at its middle, and a ball collides elastically with one end, as shown in Fig. 8.10. During the collision, what are all the quantities ...
0
votes
2
answers
93
views
Why is $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$?
I'm trying to prove that the divergence of the energy-momentum-tensor is zero by expressing it in terms of the field strength tensor: $\partial_\mu T^{\mu\nu}=0$.
In doing this, letting the derivative ...
133
votes
8
answers
12k
views
Does a particle exert force on itself?
We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.
I want to ask, does a particle ...
2
votes
3
answers
109
views
What's the need for 2 separate laws of motion when the first law is an special case of the second one? [duplicate]
The first law of newton tells us that a body shall remain unaccelerated when the net force acting on it is 0, but the second equation gives us the relation F=ma so, ain't the first law just an special ...
1
vote
0
answers
54
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How does spring pitch affect stiffness in compression spring design equations?
I'm designing a compression spring and I'm confused about the relationship between spring pitch and stiffness. The spring constant equation I'm using is $k = (Gd^4) / (8D^3N)$, where $G$ is the shear ...
0
votes
1
answer
70
views
Interesting Aerofoil Logical Fallacy
I am new to physics in general having just finished AP Mechanics and have limited knowledge of how fluid dynamics work. But just using forces and a simplified understanding of drag if have come to the ...
1
vote
1
answer
80
views
How can you have a potential in a theory without any forces?
Consider the typical Lagrangian:
$$L=\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi) - V(\phi).$$
I interpret the above (please correct me) as a theory consisting of a field which can move through ...
0
votes
0
answers
59
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Covariant derivative with torsion
The covariant derivative is defined (on contravariant vectors) as:
$$\nabla_\mu V^\nu = \partial_\mu V^\nu + \Gamma^\nu_{\mu \rho} V^\rho \tag{1}$$
The purpose of the covariant derivative is to ...