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5 answers
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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 ...
ajotatxe's user avatar
  • 213
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 ...
L. G. Romero's user avatar
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 ...
Tom's user avatar
  • 71
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 ...
guoxu's user avatar
  • 119
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 \...
physstudent11's user avatar
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 ...
Hitarth Vyas's user avatar
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, ...
Andrea Andrea's user avatar
0 votes
0 answers
39 views

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 ...
Kanokpon Arm's user avatar
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 ...
Kaia's user avatar
  • 109
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 ...
Jbag1212's user avatar
  • 2,740
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?
Niteesh Kumar's user avatar
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. $$D_zW[A; z_0, z] = 0~?$$
Dr. user44690's user avatar
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 ...
Georgy Zhukov's user avatar
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 ...
QuestionTheAnswer's user avatar
0 votes
0 answers
50 views

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}{\...
KP99's user avatar
  • 1,992
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 $e^{\omega t}$ ...
Ee Kin Chan's user avatar
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 ...
KDP's user avatar
  • 10.1k
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 ...
megaproba's user avatar
  • 111
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 ...
Dubious's user avatar
  • 157
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}\...
Mathieu Krisztian's user avatar
0 votes
0 answers
53 views

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 ...
Rutajit45 a dude's user avatar
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 ...
qubitz's user avatar
  • 364
0 votes
2 answers
54 views

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 ...
Physoverlord's user avatar
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 ...
Jhn's user avatar
  • 31
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 ...
jazzblaster's user avatar
-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 ...
zzz's user avatar
  • 123
-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.
Toboraton's user avatar
  • 119
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) ...
Chetan's user avatar
  • 19
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 ...
Sphyr's user avatar
  • 51
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 ...
SRobertJames's user avatar
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 ...
Cham's user avatar
  • 7,687
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 ...
paulina's user avatar
  • 2,446
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 ...
Harshitha Sridhar's user avatar
-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
Sambhav Antriksh's user avatar
-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". ...
moshtaba's user avatar
  • 1,419
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 ...
Dubious's user avatar
  • 157
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 ...
Xhorxho's user avatar
  • 309
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{\...
qubitz's user avatar
  • 364
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 ...
stowyn's user avatar
  • 1
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 ...
Ben94's user avatar
  • 11
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 ...
John Doe 's user avatar
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 ...
user410662's user avatar
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 ...
Shreyansh Pathak's user avatar
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 ...
Manish's user avatar
  • 51
1 vote
0 answers
54 views

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 ...
Saveer Jain's user avatar
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 ...
Frontiers Aerospace's user avatar
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 ...
Peter Petrov's user avatar
0 votes
0 answers
59 views

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 ...
Frederic Thomas's user avatar

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