Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
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A problem inspired by the ice hockey game

Question shortly: How far would a hockey puck slide in two different cases: The puck is sliding (translation) on ice and spinning on its flat surface. The puck is sliding on ice without spinning. ...
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487 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
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Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?

Problem If you had a long bar floating in space, what would be the compressive force at the centre of the bar, due to the self-weight of both ends? Diagram - what is the force at point X in the ...
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441 views

Car accident, put in park or neutral?

I was waiting on a red light the other day and was wondering. If I'm in my car, not moving and I see a car that's going to hit me from behind. Would I (my body) be safer if I put on the break or if ...
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Basic mechanics problems, unsolvable by brute-force numerical integration

I'm looking for simple problems in theoretical mechanics that are impossible or unreasonably difficult to solve by means of "brute-force" numerical integration of Newton or Euler-lagrange equations. ...
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Are there examples in classical mechanics where D'Alembert's principle fails?

D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero. This is obviously true for the ...
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761 views

How to model/simulate pressures and flows in a network of pipes

I'm having a hard time finding information on how to model/simulate this. I attached a couple files, both of which show an example tank & pump network. It's just nonsense that I made up for this ...
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Why do we use operators in quantum mechanics?

In classical mechanics, physical quantities, such as, e.g. the coordinates of position, velocity, momentum, energy, etc, are real numbers, but in quantum mechanics they become operators. Why is this ...
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196 views

Theorems on instability of classical systems of charged particles?

Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
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When is the Hamiltonian of a system not equal to its total energy?

I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
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361 views

Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt} $

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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803 views

In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
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648 views

If the Earth didn't rotate, how would a Foucault pendulum work?

How does the Foucault pendulum work exactly, and would it work at all, if the Earth didn't rotate?
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Meaning of the Poisson bracket as a coordinate transformation

Well, the Possion bracket: $ \{ A(q,p),B(q,p) \} \equiv \sum_{s} \left( \dfrac{\partial A}{\partial q_{s}} \dfrac{\partial B}{\partial p_{s}} - \dfrac{\partial A}{\partial p_{s}} \dfrac{\partial ...
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What is the difference between translation and rotation?

What is the difference between translation and rotation ? If this were a mathematics site, the question would be at best naive. But this is physics site, and the question must be interpreted as a ...
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395 views

D-brane Lagrangian?

As I understand it from the threads I read, D-branes are viewed as somewhat secondary to strings: If I know what all the open strings do, then I know what the D-branes do as well. But if the D-brane ...
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Is there a trajectory which is not a solution of the equation of motion but satisfies all conservation laws?

I'm wondering whether conservation laws are sufficient to imply equations of motions. Specifically: 1) In classical mechanics of point particles, are conservation of energy, conservation of momentum ...
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Why does my door shut faster when the window is open?

I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if ...
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594 views

Why does a cuboid spin stably around two axes but not the third?

Let $C$ be a cuboid (rectangular parallelepiped) with edges of lengths $a < b < c$. Consider an axis that passes through the centers of two opposite faces of $C$. There are three such axes, ...
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190 views

Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
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What's the physical intuition for symplectic structures?

I always thought about symplectic forms as elements of areas in little subspaces because of the Darboux theorem, however I cannot get the physical intuition for it and for the hamiltonian vector ...
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638 views

Which direction will Coriolis forces deflect a bubble?

If I throw a ball straight up, it deflects slightly to the west due to Coriolis forces. If instead I watch a bubble float up in water, is the bubble deflected west, east, or neither? I think the ...
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Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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Book about classical mechanics

I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
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Why F=ma and not F=ma'?

What would happen if instead of $F=m*d^2x/dt^2$, we had $F=m*d^3x/dt^3$ or higher? Intuitively, I have always seen a justification for ~1/r^2 forces as the "forces beeing divided equally over the ...
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How can things be chaotic on a quantum level, yet tangible on a classical level?

This may seem basic, but I am wondering if anyone has any input on this topic. It doesn't make any sense to me (I mean I don't need to use the Schrödinger equation to find my cell phone...). I just do ...
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Question about canonical transformation

I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from $(q, p)$ to $(Q, P)$ is one that if which the original coordinates obey ...
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173 views

The most stable way of standing in a bus

Here's what's bugging me for quite a long time. Imagine the every day situation, that you are standing in a bus with your back on wall having only limited space on the floor and no handle to hold. You ...
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424 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
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380 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
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Fractal nature of turbulence

Someone described to me the difficulty of numerically simulating turbulence as that as you look at smaller length scales you see more structure like you do in a fractal. Searching on google for ...
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Driving on snowy roads

'tis the season as they say! It seems to me obvious that it's better to drive in high gear on snowy roads to reduce the torque. However, there are completely opposite advices being given on ...
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Are the Hamiltonian and Lagrangian always convex functions?

The Hamiltonian and Lagrangian are related by a Legendre transform: $$ H(\mathbf{q}, \mathbf{p}, t) = \sum_i \dot q_i p_i - \mathcal{L}(\mathbf{q}, \mathbf{\dot q}, t). $$ For this to be a Legendre ...
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Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
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How do we explain accelerated motion in Newtonian physics and in modern physics?

Maybe my question will seem stupid, but I am not a physicist so I have some problems understanding a classic Newtonian experiment: in the bucket experiment, why does he have to introduce the absolute ...
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Shape of rotating rope (lasso problem?)

Let's take a wire or a rope. I usually do this with a chain or my scarf. I fixate one end in my hand and apply rotation (by subtle movements of this endpoint like spinning a lasso). The rope gets ...
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What happens when a ball stops bouncing?

If I were to drop a bouncy ball onto a surface, each successive bounce will be lower in height as energy is dissipated. Eventually, however, the ball will cease to bounce and will remain in contact ...
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What makes a Lagrangian a Lagrangian?

I just wanted to know what the characteristic property of a Lagrangian is? How do you see without referring to Newtonian Mechanics that it has to be $L=T-V$? People constructed a Lagrangian in ...
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Classical mechanics: Generating function of lagrangian submanifold

I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation. One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
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Which is easier, pushing or pulling?

It is generally assumed, from a person's perspective, that pushing a cart is more easier than pulling one. But why? Is there any difference in terms of force required to achieve the same amount of ...
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Are water waves (i.e. on the surface of the ocean) longitudinal or transverse?

I'm convinced that water waves for example: are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
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Simple Harmonic Motion - What are the units for $\omega_0$ ?

I'm trying to understand the units in: $mx''+kx=0$ And the general solution is $x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t)$ Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring constant $k$ ...
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Examples where momentum is not equal to $mv$?

I am aware that momentum is the thing which is conserved due to symmetries in space (rotational symmetry, translaitonal symmetry, etc). I am aware that in some systems, the generalized momentum, ...
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Formalism to deal with discontinuous potentials in classical mechanics (hard wall, hard spheres)

It seems to me that Hamiltonian formalism does not suit well for problems involving instantaneous change of momentum, like particle collisions with hard wall or hard sphere gas model. At least I could ...
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Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they ...
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Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...
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Shaking a jar of balls

A jar is filled with two types of balls, red and green. Red balls have radius $r_1$ and mass $m_1$, green balls have radius $r_2$ and mass $m_2$. If initially the balls are randomly placed throughout ...
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Force through quantum mechanics

In classical physics force is: $$F=\frac {dp}{dt}$$ How about quantum mechanics? In Old Quantum Mechanics momentum is: $p=\hbar \cdot k$ so force will be: $$F=\hbar \frac {dk}{dt}$$ what does $\frac ...