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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Tree level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree level cross-section for electron-electron scaterring ...
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The natural metric of a phase space and the Lyapunov exponent

For me, it seems that there is no apparent metric on a phase space of a dynamical system. Of course one can naively define an Euclidean metric on it, but it seems that this metric has not much to do ...
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Are there forces which do not involve a change in momentum?

I am familiar with the equation $$\vec{F}=m \vec{a}$$ I am wondering as to whether it is possible for something to exert a force on another object without changing the momentum of said object. My ...
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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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Force as change in momentum vs. change in velocity

Is there ever a situation where the distinction between $F = m \frac{dv}{dt}$ and $F = \frac{dp}{dt}$ is important? I can't think of a situation where one is true and not the other (assuming only ...
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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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Significance of the second focus in elliptical orbits

1.In classical mechanics, using Newton's laws, the ellipticity of orbits is derived. It is also said that the center of mass is at one of the foci. 2.Each body will orbit the center of the mass of ...
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What are good mechanics experiments for 10 year olds? [closed]

I'm trying to explain elementary mechanics - without the benefits of calculus or even algebra - and struggling. I'd like to find reasonable ways to demonstrate Newton's laws, minimally, and possibly ...
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Classical results proved using quantum mechanics

Are there any results in classical mechanics that are easier to show by deriving a corresponding result in quantum mechanics and then taking the limit as $\hbar\rightarrow0$? (Are there classical ...
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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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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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How to sail downwind faster than the wind?

Recently a group set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a page talking about it, but it doesn't explain exactly how ...
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Is kinetic energy a relative quantity? Will it make inconsistent equations when applying it to the conservation of energy equations?

If the velocity is a relative quantity, will it make inconsistent equations when applying it to the conservation of energy equations? For example: In the train moving at $V$ relative to ground, ...
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Can we quantize Aristotelian physics?

Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an ...
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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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Why do rockets have multiple stages?

What is the advantage for rockets to have multiple stages? Wouldn't a single stage with the same amount of fuel weigh less? Note I would like a quantitative answer, if possible :-)
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Why does vibration loosen screws?

I am trying to figure out why vibrations (say, from an engine) loosen screws. It seems to me that there is evident symmetry between loosening and tightening a screw. I am wondering what breaks this ...
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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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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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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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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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Non-linear systems in classical mechanics

In general, what is meant by non-linear system in classical mechanics? Does it always concern the differential equations one ends up with (any examples would be greatly appreciated)? If so, is it ...
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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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What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
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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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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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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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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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What exactly is a virtual displacement in classical mechanics?

I'm reading Goldstein's Classical Mechanics and he says the following: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
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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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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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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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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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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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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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Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
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Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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Which Mechanics book is the best for beginner in math major?

I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through Goldstein's Classical Mechanics. ...
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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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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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Is there a proof from the first principle that the Lagrangian L = T - V?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are ...
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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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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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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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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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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 isn't temperature frame dependent?

In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't ...
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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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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 ...