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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Lagrangian formalism and Contact Bundles

In his Applied Differential Geometry book, William Burke says the following after telling that the action should be the integral of a function $L$: A line integral makes geometric sense only if ...
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What is the physical interpretation of the Poisson bracket [duplicate]

Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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426 views

Is there a fundamental reason not to define the work vice-versa

My question arises from something which has never been really clear: in continuum mechanics, why is strain energy defined as: $$W=\int_\Omega ...
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Trouble with classical mechanics self-learning (How to avoid going down the Physics rabbit hole?) [duplicate]

I'm a retired police officer trying to learn classical mechanics on my own. I have gone through many links on the Internet including the classical mechanics quick reference textbooks from Physics ...
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How does one quantize the phase-space semiclassically?

Often, when people give talks about semiclassical theories they are very shady about how quantization actually works. Usually they start with talking about a partition of $\hbar$-cells then end up ...
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Why does higher acceleration minimize a car's fuel consumption?

I generally try to optimize my car's fuel consumption when driving, using my car's real-time MPG gauge and average-trip MPG indicator. Until recently, I believed the slower the acceleration, the ...
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Non-Integrable systems

Integrable systems are systems which have $2n-1$ time-independent, functionally independent conserved quantities (n being the number of degrees of freedom), or n whose Poisson brackets with each other ...
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Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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Why can we inflate the balloon?

I have an elementary question: I know from experiences that human can inflate (or fill with water) the standard ballon or latex medical glove. But I know also that in rubber/latex there are a pores. ...
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How do you produce electricity from a wind mill?

How does a spinning windmill produce electricity?What is the principle behind the windmill?
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Classical vs. quantum energy of the hydrogen atom

If I have an electron and a proton and calculate the classical energy which I get by bringing the electron from infinity to the distance of a Bohr radius to the proton, I get 27.2 eV, but the electron ...
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How fast does force propagate through matter? [duplicate]

Possible Duplicate: Is it possible for information to be transmitted faster than light? Consider the following thought experiment. You have a long perfectly rigid beam (for the sake of ...
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Is rotational motion relative to space?

Let's assume that there is nothing in the universe except Earth. If the Earth rotates on its axis as it does, then would we experience the effects of rotational motion like centrifugal force and ...
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Conceptually, what is negative work?

I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
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Connection between Poisson Brackets and Symplectic Form

Jose and Saletan say the matrix elements of the Poisson Brackets (PB) in the $ {q,p} $ basis are the same as those of the inverse of the symplectic matrix $ \Omega^{-1} $, whereas the matrix elements ...
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Forget Hooke's law. Why does a spring exert a force?

Forgetting Hooke's law for a minute why, from a microscopic perspective (preferably quantum) on up to a macroscopic one, does a spring under tension exert a force? I was thinking that there might be ...
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364 views

Any good resources for Lagrangian and Hamiltonian Dynamics?

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
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How do we know if a formulation of classical mechanics is correct?

For example, the Lagrangian formulation. I may be missing something, i.e. not having done it in enough detail, but here is my issue: from the definition of the lagrangian ($\mathcal{L}$) and from ...
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Why is the Hodge dual so essential?

It seems unnatural to me that it is so often worthwhile to replace physical objects with their Hodge duals. For instance, if the magnetic field is properly thought of as a 2-form and the electric ...
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Can a deformable object “swim” in curved space-time? [duplicate]

Possible Duplicate: Swimming in Spacetime - apparent conserved quantity violation It is well known that a deformable object can perform a finite rotation in space by performing deformations ...
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Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that ...
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Does Hamilton Mechanics give a general phase-space conserving flux?

Hamiltonian dynamics fulfil the Liouville's theorem, which means that one can imagine the flux of a phase space volume under a Hamiltionian theory like the flux of an ideal fluid, which doesn't change ...
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When is the principle of virtual work valid?

The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints. Goldstein says something I don't understand. He says ...
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How do traveling waves pass through a standing wave node, if the node doesn't move?

I'm having trouble with the explanation that a standing wave in a string is the superposition of traveling waves. The nodes in the diagram above are points where the particles of the string's ...
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Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
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Rotationally invariant body and principal axis

Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$). Is it true that in this case the ...
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Pendulum with water dripping out

Consider a pendulum, consisting of a string of length $l$ tied to a ball of negligible mass and radius $r$. The bob is filled with water, which has density $d$, and the pendulum is given a small push ...
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Naive questions on the concept of effective Lagrangian and equations of motion?

Let us consider a LC circuit containing an electric dipole moment, the quantum system (electric field $E$ coupled with a dipole moment) can be described by the path integral $$Z=\int DEDxe^{i\int ...
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Hamiltonian and the space-time structure

I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian. Space-time structure dictates the form of ...
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How should I throttle my rocket to reach highest altitude? [closed]

"Real world" problem. Suppose we want to launch a rocket equipped with an engine which can be throttled as we prefer. Suppose also that the amount of fuel burnt per time is directly proportional ...
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How do levers amplify forces?

This is really bothering me for a long time, because the math is easy to do, but it's still unintuitive for me. I understand the "law of the lever" and I can do the math and use the torques, or ...
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Phase Space Flow

Phase space flow shares characteristics with fluid flow such as incompressibility by Liouville's theorem. Extending the similarities one might be curious, does phase space flow have a characteristic ...
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Three Pendulum Rotary Harmonograph

I'm trying to create a simulation of a three pendulum rotary harmonograph, the one you can see in action in this video or in these instructions. As you can see in the video, there are 2 pendulum with ...
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Physics of scaling up an animal: the neck

Consider an animal like a horse. Now scale its neck longer and longer. How can a giraffe, or even worse a huge dinosaur, raise its neck without the tendons snapping? The dinosaur case in particular ...
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Will a wave packet undergo dispersion when traveling down a hanging rope?

Suppose I tie one end of a rope to my ceiling and the other end to a spot on my floor directly underneath it. Because the rope has some mass, the tension varies along the rope, from highest at the ...
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Constants of motion vs. integrals of motion

Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
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Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
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Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
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Liouville's theorem and gravitationally deflected lightpaths

It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane. Then, ...
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How did Feynman derive the physics of medallion vs. plate wobble rate?

I am referring to this: Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red ...
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What are the properties of two bodies for their collision to be elastic?

For example, must the shock wave in each body be of a particular form which influences the shape and material properties of the bodies? I suspect part of the the answer is that the objects must be ...
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The virial theorem and a delta function potential

So the virial theorem tells us that: $2\langle T\rangle = \langle \textbf{r}\cdot\nabla V\rangle$. Now I was wondering what would happen if V has te form: $V(\textbf{r}-\textbf{r}') = ...
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Mechanical similarity in Landau

I've read this very short paragraph from Landau & Lifshitz's Mechanics (Chap.2, Par.10) (that you can find here) about Mechanical similarity. I was looking for some more detailed explanations of ...
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Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry

Background: Classical Mechanics is based on the Poincare-Cartan two-form $$\omega_2=dx\wedge dp$$ where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
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How to explain independence of momentum and energy conservation in elementary terms?

I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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Classical Mechanics contradicts Conservation of energy?

Imagine a Stanford torus rotating with 1 rpm so that centripetal/reactive centrifugal acceleration provides about 1.0g of artificial gravitational acceleration inside the ring. The picture below shows ...
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The other side of the lever

If I have a lever, but I can see only up to the hinge and not the other half, can I know whether the other half is 1 m long with a weight of 3 kg on it, or 3 m long with a weight of 1 kg on it?
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What sustains the rotation of earth's core (faster than surface)?

I recently read that the earth's core rotates faster than the surface. Well, firstly, it's easier to digest the concept of planetary bodies, stars, galaxies in rotation and/or orbital motion. But, ...