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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What is the physical meaning of diffusion coefficient?

In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
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2answers
4k views

Lagrangian of two particles connected with a spring, free to rotate

Two particles of different masses $m_1$ and $m_2$ are connected by a massless spring of spring constant $k$ and equilibrium length $d$. The system rests on a frictionless table and may both oscillate ...
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545 views

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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1answer
90 views

Showing $ \textbf{F} \cdot d\textbf{s} = -dV$ is equivalent to $ F_s = -\frac{\partial V}{\partial s}$

Can someone please explain how the following $$ \textbf{F} \cdot d\textbf{s} = -dV$$ is equivalent to $$ F_s = -\frac{\partial V}{\partial s}$$ using some intermediate steps. I don't follow this ...
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2answers
530 views

Standing wave and energy flux

Here is a problem I have been asked that I do not know the answer. Consider two ideal wave generators (it can be sound generator or whatever) separated by a distance L and facing each other. At t=0 ...
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4answers
599 views

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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2answers
265 views

Is it possible to control a treadmill's tread speed such that a plane on the treadmill will be prevented from moving?

I've posed the question in this particular way to avoid the ambiguity usually found in the posing of the "airplane on a treadmill" puzzle, e.g. I'm not specifying how the treadmill is controlled but ...
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7answers
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What will happen if a plane trys to take off whilst on a treadmill?

So this has puzzled me for many a year... I still am no closer to coming to a conclusion, after many arguments that is. I don't think it can, others 100% think it will. If you have a plane trying to ...
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2answers
2k views

Hamilton-Jacobi Equation

In the Hamilton-Jacobi equation, we take the partial time derivative of the action. But the action comes from integrating the Lagrangian over time, so time seems to just be a dummy variable here and ...
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2answers
936 views

Classical Limit of the Feynman Path Integral

I understand that in the limit that h_bar goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...
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5answers
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Classical limit of quantum mechanics

I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ ...
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1answer
475 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
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3answers
295 views

What are some mechanics examples with a globally non-generic symplecic structure?

In the framework of statistical mechanics, in books and lectures when the fundamentals are stated, i.e. phase space, Hamiltons equation, the density etc., phase space seems usually be assumed to be ...
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4answers
335 views

Is this a valid understanding of Newtonian mechanics?

This is a conceptual understanding of Newtonian mechanics. What the laws mean, how we know they're true, etc. I'm looking for criticism. I know this is really border line on the "don't ask questions ...
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3answers
1k views

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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3answers
3k views

Rotational speed of a coil in a uniform magnetic field at equilibrium

I'm looking at the following problem from "Physics 3" by Halliday, Resnick and Krane (4th edition): The armature of a motor has 97 turns each of area 190 cm² and rotates in a uniform magnetic ...
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1answer
496 views

Angular momentum conservation in a central field through the Hamiltonian

In my teacher's notes there is a discussion of the Hamiltonian for a central force field with potential $V(r)$. The Hamiltonian is formulated in spherical polar coordinates: ...
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2answers
300 views

Calculating the period of a quasi-circular orbit

In solving an exercise I had to find the equation of the quasi-circular orbits of an object with the potential $V(r)=-\alpha r^{-1-\eta}$ and I expressed it as: $$r(\phi)=\frac{r_c}{1+\epsilon ...
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3answers
2k views

Phase space volume and relativity

Much of statistical mechanics is derived from Liouville's theorem, which can be stated as "the phase space volume occupied by an ensemble of isolated systems is conserved over time." (I'm mostly ...
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2answers
650 views

Instability of a thrown tennis racquet

Someone once mentioned to me that it's impossible to throw a tennis racquet (or similarly shaped object) into the air, perpendicularly to the string plane, in such a way that it won't turn. What is ...
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1answer
514 views

Angular momentum components as independent integrals of motion

I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
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2answers
798 views

What is the purpose of iron bars in concrete?

What purpose do iron rods in concrete serve? Do these iron rods impart any strength to the concrete apart from defining the framework for the concrete to solidify upon initially?
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2answers
1k views

Meaning of angular velocity in a rotating system

When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
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2answers
335 views

Why are the solution coefficients for a harmonic oscillator proportional to minors of the determinant?

I'm studying the oscillations of systems with more than one degree of freedom from Landau & Lifshitz's Mechanics Third Edition (for those who have the book, my question corresponds roughly to ...
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2answers
116 views

Precessional motion of active galactic nuclei

I want to set a simulation for jet which has a precessional motion. The symmetry axis of jet is $z$ axis, i.e. jet is propagating along $z$ direction making angle $\theta$. I set the velocity ...
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1answer
297 views

Determining axis of rotation from angular speeds about axes

I think my pure-math head is messing with me on the question below: my physics and CS friends both seemed to think it was a simple computational thing, and my program says the method works, but now ...
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1answer
602 views

What's the optimal shape for a continuous Galilean Cannon?

A Galilean Cannon is a toy similar to the famous basketball-and-tennis-ball demonstration. You take a tennis ball, balance it on top a basketball, and drop them both. The tennis ball will bounce up to ...
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1answer
144 views

Maximum precision of deterministic measurements

Okay, I tend to have some weird thoughts, so bear with my odd question here. Suppose you have a collection of particles that obey Newtonian mechanics. For simplification, all particles are identical ...
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4answers
131 views

Path traced out by a point

While studying uniform circular motion at school, one of my friends asked a question: "How do I prove that the path traced out by a particle such that an applied force of constant magnitude acts on ...
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1answer
365 views

Euler's buckling formula applicable for impact calculations?

$$F = \frac{\pi^2 EI}{(KL)^2}$$ Is Euler's buckling formula applicable for impact calculations, considering speeds relevant for a car or aircraft crash? If there is a level where the formula ...
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1answer
82 views

Does this relation about direction of particles make sense?

Maybe I've just stared at this statement too long and I've missed something obvious. Nevertheless, here's the problem: Landau-Lifshitz vol. 1§16, problem 1. Consider (classical) collision of two ...
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1answer
719 views

Analogy between magnetic bottle and Van Allen's radiation belt

A magnetic bottle is an arrangement that permits to confine charged particles. Here you can find a review for charged particle rotating in a magnetic field and at the bottom of the page a description ...
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0answers
74 views

Nature of orbit due to central force! [duplicate]

Possible Duplicate: Kepler problem in time: how do two gravitationally attracting particles move? How do we get the shape of orbit under the condition that Force is centrally directed ...
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1answer
220 views

Why doesn't relativistic momentum appear conserved in this frame?

Suppose I have an inelastic head on collision between two idential particles of mass $m$ that come to rest in the centre of momentum frame where relativistic momentum is obviously conserved. If I now ...
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1answer
143 views

What's the amount of deviation of cellestial orbits from perfect ellipses

It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated ...
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4answers
593 views

Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system?

I am a Physics undergraduate, so provide references with your responses. Landau & Lifshitz write in page one of their mechanics textbook: If all the co-ordinates and velocities are ...
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0answers
21 views

On Bolte's semiclassical law

i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $ ...
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3answers
1k views

How to determine an exponential acceleration curve?

I've always been not so bad in mathematics, but I'm terribly bad at physics. For me, abstract concept are totally understandable, but when it come to reality, I'm lost ! So, for my job, I need to ...
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3answers
101 views

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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1answer
690 views

Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...
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3answers
558 views

Why Liouville's theorem is obvious?

In Florian Scheck's Mechanics, he stated the local form of Liouville's theorem as follows: Let $\Phi_{t,s}(x)$ be the flow of the differential equation $-J\frac{d}{dt}x=H_{x}$. Then for all $x,t,s$ ...
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1answer
2k views

Rubber Band Forces

I have a question regarding the force a band places on an object. Say I have a rubber band wrapped around 2 pegs at a certain distance, and at that distance I know the pounds of force per inch it is ...
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1answer
266 views

Why $\frac{d}{dt}r_{a}\nabla_{a}U_{ab}+\frac{d}{dt}r_{b}\nabla_{b}U_{ba}=\frac{d}{dt}U_{ab}?$

In classical mechanics for two mass particles $a$,$b$ we assume the symmetric potential arising from $F_{ab}$ and $F_{ab}$ given by $$U_{ab}(r)=-\int^{r}_{r_{0}}F_{ab}(r')dr'$$ and ...
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1answer
152 views

Say we're driving a bike and suddenly hold the brakes?

It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip. On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I ...
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2answers
33k views

Has any permanent magnet motor been proven to run?

I have read lots of articles about permanent magnet motors, some of which claim the possibility and other which refute it. Is it possible to have a permanent magnet motor that runs on the magnetic ...
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2answers
310 views

Numerical torque calculation

Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically ...
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2answers
159 views

Linking two balls together

I have a physics simulator that simulates a bunch of balls moving and colliding with each other, and I would like to be able to "link" two balls together so they stick to each other (are always ...
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3answers
1k views

Why do we need the quantity momentum?

Why do we need the quantity Momentum in physics when we have the quantities like Force and Energy? Isn't it possible to substitute the usage of Momentum with equivalent of Force and Energy?
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1answer
519 views

How does a star wobble due to orbiting bodies

What equations determine how a star wobbles in response to an orbiting planet, and can it be used to determine the mass of distant objects based on the wobble? If there are other more reliable ...
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2answers
2k views

Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...