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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If a pendulum is on a rotating table, will a torque be generated?

Here is the set up. Very simple. A flat (i.e. horizontal table, there is no gravity) and rounded table that spins on its axis (through the center of the table). A spring mass system is now put on the ...
5
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2answers
266 views

Is it normal for physical functions to lack a 2nd derivative?

My question is about the appearance of a non-analytic function in the formula for the resistive force in air or other medium. Considering the 1-dimensional case as covered by Walter Lewin in his 8.01 ...
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3answers
134 views

How can one know if a theory allow action at a distance effects or not?

1-In general, if a theory has action at a distance effects, where can that appear exactly in the theory? 2-Does it appear in the dynamical law of the theory? (does it appear in Newton's 2nd law? ...
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1answer
75 views

Does reactive force require the two force involved have to have two different medium for reactive force to occur?

Does reactive force require the two force involved have to have two medium for reactive force to occur? I know the fuel-thruster is working on vacuum space, but we human could not use arm to swim in ...
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1answer
50 views

Is it possible to make use of paper/bill permeate by chemical compound to became a paper-made bullet-proof vest?

Is it possible to make use of paper/bill permeate by chemical compound to became a paper-made bullet-proof vest? This is inspired by Greece and Italy tend to have more riot than rest of the Europe ...
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2answers
497 views

Classical Limit of Commutator

In Dirac's book Principles of quantum mechanics (4th ed., pgs 87-88), he seems to give a very elementary argument as to how the commutator $[X,P]$ reduces to the Poisson brackets ${x,p}$ in the limit ...
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3answers
2k views

Classical Limit of Schrodinger Equation

There is a well-known argument that if we write the wavefunction as $\psi = A \exp(iS/\hbar)$, where $A$ and $S$ are real, and substitute this into the Schrodinger equation and take the limit $h \to ...
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2answers
449 views

Energy required to kick a planet orbiting the Sun from an elliptical to a parabolic path

I am trying to solve the following problem from Goldstein's Classical Mechanics: A planet of mass $M$ is in orbit of eccentricity $e=1-\alpha$ where $\alpha<<1$, about the Sun. Assume that the ...
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2answers
274 views

What does $\textbf{f} = -\boldsymbol{\nabla} u$ mean in practice and how is it computed?

In classical computer simulations such as molecular dynamics (MD) simulations, one integrates Newton's equations of motion to determine particle trajectories. If we think of Newton's Second Law as ...
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1answer
417 views

Scattering problem: Expression for angular momentum of particle

I'm reading Goldstein's Classical Mechanics, the part on "Scattering" in the "Central Force" chapter. In relation to the figure below, he says that angular momentum, $l$, is given by $$l=mv_0s$$ ...
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3answers
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What is the difference between a bounded orbit and a closed orbit?

Goldstein's Classical Mechanics has a puzzling few sentences in his discussion of orbits. Referring to the case of orbit where the energy is low enough for the orbit to be bounded, he says :"This ...
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2answers
370 views

Ideal 2D Unicycle Kinematics

A particle is connected to a massive wheel by a rigid rod. The wheel can roll without slipping on a horizontal surface. The particle is free to rotate around the centre of the wheel. I believe the ...
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1answer
416 views

Question about units in Lagrangian dynamics (inertia matrix)

I have a 3 degree of freedom system and my equation of motion is like this: $$M(q)q_{dd} + C(q,q_d)q_d+G(q)~=~0$$ $M(q)$: inertia matrix $C(q,q_d)$: Coriolis-centrifugal matrix $G(q)$: potential ...
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3answers
733 views

Why are bricks typically constructed to have six faces at, or near right-angles to each the other?

Looking around it appears that bricks, through history, have been constructed in cuboid form i.e. with six faces at right-angles to each other. This is also apparently the case with stone construction ...
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2answers
2k views

Why does tension not do work in this pulley system? etc

I have a slight difficulty understanding the solution to the following problem: A light inextensible string with a mass $M$ at one end passes over a pulley at a distance $a$ from a vertically fixed ...
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1answer
1k views

The trajectory of a projectile launched from a hilltop

Here is the problem: A boy stands at the peak of a hill which slopes downward uniformly at angle $\phi$. At what angle $\theta$ from the horizontal should he throw a rock so that it has the greatest ...
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3answers
391 views

Poisson structure comes from hamiltonian?

I am interested in studying quantization, but it seems I am lacking the basics of classical mechanics. Any help would be appreciated. I would first like to ask what is necessary to have a ...
3
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1answer
976 views

Finding the tension in rope tied to ladder using the principle of virtual work

A ladder $AB$ of mass $m$ has its ends on a smooth wall and floor (see figure). The foot of the ladder is tied by an inextensible rope of negligible mass to the base $C$ of the wall so the ladder ...
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1answer
215 views

Working with $\delta$s to use principle of virtual work

I'm trying to do the following problem: A lever $ABC$ (see figure) has weights $W_1$ and $W_2$ at distances $a_1$ and $a_2$ from the fixed support $B$. Using the principle of virtual work, prove that ...
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3answers
11k views

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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2answers
595 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
93 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
545 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
627 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
271 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
9k views

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
973 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
2k views

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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votes
1answer
481 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
316 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
346 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
521 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
305 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
691 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 ...
2
votes
1answer
521 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
910 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
343 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
117 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
306 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
625 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
146 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
132 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
377 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 ...