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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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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1answer
561 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
167 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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2k 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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88 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
410 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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2answers
948 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
190 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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2answers
231 views

Tracking photon color in Bell experiments

In parametric down-conversion, it is said that a driving photon is converted into two entangled photons whose frequencies add up to the driving frequency. Yet in discussions about entanglement ...
5
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2answers
267 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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1answer
253 views

How do I visualize the non-coaxial rotation of this device?

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass ...
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3answers
230 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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266 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
761 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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1answer
305 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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3answers
504 views

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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5answers
403 views

Find drag force on link of rotating chain

Given a closed chain with a total length of 1.2m rotating at 1'800 rpm and a total mass of 0.4kg, what is the drag force pulling on one chain link? I originally thought that since no link size was ...
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2answers
232 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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2answers
220 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
207 views

Differential cross section in momentum space?

Suppose I have a spherically symmetric potential and I can find its cross section in configuration space (i.e position-space), $d\sigma / d\theta$. Now I need to find its distribution $d^2\sigma / ...
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1answer
367 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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3answers
777 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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445 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
879 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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1answer
731 views

The gravitational potential of ellipsoid

In the literature (Kirchhoff G. - Mechanic (1897), Lecture 18 or Lamb, H. - Hydrodynamics (1879)) one can find the following analytical closed form expression for the gravitational potential of ...
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2answers
111 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
236 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
375 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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4answers
122 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
281 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
77 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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0answers
70 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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3answers
356 views

How does solar activity affect the ISS?

Currently the sun is launching some intense solar flares. http://www.guardian.co.uk/science/2011/feb/17/solar-flares-northern-lights-uk Th article I've linked also mentions how a "coronal mass ...
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1answer
158 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
114 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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1answer
949 views

What phrases describe collisions with coefficients of restitution less than zero or greater than one?

The coefficient of restitution describes the elasticity of a collision: 1 = perfectly elastic, kinetic energy is conserved 0 = perfectly inelastic, the objects move at the same speed post impact ...
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0answers
20 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
480 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
94 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 ...
2
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1answer
506 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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6answers
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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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3answers
414 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
261 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
853 views

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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1answer
140 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 ...
2
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2answers
474 views

Calculate relativistic boost to COM frame from two arbitary velocities?

Looking in Goldstein's book, there doesn't seem to be a standard formula to calculate the COM frame velocity for two particles, from their relativistic velocities in the lab frame, although it is done ...
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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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1answer
314 views

What conditions must be met for a ball to roll perfectly down an incline without slipping?

What conditions must be met for a ball to roll perfectly down an incline without slipping? A mathematically rigorous definition, please. I honestly don't know where to begin with answering this ...
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2answers
137 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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4answers
642 views

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 ...