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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Is an “infinitely sharp blade” possible?

A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to ...
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What exactly is the relationship between the symplectic 2-form and the frequency of leaves of integrable systems in classical mechanics?

In classical mechanics we equip a differential manifold with a closed symplectic 2-form $\omega$. The symplectic leaves of integrable systems also have a unique frequency, in literature denoted ...
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Kinetic energy dissipation in braking a vehicle

Let's say a vehicle that weighs 20t is hauling along at 50m/s and we want to brake it down to a full stop. The kinetic energy we need to dissipate into heating up the brakes is ...
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164 views

Derivation of law of inertia from Lagrangian method (Landau)

I'm reading Landau's Book. He tries to conclude the law of inertia from the Lagrange equations. For that, he argues (by nice suppositions about space and time), that the lagrangian must depend only ...
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199 views

How does the masless pulley gets the force from rope?

I have seen whenever we solve for forces on pulley by rope we take the force on pulley exactly as the tensions in the rope around it. But , why do we do this ? Exactly how does the rope exerts forces ...
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When considering the acceleration as constant? [closed]

I'm solving a simple dynamic exercise, exercise says: "What is the absolute value of the force necessary to speed up a 500kg mass subject to 1600km/h in 1,8s, with the object from rest?" Then I had ...
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Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?     ...
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63 views

By what factor would you have to slow down time for water to feel like glass?

I have been told that though glass seems like a solid, it is somehow, in theory, a liquid -- but is just somehow a liquid that is so thick that it appears to be solid. (Of course --- if this premise ...
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249 views

Symplectic leaves, tori and Poisson manifolds

For classical systems we can define a configuration manifold, whose cotangent bundle is a momentum phase space equipped with a closed, non-degenerate 2-form. Upon the commutative algebra of smooth ...
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43 views

Bezier curve and deceleration

I have a question regarding calculation of a bezier curve. I'm programming an app where in there's continuous straight line motion of a vehicle at a constant speed. (Let's call it 'u'). When the user ...
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1answer
261 views

Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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2answers
238 views

Converting Pendulum into Electricity? [closed]

I've been thinking about this, I want to use this as my science project. The two viable solutions I've thought of so far are magnet or rotary based. Pendulum clocks could be powered once a day and ...
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228 views

Do waves accelerate?

Typically we think of acceleration as a particulate property but a previous question on this forum got me thinking. If we think of a wave increasing its velocity by increasing its energy/frequency ...
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Integral of absolute value of spin angular momentum of $N$-body system

There are $N$ particles moving freely in a plane. Let $J(t)$ be the spin angular momentum of the system of particles about its center of mass. (even center of mass keeps changing with time as ...
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53 views

Normal coordinates for harmonic approximation (classical lattice vibration)

I am reading Jenő Sólyom's "Fundamentals of the Physcs of Solids" vol. 1. and i am very much stuck at this point (chapter 11.3.2 in the book): In the harmonic approximation the potential energy of a ...
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0answers
61 views

Cylinder swinging in a halfpipe [closed]

I'm having a problem while solving this exercise: Consider a cylinder of radius 'a' swinging in a halfpipe whose radius = 10a. Find the equation of motion of the cylinder using the angle $\phi$ ...
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1answer
64 views

Potential for particle rolling down slope of arbitrary shape

I've been thinking about how to calculate the potential $V(x)$ of a particle rolling under the force of gravity down some curve, given by $f(x)$ (suppose nonincreasing). My idea was to simply ...
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2answers
283 views

Relation between (super)integrability and closed orbits

Inspired by this recent question, I would like to understand from a more general and mathematical perspective why closed orbits are only found for the Kepler ($V(r) \sim 1/r$) or harmonic ($V(r) \sim ...
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1answer
151 views

Minimum distance between two bodies attached by a spring

Take two bodies of masses m and M attached by a spring of constant K on a smooth horizontal surface. The system is at rest. A constant force F acts on body M, horizontally. To study the motion of the ...
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1answer
47 views

Why is a bending rod assumed to be undergoing torsion?

If I take a rod and bend it at both ends as far as it will go, why is there an assumption that I am also exerting a torsion along with my bending? Referencee: ccording to the third edition of "Theory ...
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29 views

Conserved charge for boosts? [duplicate]

In (3+1) dimension Poincare group has three types of Symmetries : a) Four space-time translations b) Three spatial rotations and c) Three boosts Among them, (a) implies "conservation of ...
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90 views

calculate the tile of rotation axis of a rolling ball

I want to solve the problem of friction effect on rotation axis of a rolling ball on collision with another ball. I've read Tennis racket theorem in this wikipedia article and thought it might ...
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2answers
284 views

Summation notation for Kronecker delta

I'm having some problems on notation for indices: I've found in Goldstein, 3rd edition, that the Kronecker delta satisfies the following property: $$\delta_{ij}\delta_{ik}=\delta_{jk}$$ But ...
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Fluid mechanics -Question about boundary?

Problem statement: A two-dimensional fluid stream of thickness $S$ and velocity $c$ (evenly distributed through the thickness of the stream) falls on a stationary plate and gets separated. Calculate ...
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What are possible explanations for the permeability of balloon rubber, PET plastic and other synthetic materials for carbon dioxide?

Balloons are definitely not gas-tight. Carbon dioxide just leak by the rubber away. A balloon is filled with carbon dioxide. Knot in it. And play. Shrinkage. After an hour or two the carbon dioxide ...
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2answers
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Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
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1answer
220 views

Analytical Mechanics [closed]

I see that $W_a(1) = \dot U_a(1)=\ddot{X_a}(1) = 0.3 $ Since $U_{O'}=0 $ then O' is Instant centre of rotation. Then $U_b = 2U_a = 0.6$ I tried a lot, about a week, i find the speed, but there ...
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Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free particle ...
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6answers
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Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice) I understand it being related to the resistance caused by fluid in the ...
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2answers
322 views

Turning points of particle

A particle of mass $m$ and energy $E<0$ moves in a one-dimensional Morse potential: $$V(x)=V_0(e^{-2ax}-2e^{-ax}),\qquad V_0,a>0,\qquad E>-V_0.$$ Determine the ...
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0answers
77 views

Area Integrals when Calculating Force Exerted by Air Pressure [closed]

I'm trying to find the force exerted on the walls of a cavity being filled with air. This involves doing area integrals, which I'm struggling with. The setup below is slightly complicated, see the end ...
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0answers
38 views

How did we get rid of the term $\overrightarrow{G}_W$? [closed]

Equation of conservation of momentum: $$\frac{d}{dt}\int_{W}\rho \overrightarrow{u}dV+\int_{\partial{W}}\rho \overrightarrow{u} (\overrightarrow{u} \cdot ...
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1answer
75 views

Using tensors on Lagrangian and Hamiltonian

We can write the Lagrangian (with $n$ generalized coordinates) using the following expression: ...
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1answer
105 views

Trivial conserved Noether's current with second derivatives

I'm considering a symmetry transformation on a Lagrangian $$ \delta A = \int L(q +\delta q, \dot{q} + \delta \dot{q} , \ddot{q} + \delta \ddot{q}) dt $$ the general variation takes the form $$ ...
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0answers
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Conservation Laws and time-reversal symmetry [duplicate]

In most dynamics books I've read they refer to conservation laws and their associated symmetries, cf. Noether's theorem. I know that the conservation of momentum is a result of the homogenity of ...
2
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1answer
69 views

How does the Hamiltonian change when going to a moving frame?

The Hamiltonian of a free particle in a rotating frame is given by $$ H = H_0 - \omega \cdot J, $$ where $H_0$ is the Hamiltonian in the non-rotating frame, $\omega$ is the angular velocity of the ...
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2answers
65 views

Proof that oscillations in 1d potential well occur between certain points

In >>this<< situation, a particle with energy $E$ will oscillate between the positions $x_1$ and $x_2$ indicated on the diagram. This simple fact is taught in many introductory courses however I ...
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1answer
113 views

simple question on torques on an ellipsoid

I have an ellipsoid, and in the reference frame where the x-, y- and z-axis are aligned with its eigenvectors I compute the torque $\vec\tau$ acting on it. And I'm asking myself how can I quantify ...
3
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1answer
891 views

Hamiltonian Noether's theorem in classical mechanics [duplicate]

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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0answers
37 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
2
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0answers
28 views

What physical parameters are really being described when a rope manufacturer cites “elongation %”?

I have a precision pulley system sensitive to micron displacements. I am having issues because I need a cord with low tensioning force, but also low stretch. I am getting some weird hysteresis in the ...
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1answer
28 views

Motion in oscillating field: expanding in powers of $\xi$ [closed]

I'm reading an excerpt from Landau/Lifschitz's Mechanics book about motion in oscillating fields. Two equations for the motion of a particle with mass $m$ are set out: \begin{equation} m\ddot{x} = ...
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2answers
67 views

How 'rare' is no-slipping?

I have come across a lot of questions that say something like: A ball rolls down a hill without slipping... But I have done the maths and found that a ball would only 'not slip' if the friction ...
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1answer
122 views

Work and chemical energy “paradox”

This is a mistake I've seen many people make, a few physicists included, but I haven't ever seen a satisfactory explanation for what's going on. Apologies for the lengthy setup. Setup Suppose I ...
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1answer
55 views

What does a scale accelerating on an incline read?

I was watching an online video lecture about dynamics, and then I came across this brain teaser, and I've been thinking it over for a couple of hours but can't seem to find the solution. I hope ...
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0answers
51 views

Force acting on a wheel of a two-wheeled self balancing bot

Proceeding further with my work on a self-balancing bot as posted here: http://bit.ly/1FfI6LK I've gotten stuck at the following equation: n = Gear ratio $K_t$ = DC motor torque constant $i_l$ = DC ...
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1answer
122 views

Angular acceleration as a function of torque

I know that the angular momentum $\mathbf{L}_{cm}$ with respect to the centre of mass of a rigid body can be expressed as $I\boldsymbol{\omega}$ where $I$ is the inertia matrix and ...
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1answer
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Can someone explain what's the difference between all these terms in “Simple Words” with their “applications”? [closed]

I'm very confused between all these terms. Can someone explain what's the difference between Classical Mechanics, Relativistic Mechanics, Quantum Mechanics, Quantum Field Theory, ...
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1answer
127 views

How does one express a Lagrangian and Action in the language of forms?

In Lipschitzs Classical Mechanics a Lagrangian is defined as: $L(q,q',t)$ for some trajectory $q(t)$ of a particle And the action is defined as: $S:=\int^a_b L(q,q',t) dt$ How does one ...