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's driving the bucket up?

Just saw this cool video from Plymouth University, which I actually found through Matthen's blog. They fill a plastic bottle with liquid nitrogen, screw the cap on, drop it in a bucket full of warm ...
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160 views

Rigid body/moment of inertia problem

I have a homework assignment about rigid body dynamics. Take a disc of radius $r=2m$ with uniform mass density $\rho=1$ $kg/m^2$ in the x-y plane, resting in an inertial frame. At some instant, a ...
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425 views

Meaning of subscript in $V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$

This is probably a simple question, but what does the subscript $0$ mean in the following expression? $$V=\frac{1}{2}\left(\frac{d^2 V}{{dq_i}{dq_j}}\right)_0$$
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69 views

If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion

If a people happen to be fall into the ocean from 50m high, then would the diving pose in the olympiad make less percussion then the leg going first into the water so that the body receive less ...
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Is the principle of least action a boundary value or initial condition problem?

Here is a question that's been bothering me since I was a sophomore in university, and should have probably asked before graduating: In analytic (Lagrangian) mechanics, the derivation of the ...
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429 views

Hamiltonian Flow Map

I'm reading this article and am struggling with some of the terminology. What is the flow map for a Hamiltonian system? I'm looking for a rigorous definition really! Many thanks in advance.
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350 views

What shape of track minimizes the time a ball takes between start and stop points of equal height?

I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end ...
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Deriving the action and the Lagrangian for a free point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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775 views

Centrifugal Force and Polar Coordinates

In Classical Mechanics, both Goldstein and Taylor (authors of different books with the same title) talk about the centrifugal force term when solving the Euler-Lagrange equation for the two body ...
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131 views

Mechanics Energy (Calculus)

A particle moves with force $$F(x) = -kx +\frac{kx^3}{A^2}$$ Where k and A are positive constants. if $KE_o$ at x = 0 is $T_0$ what is the total energy of the system? $$ \Delta\ KE(x) + \Delta\ ...
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115 views

Why is my speed imaginary?

A particle is released from a dense atmosphere free planet of radius r at a distance R (R >> r ). find the speed on impact. $$F = \frac{GmM}{(r + R)^2} = m \frac{dv}{dt} = mv\frac{dv}{dR}$$ ...
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288 views

Quantum $n$-body problem

Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential ...
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223 views

A good example of a nonlinear symplectomorphism?

What is a good example of a simple, physically useful nonlinear symplectomorphism $\kappa: \mathbb{R}^{2n} \rightarrow \mathbb{R}^{2n}$? I'm not much of a physicist, and all the examples I've worked ...
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626 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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Why doesn't a fly fall off the wall?

Pretty simple question, but not an obvious answer at least not to me. I mean you can't just place a dead fly on the wall and expect it to stay there, he will fall off due to gravity. At first I ...
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926 views

What kind of force is it when you push a door shut? [duplicate]

Possible Duplicate: How can I stand on the ground? EM or/and Pauli? It probably seems like a silly question to a physicist, but I'm from a pure maths background and don't know an awful lot ...
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Hamiltonian is conserved, but is not the total mechanical energy

I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
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868 views

Energy used to stop / slow an object

I'm trying to workout how much energy (if any), I use (imagining me as an efficient machine rather than a complex bio-mechanical human) when I lower or catch a weight. I understand that when I push it ...
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Formulas for compressibility of solids (physics) [duplicate]

Possible Duplicate: Formulas for compressibility of solids I have a question which is technically a physics question, but since I have yet to find a good physics forum which accepts Latex, ...
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818 views

Lever Mechanics - How to formulate an ideal lever launch

Let's say I have a simple lever as shown below, and the lever is massless and the pivot is frictionless and there is no air resistance. I'm thinking the cradle for the projectile would have to have a ...
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86 views

Modeling falling spheres

The following situation interests me and I was wondering if there is software to model it? A large set of n spheres of uniform density and discrete sizes, mass proportional to volume, are dropped ...
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2k views

Where does the lost energy go in a rubber band powering a rotating shaft?

Okay, I'm no physics whiz, and this has me stumped. You know those toy airplanes you can get with the rubber-band driven propellers? You twist the propeller a bunch of times, and this stores ...
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448 views

speed of sound and the potential energy of an ideal gas; Goldstein derivation

I am looking the derivation of the speed of sound in Goldstein's Classical Mechanics (sec. 11-3, pp. 356-358, 1st ed). In order to write down the Lagrangian, he needs the kinetic and potential ...
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436 views

Complete set of observables in classical mechanics

I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case: The functions $q^k$ and $p_l$ form a complete ...
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degree of freedom of a rigid body 5 or 6?

I'm confused here. I have a three particle (rigid) system. What would be the degree of freedom? I found out five. 3 coordinates for center of mass and 2 for describing orientation. But we have only ...
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604 views

Rotating/Translating Disk

I was trying to understand an aspect of rotational dynamics and thought of a problem to help me learn. I'm sure this problem has been considered by countless people in the past, but I'm having some ...
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637 views

the difference between the operators between $\delta$ and $d$

In classical mechanics, when talking about the principle of virtual work, what is difference between $\delta r$ and $dr$? e.g. $W=\int \overrightarrow{F} \cdot \delta \overrightarrow{r} $ and ...
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595 views

Explanation for classic mechanics puzzle

I'm trying to figure out a nice way to describe to a kid the physics behind these experiments: Assuming ideal conditions, we have a small boat with a sale, close to a lake's shore and a fan fixed on ...
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111 views

Complex part of the solution for physical values

What's a physical meaning of, for example, complex part of the solution for coordinate change of the anharmonic oscillator? Why after substitute (for diff. equation solve) for real x we can earn $x = ...
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272 views

Classical mechanics. One-dimensional motion

Here is one task below. How to solve equation $$ m\ddot {x} + ax = F(t), x(0) = \dot x (0) = 0 $$ in quadratures by using two methods? I tried to create a system of equations $$ \begin{matrix} \dot ...
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155 views

Why is the $\langle v_{x}^{2} \rangle=\frac{1}{3} \langle v^2 \rangle$?

For a randomly moving particle. Or, I suppose that 1/3 could generalise to 1/n, where n is the non rotational degrees of freedom for that particle. Related reference Kinetic Theory of Gasses.
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include the stretch of the spring own weight in potential energy for spring pendulum?

we are given a problem with spring with its own mass $m$. I am confused how to set up the PE term in the Lagrangian. Assume the spring has length of $L_{0}$ when it is laying on a table horizontally. ...
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Stationary Solutions

An unbelievably basic question, but it's something I've never been taught. Am I right in thinking that the following defines a stationary solution? Let $\phi$ be some dynamical variable satisfying a ...
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2k views

Direction of friction on particle placed on a rotating turntable

If a particle is placed on a rotating turntable then the particle has a tendency to slip tangentially with respect to the underneath surface... So the friction should act tangentially to the ...
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28k views

Formula for a ball rolling down an Inclined Plane

Suppose we set up an experiment where we have an inclined ramp, and a spherical basketball. If we were to assume the ball to be perfectly round, and rolls down in a vertical manner and the situation ...
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2answers
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What the difference between “orbital” and “orbit”?

What's the difference between "ortibal" and "orbit"? Which one should be used in physics? In quantum mechanics, is "atomic orbital" or "atomic orbit" used? And what about in classical mechanics? A ...
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Which angle causes an object to land quickest?

Say a canon is where the circle is, and it shoots two different canonballs at different angles, but at the same speed, which angle would make the cannonball hit the ground first? Intuitively I'd ...
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324 views

Parachute jumping (high altitude)

I heard about parachute jumping at an initial altitude of 30km. I want to simulate this flight numerically. How could I simulate the air drag (I mean, Which equation gives the air drag)? Normally I ...
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245 views

Is it easier to move or rotate an object? [closed]

This is a problem I'm facing on designing a moving bookcase for my home, I just don't have enough physics background to tackle the problem. Which of the following requires more force/effort? A ...
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1answer
106 views

state for a classical particle [duplicate]

Possible Duplicate: Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system? In classical mechanics, if ...
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22 views

How does a treadmill incline mechanism work? [duplicate]

Possible Duplicate: What's the difference between running up a hill and running up an inclined treadmill? I want to know how a system can give so many small steps of inclination and so ...
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4k views

When does not Newton's 3rd law apply?

Is Newton's 3rd law valid in non-inertial frames? If so, then are there other cases for which Newton's 3rd law is not applicable?
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Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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1answer
236 views

Horsepower achieved with multiple motors

Scenario I'm planning to build an electric motor for fun (not for any practical purpose). I recently purchased a shapeoko CNC mill kit and intend to manufacture most of the parts housing, stator etc. ...
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1answer
2k views

How do you know if a coordinate is cyclic if its generalized velocity is not present in the Lagrangian?

Goldstein's Classical Mechanics says that a cyclic coordinate is one that doesn't appear in the Lagrangian of the system, even though its generalized velocity may appear in it (emphasis mine). For ...
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1answer
224 views

In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential: $$\textbf{f} = -\boldsymbol{\nabla} u$$ where force $\textbf{f}$ is a vector and $u$ is a scalar. This is a relatively soft question, ...
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100 views

Can a mechanical systems on hold be switched off, in another way than just letting it do it's thing?

Can the value of the potential energy, which is responsible for driving the system, diminish in time, while the system itself is stationary during that time? Can there be dissipation in a system, ...
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785 views

Elementary derivation of the motion equations for an inverted pendulum on a cart

Consider a cart of mass $M$ constrained to move on the horizontal axis. A massless rod is attached to the midpoint of the cart, having a mass $m$ on its endpoint. See wikipedia for a picture and for a ...
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673 views

What is the significance of action?

What is the physical interpretation of $$ \int_{t_1}^{t_2} (T -V) dt $$ where, $T$ is Kinetic Energy and $V$ is potential energy. How does it give trajectory?
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Having Trouble With The Principle Of Conservation Of Momentum For a Multiparticle System

I'am reading John Taylor's Classical Mechanics chapter 1 page 20 where he proves the principle of conservation of momentum which states "If the net external force $F^{ext}$ on an $N$-particle system ...