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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Rigid bodies - the wheel

As I've been taught lately in my mechanics course: the wheel has a unique property: at every moment of motion, the touching point between the wheel and the ground is not in movement and ...
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83 views

How does this help an aeroplane to fly? [duplicate]

I read it somewhere on the internet that wings of an aeroplane are designed in such a way, that they increase the velocity of air above the wings and so pressure above the plane becomes less than the ...
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1answer
219 views

Can the Lagrange Multipliers depend on the coordinates?

When dealing with Lagrange multipliers to solve systems with constraints we usually have two ways if the constraints are holonomic: Differentiate the constraint and add the appropiate term to the ...
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1answer
128 views

Cayley-Klein Parameters

I have a very simple question(I guess )to ask $$\frac{d\mathbf{m}}{dt}= \mathbf{C} \times \mathbf{m}$$ where $\mathbf{m}$ and $\mathbf{C}$ are vectors. Assume that $\mathbf{C}$ is constant over a ...
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4answers
377 views

Is it possible to sky dive without a parachute and land safely?

Let's assume an averaged sized man (1.8 meters height 80 kg) who's sky-diving from a 5000 m height. Let's also assume he's using tight clothes and no parachute. The idea is: Is it possible for him ...
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2answers
157 views

Can a bullet leave a gun and tumble to the ground?

This question seems to have been asked a few times in different configurations, but none of them answer my variation. I've struggled to understand this for nearly 15 years and had conflicting answers ...
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1answer
343 views

Minimum separation distance between two masses cushioned by a spring [closed]

I think this problem is much more difficult than what I've learned so far. B) is the problem I'm having a hard time with. I think it is much more difficult to consider because as the red object ...
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0answers
67 views

How can I answer the critical questions of mechanics? [duplicate]

I have passed my 1st year of undergraduate study life somehow I could have managed. But recently I have decided to fill up the emptiness of knowledge over mechanics. Besides I have my studies of 2nd ...
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1answer
102 views

Symmetries for an inertial frame

According to Noether's theorem, a symmetry of space-time w.r.t. an observer, will yield a corresponding conservation law for a closed system w.r.t. that observer. Now if our space-time has 3 ...
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163 views

Landau's argument for dependence of Lagrangian on magnitude of velocity

In chapter 1, of Landau-Lifshitz Mechanics' book, Landau through isotropy and homogeneity of space and homogeneity of time proves that the Lagrangian must depend of magnitude of velocity of the ...
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1answer
88 views

How to check $\renewcommand{\vec}[1]{\mathbf{#1}} \vec{v'}\cdot\vec{V}$ and $\vec{v}'^2$ are time derivatives of some other functions?

From Landau, Lifshitz Mechanics p.127 $\renewcommand{\vec}[1]{\mathbf{#1}}L'=\frac{1}{2}m(\vec{v}'^2+\vec{v'}\cdot\vec{V}+\vec{V}^2)-U $ He states that "$\vec{V}^2(t)$ can be written as the total ...
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3answers
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Looking for an intuitive understanding of normal force

I understand normal force to be the perpendicular force to a surface of contact. However, I have come across a problem which has caused me to rethink this. My initial understanding of force is ...
3
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4answers
281 views

Why doesn't Newton's Second Law include higher-order mass?

I suspect this has been asked here before, but I didn't find anything using Search. Why is Newton's second law only second-order in position? For instance, could there exist higher-order masses $m_i$ ...
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0answers
27 views

Expansion of $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ [duplicate]

How can I find the expansion of the Lagragian (it it only dependent on $v^2$) $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ in powers of $\vec{\epsilon}$ ? (From L.Landau, E. Lifshitz, Mechanics , ...
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7answers
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What properties do you need for building a tower?

When I was a boy I used to daydream about building a tower so tall that the top of it would stick out of the top of Earth's atmosphere project into near space. There would perhaps be a zero gravity ...
10
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2answers
421 views

Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}\delta q=\delta \frac{dq}{dt} $

I am reading about Lagrangian mechanics. At some point the difference between the temporal derivative of a variation and variation of the temporal derivative is discussed. The fact that the two are ...
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2answers
70 views

Fixed lever arm spinning under gravity, why am I getting these results?

Suppose there is a lever arm of length $L$, a mass $m$, and it is fixed at one end. The lever is parallel to the ground. So the force acting on the center of mass of the lever would be $mg$. Now ...
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2answers
168 views

Does an object on top of a lever arm have angular velocity at the moment when the lever is released?

Suppose there is a lever arm fixed at one end, and it is parallel to the ground. There is an object resting somewhere on top of the lever arm (the object is not attached to the lever). At the moment ...
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3answers
770 views

Boundary layer theory in fluids learning resources

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
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4answers
426 views

Classical Limit in Quantum Mechanics

Suppose I have a wave function $\Psi$ (which is not an eigenfunction) and a time independent Hamiltonian $\hat{\mathcal{H}}$. Now, If I take the classical limit by taking $\hbar \to 0$ what will ...
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2answers
185 views

Classical point particles to classical fields

I often hear that in the continuum limit we can study large numbers of particles as fields. I always imagined that by removing all bounds on the number of particles (while keeping total energy, ...
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2answers
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Rigid body dynamics joints

I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
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2answers
235 views

Are Poisson brackets of second-class constraints independent of the canonical coordinates?

Say we have a constraint system with second-class constraints $\chi_N(q,p)=0$. To define Dirac brackets we need the Poisson brackets of these constraints: $C_{NM}=\{\chi_N(q,p),\chi_M(q,p)\}_P$ . Is ...
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3answers
768 views

Deriving the law of moments

Recall the Law of Moments for a one dimensional rod: "When an object is in equilibrium the sum of the clockwise moments is equal to the sum of the anticlockwise moments." I understand that we ...
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1answer
212 views

Are the the elongation the same when one end of a spring is attached to the wall and

Consider there are 2 identical springs. One end of the first spring is attached to the wall and the other end is pulled by a force $\vec{F}$. It is depicted as shown in the first figure below. Both ...
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2answers
183 views

Mechanics Landau Galilean Principle

I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is ...
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4answers
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Why can't we feel the Earth turning?

The Earth turns with a very high velocity, around its own axis and around the Sun. So why can't we feel that it's turning, but we can still feel earthquake.
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1answer
69 views

Classical Mechanics & Coordinates [closed]

What is the meaning generalised coordinates in Classical Mechanics? How is Lagrangian formalism different from Hamiltonian formalism? How are they related to Hamilton's Principle? How are they ...
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2answers
230 views

Why does Lagrangian of free particle depend on the square of the velocity ?

Why does Lagrangian of free particle depend on the square of the velocity ? For example, $L(v^4)$ also doesn't depend on direction of $v$.
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2answers
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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 ...
12
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9answers
6k views

Book about classical mechanics

I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
7
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5answers
5k views

Trouble with classical mechanics self-learning (How to avoid going down the Physics rabbit hole?) [duplicate]

I'm a retired police officer trying to learn classical mechanics on my own. I have gone through many links on the Internet including the classical mechanics quick reference textbooks from Physics ...
3
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1answer
105 views

What if the kinetic energy of a particle was some other function $f(v)$?

This is a "what if this was how the universe worked" kind of question. I don't know if those belong in Physics StackExchange, and I apologize if they don't. Suppose we have two reference frames ...
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How to calculate the van der Waals force from the van der Walls equation?

Given the van der Waals equation $$\left(p+\frac{n^2a}{V^2}\right)\left(V-nb\right)=nRT$$ and the van der Waals constants $a$ and $b$, how can I find the van der Walls force between two atoms at ...
6
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2answers
194 views

Is it possible to estimate the speed of wind by the sound emitted by a cable of an overhead power line?

I was near ($\approx40m$) an overhead power line and I heard a sound coming from the cables of the power line; I think the sound was made by the vibrations of the power cables due to the wind but I am ...
2
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1answer
89 views

Stationary action with maximized action [duplicate]

I would like to ask for an example (a lagrangian) both in classical and quantum level for which the action is maximaized (rather than minimized). What is special in these cases?
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2answers
1k views

Friction on an object moving with momentum over a surface

I'm familiar with the equations for friction for a static object and an object moving at steady speed over a surface from high school physics. But we never learned how an object moving only due to ...
0
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1answer
127 views

Diffraction of sound

The sound waves, by the virtue of it being a wave, shows diffraction and interference. But in diffraction, I learnt that if the wave is allowed to enter through a small aperture, there is a central ...
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0answers
47 views

prediction of a moving object

OK, this may be a hard question to answer and really all I am looking for is an equation as I don't even know what to call this. This is all for a game so bare with me please. In the game two ...
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1answer
103 views

Transforming a lagrangian to hamiltonian and vice versa

I am not refering to Legendre transform, but to something more simple. In analytical mechanics, the Lagrangian can be described as $L=T-V$, and the Hamiltonian is if the Lagrangian doesn't explicitly ...
1
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3answers
156 views

Classical Wave Equation - Approximations

I don't understand the derivation of the wave equation given below - $$T \sin (\theta _1) - T \sin (\theta ) = T\tan (\theta _1 )-T\tan (\theta ) = T \left. \left(\frac{\partial f}{\partial z} ...
20
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2answers
430 views

How to combine these equations of constraint?

I want to model a nonholonomic system of an arbitrary rotating disk in 3D, which rolls without slipping, and doesn't have to stay vertical. (think spinning a penny on the table) I want to use the ...
3
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1answer
166 views

Is it possible to use the parabolic shape of a rotating fluid to measure the angular frequency of the rotation of the Earth?

A fluid in a rotating bucket will take on a parabolic shape (for example of some simple derivations of this result see http://en.wikipedia.org/wiki/Bucket_argument). The assumptions that play into the ...
7
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2answers
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Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
1
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1answer
157 views

relation between Schrodinger equation and wave equation [duplicate]

I have always been confused by the relationship between the Schrödinger equation and the wave equation. $$ i\hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m} \nabla^2+ U \psi ...
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1answer
55 views

Calculating Energy & Small functional time scale

I have an electric motor that can apply a pull force of $3000 \;\mathrm{lb}$ (electric winch), it draws $180 \;\mathrm{A}$ at $12 \;\mathrm{V}$. I understand that power $P = I \cdot V = 2.1 ...
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1answer
3k views

Confused with stress, strain and linear thermal expansion

Four rods A, B, C, D of same length and material but of different radii r, 2r , 3r and 4r respectively are held between two rigid walls. The temperature of all rods is increased by same ...
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5answers
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Why is the bell, well, bell shaped?

What is the significance about the bell shape, when its hit at the rim it rings/produces sound better than other shaped objects? If so could anyone explain a little bit on it. EDIT: From the ...
3
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1answer
97 views

Stability of square of masses on strings under rotation

Imagine we have a square of masses, $m$, connected by light inextensible strings, length $l$, rotating around it's centre at angular speed, $\omega$. It's easy enough to show that there must be a ...