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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Idea of integrable systems

I do not quite understand the idea an integrable dynamical system. Does it mean that the EOMs are analytically and exactly solvable? What are the necessary and sufficient conditions such that a system ...
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1answer
256 views

Rope on an inclined plane problem

My book says the answer is (a)zero but i don't understand how it came zero. What will the acceleration if horizontal level of the two ends of the rope are different?
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1answer
646 views

Is there a better choice of coordinates for a bead on a rotating helical wire?

A bead of mass $m$ is threaded around a smooth spiral wire and slides downwards without friction due to gravity. The $z$-axis points upwards vertically. Suppose the spiral wire is rotated about the $z$...
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3k views

Euler-Lagrange equations and friction forces

We can derive Lagrange equations supposing that the virtual work of a system is zero. $$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\...
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1answer
101 views

Power of viscous friction on a falling sphere

I have derived a simple model of a rotameter using an homogeneous solid ball in a rigid cone where a fluid flows. I consider 4 forces: Weight, Buyancy, Viscous Friction and Drag. I have written my ...
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1answer
129 views

Canonical partner of time in QFT and string theory

In analytical mechanics, the Hamiltonian or total energy becomes the conjugate momentum of the time in the symmetric form of the equations. This seems very strange and interesting to me. Does it have ...
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2answers
346 views

Electrical analogy for stress and strain

It feels like the relation between stress and strain (and other mechanical properties) is analogous to that of some electrical properties (voltage and current?). I'm comfortable with electrical ...
10
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1answer
518 views

The most stable way of standing in a bus

Here's what's bugging me for quite a long time. Imagine the every day situation, that you are standing in a bus with your back on wall having only limited space on the floor and no handle to hold. You ...
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0answers
196 views

Virtual-work problem [closed]

I have a very specific doubt about the next exercise: I have the crane of the picture: With a force $F_a=-K\varphi$ Applied on the point B, perpendicular witch AB, and another force $F_b=-K\psi$ ...
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1answer
165 views

Is there a Lagrangian whose Euler-Lagrange equation is the gradient?

I am trying to recast a problem I am working on in terms of Lagrangian mechanics. I am in the following situation. Suppose I have a function $f:X \rightarrow \mathbb{R}$ (a field). In the its ...
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1answer
168 views

Canonical transformations in Hamiltonian mechanics

How to prove that in the new Hamiltonian, which is formed by any of the generator function will not contain $Q$ (transformed from $q$)? I.e. new Hamiltonian will only be a function of $P$ (transformed ...
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1answer
33 views

Could each non-dependent physical contant represent dimentions, and our universe be a point on this n-dimentional structure?

For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity. Our Universe would be at a point on this range (equal to our G value) where ...
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1answer
186 views

Quadrotor dynamical equations on center of propeller

I work on a quadrotor project. It is commonly wide dynamical model according to the center of quadrotor. However, I need quadrotor dynamic equations on center of one of the propellers. It seems very ...
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0answers
84 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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3answers
375 views

Law of attraction

Could you please explain that since we know Newton's law of Universal Gravitation says all masses attract each other. Thus, we humans should be attracted as well or any other daily life objects. Why ...
3
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1answer
321 views

Clarifying constraint forces in Lagrangian dynamics

In the Lagrangian formulation, the addition of constraint forces that are unknown can be done with Lagrange multipliers, which allows for the forces to be found. Taking $k$ constraints of the form $...
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1answer
220 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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2answers
3k views

Potential energy from opposing magnets repelling each other with a gap of 1 mm

I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the ...
3
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2answers
981 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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4answers
582 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
239 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
785 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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5answers
1k views

Noether Theorem and Energy conservation in classical mechanics

I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
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0answers
68 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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2answers
353 views

How to find zero-point oscillations for this system?

Consider the following Hamiltonian which is absolutely relativistic literally: only sensitive to absolute pairwise relative phase space variables of objects for a system of $N$ objects moving in one ...
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2answers
173 views

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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5answers
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Why does my door shut faster when the window is open?

I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if ...
3
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1answer
260 views

Hamiltonian for forced systems

I am trying to learn Hamiltonian mechanics. While many textbooks treat closed systems, I have a hard time finding references for forced systems. For example, if I consider simple systems of masses ($...
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1answer
116 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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2answers
218 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
105 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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0answers
28 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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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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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 let'...
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2answers
291 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 ...
16
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2answers
571 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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1answer
101 views

How do I correctly choose signs for a falling particle?

An object falls from a height $h$ above water through air with negligible drag. In the water, the upward buoyancy exactly balances the downward gravitation force. The only remaining force on the body ...
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3answers
2k views

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 ...
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2answers
207 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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1answer
482 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 ...
1
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2answers
256 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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1answer
78 views

How do you justify neglecting electron-electron interaction in the Drude model?

I'm sure there's some way to justify it. Maybe a screening effect?
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1answer
87 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 related ...
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3answers
1k 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 ...
3
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1answer
128 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 ...
9
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5answers
11k 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 ...
6
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2answers
241 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
114 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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101 views

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 ...
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2answers
3k 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 ...