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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Difference between phase space and Hilbert space? [closed]

Why is the phase space of classical mechanics not a vector space, but Hilbert space of QM is?
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697 views

Constraints of massive relativistic point particle in Hamiltonian mechanics

I try to understand constructing of Hamiltonian mechanics with constraints. I decided to start with the simple case: free relativistic particle. I've constructed hamiltonian with constraint: ...
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1answer
111 views

Quantum systems without a classical analogue? [closed]

I am now reading the quantum mechanics textbook by Dirac (chap. 4, $\S21$, p. 88). He says that his quantization procedure does not include all possible systems in quantum mechanics and there are ...
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191 views

Why is my Lyapunov exponent similar for single and double pendulum?

This is my first question here on stackexchange. I hope that I can be understood. If not, tell me and I will reformulate and fill in with details. I have simulated a single pendulum and a double ...
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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 ...
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1answer
36 views

Atmospheric pressure below sea level

If I go up in the air the amount of oxygen decrease and the atmospheric pressure gets lower. What would happen if i dig a hole 100 km down? does atmospheric pressure go up? when is the pressure so ...
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51 views

The coffee ring effect

Would spin coating a homogeneous solution of colloids also result in a coffee ring structure? Or is it just naturally drop casted evaporation methods that lead to the same.
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22 views

Can cyclic acceleration/deceleration be worse for fuel consumption?

Recently I have started to drive my car slower on the highway in order to save money on gas. However, I feel like I am spending at least as much fuel as before. One possible explanation that I thought ...
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158 views

How to reconstruct the dependence of the potential from a coordinate?

An ion moves along the x-axis of a black box with a speed $V$ and returns in a time $$T=a V^b$$ where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field ...
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263 views

Liquid column “recoils” in a sealed cylinder when hit by a piston — is it possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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28 views

Does vehicle tire mass effect efficiency?

This question has an interesting origin: A tire salesman was recommending tires (aka tyres) for a highly fuel-efficient vehicle. He said the vehicle was light (compared to most production cars), and ...
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1answer
34 views

Does a ball thrown down exert less force on the ground when we walk? [closed]

Scenario A: You stand still and throw a ball vertically down. When the ball hits the ground it exerts a specific force on the ground. Scenario B: While walking you throw a ball vertically down. When ...
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13 views

Isolated system and mutual interaction potential

We know that the total linear momentum of a closed (isolated) system is conserved due to homogeneity of space (Landau and Liftshitz, page 15, Mechanics). Hence for an isolated system of two bodies ...
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57 views

How can we tell the potential from the orbit?

The orbit is $$r(θ) = a(1+\cos θ).$$ The orbit of the particle is in polar coordinates. How can we tell the potential $U(r)$ from this? $U(r)$ goes to zero at infinity.
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58 views

Cylinder rotating without slipping on an accelerating slab [closed]

I am very confused by the following problem asked in my first year physics class: Please let me know if you can assist in any way! I've spent hours and hours on this question and gained absolutely ...
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0answers
29 views

Relation between linear and rotational motion of molecules?

The temperature of a substance, such as an ideal gas, can be related to the root mean square speed of the molecules. For example, for gases the molecules travel at about 480 meters per second. If we ...
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80 views

Conversion of angular momentum to linear momentum in free space

If two objects both with angular and linear velocity collide in free space, can the total linear velocity of the objects increase at the expense of a loss in angular momentum? In other words, imagine ...
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0answers
33 views

In what cases do we use the Routh Function? [duplicate]

As many of you, I studied Lagrangian Mechanics and Hamiltonian Mechanics, with the so famous functions called Lagrangian $\mathcal{L}$ and Hamiltonian $\mathcal{H}$ related by: $$\mathcal{H}(q_i, ...
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30 views

What is the displacement between highest points on a pendulum with discontinuous forcing? And is this dependent on gravity?

I know the question is worded horrendously, but my professor gives strange badly worded problems, so I've started to speak that way. It'll take a paragraph to pose this question properly. Consider a ...
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1answer
36 views

How do I calculate the work done on standing an object upright?

So I was trying to figure out how much work someone does when they do a sittup or crunch. I guess to make things simple, I'm imagining a really really thin rod with some uniform mass lying on the ...
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5answers
187 views

Is this a fundamentally relativistic phenomenon?

This question was inspired by some silliness in other threads but is independent of that silliness. Say that a train car sitting on a track is accelerated uniformly along its length if each point on ...
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2answers
140 views

Calculating how a polygon bounces off a plane

I'd like to calculate how polygons bounce off a plane. In this picture, the square doesn't bounce straight up, but instead it bounces somewhat to the right and starts spinning. But I have no idea ...
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0answers
29 views

General approach to Mechanics? [duplicate]

So, I know that this question may be tough to answer, but I am asking this question in all seriousness, and I don't consider myself a newbie... Lately, I am trying to find a way to "generalize" my ...
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1answer
88 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
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19 views

Which are the path variables in an intrinsic coordinate system?

This question concerns "path variables" or "intrinsic coordinates" or "normal and tangential coordinates" whichever you like to call it, in 3D. We have the three $path~~variables: ...
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1answer
142 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
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4answers
90 views

Measuring force of a punch

I'm trying to build a device that can mesure the force of a punch. ​ My initial plan was to build a platform with 4 springs (one at each corner) and an accelerometer in the middle. But, if the ...
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117 views

Matrix Representations of Galilean group

The general group element (in the vector representation) $$ \left [{ \begin{array} {c} \bar x^1 \\ \bar x^2 \\ \bar x^3 \\ \bar t \\ 1 \\ \end{array} } \right] = \left[ ...
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40 views

Good books for understanding Lagrangian formulation of classical fields?

I want to understand Lagrangian formulation for classical fields and apply it to understand constrained dynamics. Currently I am referring to "A modern approach: Classical Mechanics" by ECG Sudarshan, ...
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48 views

An interesting problem on potentials [closed]

I am thinking of an interesting problem on potentials. Consider a potential field $U(\mathbf R)$. Furthermore, consider a rocket with exhaust speed from 0 to $v$. I am wondering whether there is a way ...
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2answers
54 views

Can we measure the exact position and momentum of a ball by hitting it with other balls?

Imagine a billiard table that's is covered we can't see what's happening under the cover. Now imagine we throw in a ball whose throw in time, mass, size, position and velocity is unknown. To measure ...
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1answer
37 views

Note and homework organization [closed]

this is my first post here so please forgive any errors! I am currently in a mechanics class and having a little trouble trying to figure out how I should structure my lecture notes and my homework. I ...
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1answer
57 views

Is the Impulse-Momentum Theorem True? [closed]

This is just a general question I want to throw out there, and see arguments from both sides... Is Impulse-Momentum Theorem True? Well in my opinion I would say yes because it is a derived equation: ...
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30 views

Energy-Momentum tensor for classical field with nontrivial boundary conditions

Question: Is there a energy-momentum tensor for the potential flow equations with a free surface under the action of gravity (ie the equations governing some types of surface water waves)? ...
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52 views

On the isotropy of materials

I am working on honeycomb structures and first of all I would like to understand whether it is isotropic or not, and, if the latter holds, which kind of anisotropy does it have? How to do it? I don't ...
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1answer
101 views

Simplest Live Demonstration of Adiabatic Transport

I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
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1answer
30 views

Internal energy. Mechanics and Thermodynamics

Internal energy is defined in thermodynamics as a function of state, in such a way that, in an adiabatic process, the variation of internal energy equals to the work done, regardless of the way it has ...
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1answer
107 views

Is there conservation of momentum if there's conservation of energy? [closed]

The equation for conservation of momentum: $$m_1\vec{v}_1 + m_2\vec{v}_2 = m_1\vec{u}_1 + m_2\vec{u}_2$$ The equation for conservation of energy: $$\frac 12m_1v_1^2 + \frac 12m_2v^2_2 = \frac ...
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1answer
71 views

Why is energy in a system typically able to be described using quadratic expressions?

This might be more of an applied math question. Why is the energy of a system typically able to be described using quadratic expressions. Is there an underlying mechanic that drives this?
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14 views

Scattering in Higher Dimensions

In 2 dimensional scattering, if the scattering situation is reflexive about the beam axis then we can relate the differential cross section to the impact parameter via ...
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4answers
200 views

Is it correct to say Newtonian mechanics is a subset of Quantum mechanics?

I grew up in a three dimensional (3D) reality described quite well by Newtonian mechanics as opposed to the reality described by Quantum mechanics. That is I could go to bed at night without worrying ...
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5answers
420 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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2answers
46 views

Simple harmonic motion..direction of acceleration

To solve questions about simple harmonic motion, my book says $\ddot{x}$ (i.e. acceleration) is in the direction of increasing $x$, i.e. away from equilibrium. I don't understand why is this so, since ...
3
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3answers
57 views

Why is response of system same frequency as driving force frequency

Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ...
2
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1answer
65 views

Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. \begin{equation} T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}} \end{equation} ...
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1answer
86 views

Deeper principles in classical mechanics

While teaching introductory physics, my professor explained that the conservation of linear momentum, conservation of energy and conservation of angular momentum are based on deeper principles in ...
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1answer
73 views

Existence and Uniqueness of Newton's Laws

I'm reading Arnold's book on classical mechanics. This is kind of a dumb question, but I'm having problems understanding his explanation for existence and uniqueness of Newton's laws. On page $8$ he ...
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2answers
45 views

Impulse Equations

A solid sphere of mass $m$ rolls without slipping on a horizontal surface and collides with a vertical wall, elastically. The coefficient of friction between the sphere and wall is $\mu$. After the ...
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1answer
91 views

Second order Fermi mechanism. Is there a mistake in the Claus Grupen book?

The second order Fermi mechanism describes the interaction of charged particles with magnetic clouds. This model leads to a collision-less acceleration of cosmic rays up to ultra high energies. A ...
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1answer
20 views

Angular momentum for elliptic path in 2D isotropic oscillator

Assume a 2D isotropic oscillator, i.e $$U = \frac{1}{2}m\omega^2(x^2+y^2),$$ and assume for simplicity that the oscillator performs elliptical motion, with major axis $A$ and semi-major axis $B$. My ...