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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Classical models with unbounded particle number

Is there any classical model which deals with the birth, life and death of particles? What application could it have? I am talking about a 'billiard-ball' kind of model, but the kind in which balls ...
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106 views

Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
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435 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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37 views

Derivable Concepts in Mechanics and Electromagnetism

In Classical Mechanics, one of the possible foundations is based on three concepts aka mass(equivalent to energy), length and time. This is a foundation because we can model everything ( pressure, ...
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36 views

Prove a transformation is a variational symmetry?

My question: How to prove the family of transformations of the $(t,q)$ space, given by $(t,q) \to (t,U(\epsilon)q)$, where $U(\epsilon) \in SO(3)$, is a variational symmetry? So it depends on $L$ by ...
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418 views

Understanding Poisson brackets

In quantum mechanics, when two observables commute, it implies that the two can be measured simultaneously without perturbing each other's measurement results. Or in other words, the uncertainty in ...
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57 views

Deriving Snell's law via Lagrangian mechanics

A particle moves with kinetic energy $K_1$ in a region where its potential energy has a constant value $U_1$. After crossing a certain plane, its potential energy changes discontinuously to a new ...
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3answers
56 views

Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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316 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
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127 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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Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they ...
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26 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
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86 views

Chocolate dynamics

Now I have found a possible model on how to describe chocolate when it is chewed. It has to do with geometrical transformations when a curve $\gamma$ intersects a manifold $M$. The chocolate is ...
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33 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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20 views

Will the center of mass of the whole system change when object swims on curved surface?

In the example given here, the object can move on the frictionless surface of the sphere by changing its shape periodically. So will the center of mass of the whole system change after the object ...
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2answers
900 views

Connections between classical and quantum mechanics?

I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
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Conceptually, what is negative work?

I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
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63 views

Transfer between translative KE and rotational KE in a rigid body

I have been inspired by some sci-fi cannons that seem to operate by initially spinning up a projectile inside the cannon, and then suddenly firing the projectile out at high speed. Now, I am wondering ...
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63 views

Coupled wheel and rod (analytical mechanics)

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
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26 views

Force in colliding snooker balls

If a snooker ball is traveling at 2m/s and hits another ball, the first ball will stop dead and the second will accelerate instantaneously to 2m/s. F=ma, so this would seem to imply an infinite force. ...
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How to find out whether a transformation is a canonical transformation?

We had a couple of examples where we were supposed to calculate the Canonical Transformation (CT), but we never actually talked about a condition that decides whether a transformation is a canonical ...
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63 views

How to calculate the classical on-shell action for a harmonic oscillator? [closed]

So, short and sweet, I've been reading the path integrals book by Feynman and Hibbs, and one of the elementary problems they ask is to calculate the classical on-shell$^1$ action of a harmonic ...
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508 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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1answer
132 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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40 views

Rheological behavior of chocolate

If someone eats chocolate, the chocolate goes through the following configurations: $\chi_0:$ chocolate is solid and has a smooth Surface everywhere; the Riemann Tensor vanishes on every Point of the ...
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2answers
199 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
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1answer
312 views

Hamiltonian Noether's theorem in classical mechanics

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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80 views

How was time defined before we knew the speed of light was constant or in classical physics? [closed]

Nowadays, we now about $c$ the universal speed of light. This lets us define the notion of distance in terms of time (despite the fact that it works the opposite way for our common units.) Before ...
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69 views

Why Galilean spacetime is not $\mathbb{E}^4$?

In Newtonian mechanics the physical spacetime is a Galilean spacetime with an affine surjection $\pi : \mathbb{A}^4\to \mathbb{E}^1$ from affine space $\mathbb{A}^4$ to Euclidean space $\mathbb{E}^1$. ...
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279 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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66 views

How is this a gauge choice mathematically?

I've been reading an article about the "square cat", which is described as the system bellow Such system is a deformable body that can change $a$ and $\theta$ but has $b$ fixed. The article uses ...
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61 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
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5answers
230 views

Is the polar coordinate system non-inertial or inertial?

Consider a car driving around in a circle lying in the plane and suppose we were interested in determining its acceleration as measured by an observer stationary on the "ground" or whatever. ...
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290 views

Classical Rutherford scattering (partial) derivation

I am having trouble answering the following question, please could you help! Thank you in advance for any assistance you can give. Consider classical Rutherford scattering of a particle with mass $m$ ...
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110 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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2answers
48 views

Hockey puck collision [closed]

I have a homework question in which a sticky hockey puck traveling at constant velocity parallel to the side of the rink strikes a stationary puck and sticks to it. The angels between centres at ...
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0answers
43 views

Time reversed Abraham-Lorentz reaction force

The Abraham-Lorentz radiation reaction force on a charged particle is given by: $$\mathbf{F_{rad}} = \frac{q^2}{6\pi\epsilon_0c^3}\mathbf{\dot{a}}$$ I understand the situation where one fires a ...
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1answer
40 views

Does the moment of inertia change?

I am currently working on a practice problem for my upcoming exam and I have difficulties getting my head around moment of inertia. If the ball has mass $m$ and is going around in a circle with ...
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1answer
42 views

How much force can bolt cutters exert?

What's the mechanical advantage of an ordinary, let's say, 3 feet long bolt cutters? How many pounds can they exert? I'm asking because I have a lock which is apparently immune to over 9 tons of ...
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62 views

A question on Lagrangian dynamics an the velocity phase space

I've struggled in the past with understanding why we can treat position and velocity as independent variables in the Lagrangian, but I think I may have finally become a bit more enlightened on the ...
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36 views

Quantum chaos vs classical chaos

There is this popular conjecture from Bohigas, which says: When the analogeous classical system of a quantum system shows chaotic behaviour then the spacing distribution of the quantum system ...
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1answer
47 views

What is the criterion for a change to be adiabatic?

I'm trying to understand whether the change of a parameter $\lambda$ of a Hamiltonian $H$ is adiabatic. Reading Landau and Lifshitz "Mechanics", I see ... let us suppose that $\lambda$ varies ...
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1answer
58 views

Jumping vs pulling my hair upwards

Why can't I jump or fly if I pull my hair upwards, while I can jump using my legs? The way I see it, when jumping someone lifts its body using the muscles in the legs (while the feet are standing ...
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2answers
128 views

When can phase trajectories cross?

It's said in elementary classical mechanics texts that the phase trajectories of an isolated system can't cross. But clearly they can, for example for the pendulum, the trajectories look like this: ...
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1answer
69 views

How do I transform onto a relativistic rotating frame of reference?

In classical mechanics, the usual formula to translate the evolution of a quantity as seen from an inertial frame of reference to a rotational frame is: $$\frac{d \textbf{A} }{dt} \vert_{Inertial} = ...
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3answers
102 views

Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
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2answers
76 views

Natural Frequency of an object and the phenomenon of resonance!

I have read about the term natural frequency in quite a lot of places. But I haven't found an explanation as to what is vibrating. It was pretty awkward when I couldn't clearly answer my little sister ...
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1answer
114 views

Falling charged objects: energy conservation paradox?

Imagine that we start with two oppositely charged objects on the ground, separated by a distance $d$, with charges $+q$, $-q$ and masses $m$. We raise them both up to a height $h$. In doing so we ...
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21 views

Locally accessible dimensions of configuration space

I am reading a book called "Structure and Interpretation of Classical Mechanics" by MIT Press.While discussing configuration space and degrees of freedom,the authors remark the following: Strictly ...
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178 views

Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that ...