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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Macroscopic Forces from QED

In QED the carrier for electromagnetic interaction is a photon, while macroscopic forces are due to electromagnetic interaction (by macroscopic forces I mean: normal force, object collision, friction ...
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What could cause an asymmetric orbit in a symmetric potential?

My question can be summarized as: Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
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210 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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74 views

Where does energy go when performing a useless effort?

I went to school one day, so I thought I was able to get this simple one.. but it looks like I'm not anymore. :( One lonely little spaceship is resting into space. It has a small fuel capacity that ...
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32 views

How do I calculate motor efficiency from voltage, current and RPM?

I have a setup where a motor is spinning at a constant (known) RPM, under no load. I know the power going into the motor (voltage * current), and I can find out the rotational kinetic energy of the ...
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41 views

Why the involution condition is imposed in the definition of integrability?

For an $N$-degree-of-freedom system to be integrable, the usual definition imposes the existence of $N$ independent conserved quantities, which must be in involution to each other, i.e., $$\{ F_i, ...
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Sea surfer position displacement

Waves are means by which the energy propagates through a medium (e.g., sea water). This is not associated with a net movement of water in the direction of wave propagation. If this is the case, then ...
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364 views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
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67 views

Landau's derivation of a free particle's kinetic energy- expansion of a function?

I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact ...
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Are water waves (i.e. on the surface of the ocean) longitudinal or transverse?

I'm convinced that water waves for example: are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
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Could two identical stars revolve around each other in a common orbit if we only account for Newtonian physics?

Both a parent star and its planet revolve around the center of mass of the system, the reason we see stellar wobble. But if we take this to be true, which it is, there can be a configuration in which ...
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About the derivation of the Hamilton-Jacobi equation

It is an old question for me. In Goldstein's book, the H-J equation is derived in this way. We want to find a generating function $F(q,P,t)$ such that the transformed Hamiltonian vanishes identically, ...
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Can all canonical transformation be obtained through generation function approaches?

The question can be formulated as following: Suppose $$\delta \int_{t_1}^{t_2}{[p\cdot \dot{q} - H(p,q,t) ]dt} = 0$$ $$\delta \int_{t_1}^{t_2}{[P\cdot \dot{Q} - K(P,Q,t) ]dt} = 0$$ in which $$P = ...
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Force as change in momentum vs. change in velocity

Is there ever a situation where the distinction between $F = m \frac{dv}{dt}$ and $F = \frac{dp}{dt}$ is important? I can't think of a situation where one is true and not the other (assuming only ...
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795 views

Is there a physical system whose phase space is the torus?

NOTE. This is not a question about mathematics and in particular it's not a question about whether one can endow the torus with a symplectic structure. In an answer to the question What kind of ...
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Planar motion in central forces

In a two body problem under central force, corresponding to a potential $V(r)$(assume one body is massive compared to the other so that its motion is negligible), conservation of angular momentum ...
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162 views

Saturation of the Cauchy-Schwarz Inequality

Going to as little details as possible, here is a statement from Wald's text on QFT in curved spacetimes(I am not quoting the book) He considers two vector spaces ${\cal S}$ and ${\cal H}$. Note ...
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Action and Action integral: Different kinds of variational principles

What are the difference between: the action $\int_{t_{1}}^{t_{2}}(L+H) dt$ that we use in the principle of least action, and the action integral $\int_{t_{1}}^{t_{2}}L dt$ that we use in ...
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Invariance of canonical Hamiltonian equation when adding the total time derivative of a function of $q_i$ and $t$ to the Lagrangian

The following is exercise 8.2 in 3rd edition (and exercise 8.19 in 2nd edition) of Goldstein's Classical Mechanics. Adding the total time derivative of a function of $q_i$ and t to the Lagrangian ...
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Physics of Snow Globe

What is the physics behind snow flakes inside a 3D snow globe? If I were to implement a snow globe in computer graphics what kind of model do I need to the flakes motion like a real snow globe? What ...
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90 views

How to prove that a hamiltonian system is not integrable?

To show that a system is integrable, we just need to find $N$ independent functions $f_j$ such that $\{ f_i, f_j \} = 0$. But how to prove that such a set of functions do not exist? For example, ...
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When is this integral zero?

I have a particle with total energy $E$ confined in a potential $$U(x) = -\frac{\cos^4x}{2} - m \cos x - f \sin x. $$ The constants $f$ and $m$ are both in the range (-2,2). The energy is such that ...
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How to transfer mechanical power from the inside of a vacuum chamber to the outside while maintaining a seal?

In a vacuum chamber how would one transfer mechanical power (either rotation or linear) from inside to the external environment? I'm working on an idea for a new/different type of motor that would ...
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Are there any hamiltonian systems without a periodic orbit?

Are there any hamiltonian systems without a periodic orbit? Can anyone give me an example? If such a system exists, does this fact have any implication on its quantum version?
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Electrical force between two objects

I tried to solve the following problem: There are 2 objects . The object m1 with charge q and the object m2 with charge q.(same charge).The object m2 is connected with a rope to the ceiling. at the ...
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Antipodes are mostly ocean - so what happens after digging that hole through earth?

Digging a hole through earth is a common thought experiment, often used to explain effects of gravity. But what would happen if someone finally dug the hole? Sure, he took care to stabilize and ...
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I am learning Quantum Mechanics and I have some questions about some basic concept [closed]

What does a "STATE" exactly mean in quantum mechanics? What is the equivalence of "STATE" in classical mechanics? If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the ...
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Two boxes that are connected pushed by force - what happens between two boxes?

So when two boxes are connected together, and force is applied, two boxes move with the same acceleration. (assuming force is constant.) My question is, how are forces between two boxes get cancelled ...
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Classical vs. quantum energy of the hydrogen atom

If I have an electron and a proton and calculate the classical energy which I get by bringing the electron from infinity to the distance of a Bohr radius to the proton, I get 27.2 eV, but the electron ...
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122 views

What's wrong with my calculation of gravitational potential for a uniform sphere?

This is really embarrassing, but I'm not quite sure where I'm going wrong here... Why is this calculation of the gravitational potential inside a sphere with uniform mass distribution incorrect? ...
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126 views

Does a simple double pendulum have transients?

Suppose, we have the most simple double pendulum: Both masses are equal. Both limbs are equal. No friction. No driver. Arbitrary initial conditions (no restriction to low energies) Does this ...
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Naive questions on the classical equations of motion from the Chern-Simons Lagrangian

Consider a Chern-Simons Lagrangian $\mathscr{L}=\mathbf{e}^2-b^2+g\epsilon^{\mu \nu \lambda} a_\mu\partial _\nu a_\lambda$ in 2+1 dimensions, where the 'electromagnetic' fields are $e_i=\partial ...
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How do adhesive and cohesive forces affect surface tension? [closed]

Surface tension appears at the interface of two immiscible fluids if the cohesive force of attraction is more than adhesive force. What will be the physical effect if the adhesive force is more than ...
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In what limit do we *really* get Maxwell-Boltzmann statistics from Bose-Einstein and Fermi-Dirac?

Fermi-Dirac and Bose-Einstein energy occupation number $n(\epsilon)$ in natural units ($[T]=[\epsilon]$) read $$n(\epsilon) = \frac{D(\epsilon)}{e^{(\epsilon-\mu)/T}\pm 1},$$ where $D(\epsilon)$ is ...
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CM: Need to recover the Hamiltonian, knowing conserved quantities and information about the EOM, possibly via action-angle coordinates

Statement of the problem: I have a system with 2 degrees of freedom and I have found two independent conserved quantities, without knowledge of the Hamiltonian. I'm looking for a method to recover a ...
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From 1D problem to easier 2D problem

Here I describe an example how a 1D problem can be solved easier by considering a mathematically equivalent problem in 2D. Problem: Find the equation of motion of particle in 1D space with the ...
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1answer
74 views

Kinetic energy in Lagrangian formalism

In reading Goldstein's Classical Mechanics (2nd edition) I came across a confusing derivation. Goldstein (Eq. 1-71) derives the total kinetic energy of a system of (classical) particles as: $$ T = ...
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191 views

How should I throttle my rocket to reach highest altitude? [closed]

"Real world" problem. Suppose we want to launch a rocket equipped with an engine which can be throttled as we prefer. Suppose also that the amount of fuel burnt per time is directly proportional ...
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How coordinate system shifting is related to similarity transformations?

I know that coordinate system shifting can be represented using matrices. But how exactly are similarity transformations related to coordinate shifts ?
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88 views

Basic buoyancy question

If I have a cup of water filled with air at the bottom of a pool, then when the cup is "upside down" the air doesn't leave because the water pressure is pushing it up against the top of the container. ...
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Confusion regarding the principle of least action in Landau's “The Classical Theory of Fields”

Edit: The previous title didn't really ask the same thing as the question (sorry about that), so I've changed it. To clarify, I understand that the action isn't always a minimum. My questions are in ...
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Block on an inclined plane [closed]

If you take moments about the centre of mass of a block positioned on an inclined plane so that the gravitational force can be drawn from the centre of mass of the block to one corner of the block, ...
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2answers
68 views

How much does the sound definition vary during an LP (Vinyl)?

This question came to me when I realized how the linear speed varies while listening to a Vinyl LP. The linear speed variation has to be compensated with a variation in the resolution of the grooves, ...
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Why and how almost periodic series constitute the algebra of observable of integrable systems?

In the introduction of his book Noncommutative Geometry, p. 42, Connes explains that when a classical dynamical system has enough constants of motions, the motion of the system is almost periodic, ...
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Types of invariance and their definitions

In classical mechanics, there are three types of invariance: invariance, form invariance and gauge invariance. I am looking for a precise definition of these terms, but all I can find are sentences ...
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169 views

The boundary for quantum mechanical behavior and classical mechanical behavior

To what size and how does "quantum weirdness" such as entanglement and superposition stop applying to larger objects (mere unions of these quantum particles). How do these macro objects that behave as ...
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(air pressure and displacement) Isn't this image wrong?

Isn't this figure wrong? P(x,t) = -B(dy/dx) . If the derivative of air displacement has a maximum, then this is where the pressure is minimum, not maximum as this figure suggests. Could someone ...
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453 views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? ...
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310 views

Quantum Mechanics or Classical Mechanics? [closed]

I'm just a student of grade 11 but, I was interested in knowing about Physics much deeper. In order to start my interest in Physics, I watched this video of Quantum Physics NOVA : Quantum ...
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309 views

How do centripetal forces and gravity work for objects in a rotating cylinder?

The following is a question from a past exam paper that I'm working on, as I have an exam coming soon. I would appreciate any help. A fairground ride takes the form of a hollow, cylinder of radius ...