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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Finding boundary condition of stationary solid body

A fluid flows past a stationary solid body of arbitrary shape. Write down the boundary condition on the fluid velocity $\textbf u$ for an inviscid fluid and for a viscous fluid, at the solid surface. We ...
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Are one photon at-a-time experiments regarded as the Quantum versions of Classical experiments? [closed]

Is it a correct distinction to regard classical experiments conducted one photon at-a-time as the quantum version of the experiments? For instance, if we take Young's original double-slit, and convert ...
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how are the infinitesimal generators of translation related to the lagrangian?

In studying analytical mechanics (or it's quantum analog), one will come across statements such as: $$f(x^{i}+\delta x^{i})=f(x^{i})+\delta f(x^{i})=f(x^{i})+\frac{\partial f(x^{i})}{\delta x^{i}}\...
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34 views

change of energy in changing frame of reference

Let's imagine a car that can jump onto, or off a moving train. The train moves at 10m/s. The car, on a road next to the train, accelerates to the same 10m/s, jumps off a ramp and lands on the train, ...
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40 views

Probable mistake in the derivation of the vector form of Biot-Savart's Law

In the course of "Classical Electrodynamics", our professor stated Biot-Savart's Law as follows: $$\vec {dB}=\frac{\mu_0}{4\pi}\cdot \frac{i\vec {dl} \times \vec r}{r^3}$$ Then he proceeded to derive ...
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Finding Amplitudes of Resultant Mechanical Waves

Let's say I have two arbitrary mechanical waves $y_1$ and $y_2$ propagating on a string in the same direction. The waves $y_1$ and $y_2$ differ in phase by an arbitrary angle $\phi$ and the ...
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Is there any case in physics where the equations of motion depend on high time derivatives of the position?

For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order ...
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46 views

Natural Frequency and Inertia Tensors

The natural frequency of an oscillating object attached to a torsional spring is obtained by $\omega _n=\sqrt{\frac{k}{I}}$ In the case of single DOF motion, the moment of inertia is simple. ...
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34 views

Confused about shear elasticity and complementary shear stress

I am a self learner of continuum mechanic. I am confused about simple shear stress in situation similar to figure 1, in case $F_\textrm{ext}$ is caused by external perturbation by i.e., human, what ...
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39 views

Why we can use partial derivatives to tell if a force is conservative? [duplicate]

Let us, initially, analysis only a two dimension situation. Assume that $F(x,y)$ is a force dependent on the particle position (give by $x,y$) is proposed that if \begin{equation} \frac{\partial \...
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28 views

Is it true that the free body cannot remain at rest in inhomogeneous and anisotropic space?

In the page 5 of which Mechanics by written L.D.Landau, this book said "If we were to choose an arbitrary frame of reference, space would be in-homogeneous and an-isotropic. This means that, even if a ...
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45 views

Lyapunov exponents of a damped, driven harmonic oscillator

I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by $\ddot{x} + 2\beta \dot{x} + \omega_0^2 x = f\cos(\omega t)$ Lyapunov exponent is $\lambda$ in $\delta x(...
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37 views

Inconsistent Mass matrix in Euler Lagrange dynamics

I am trying to derive Euler Lagrange dynamics of a two body system that is translating and rotating in a plain. First body is given by $(x,z,\theta)$ where $(x,z)$ is position of the center of first ...
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What is the speed of transferring of energy in an inelastic solid? [duplicate]

Assuming that there is an inelastic, very low mass, very long, solid rod which is 150 million km long. This distance requires approximately 8.333 minutes for light to travel. If I apply a force at one ...
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Advantages of Lagrangian Mechanics over Newtonian Mechanics [closed]

Here, I'm going to pose a very serious list of doubts I have on Lagrangian Mechanics. Can we learn Lagrangian Mechanics without studying Newtonian Mechanics? Does Lagrangian help in solving problems ...
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204 views

Why are there only 3 Additive Integrals of Motion?

1. I was reading Landau & Lifschitz's book on Mechanics, and came across this sentence on p.19: "There are no other additive integrals of the motion. Thus every closed system has seven such ...
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Slowly Varying Functions for Adiabatic Invariants - The Same as Karamata's?

In section 49 (and 50) of Landau and Lifschitz's "Classical Mechanics", adiabatic invariants are discussed, which are related to functions which vary adiabatically or "slowly" with time. Admittedly ...
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Understanding potential energy

I am self-studying the classical mechanics using the book by Taylor, and I have a question about the potential energy. The book (pg 111) says: If all forces on an object are conservative, we can ...
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Why is the Virial Theorem not a Special Case of the Ergodic Theorem? What is their Relationship?

The virial theorem involves the time-averages of the potential and kinetic energies if the motion of the system is bounded to a finite region of space. An ergodic theorem relates the time and space ...
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Complete vs General Integral of first order PDE

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics: ... we should recall the fact that every first-order partial differential equation has a solution depending ...
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Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
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Springs and Cantilevers - how linear and repeatable are they under deformation?

I know you guys only deal with the ideal, but in practice how linear and repeatable is the response of a spring or cantilever when deformed under a test mass?
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106 views

Why does holding an object cost energy while no work is being done? [duplicate]

I was reading the discussion here: Why does holding something up cost energy while no work is being done? I feel as though the question is being avoided. Suppose instead of holding an object by hand ...
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67 views

Find the acceleration of the bead [closed]

Two identical, uniform large rings, each of mass $\text{m}$ are connected through a bead of same mass, which can move freely. When bead is released, it starts sliding down. The large rings roll over a ...
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36 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
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Light's inverse square law: Does it require a minimum distance from the source?

Does the inverse square law begin to take effect the moment light leaves its source? For example, does light's intensity decrease, i.e. does the area in which the photons might land increase, at a few ...
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Could 1 force cause a pure moment?

A friend of mine told me if there is only one force, it cannot cause only rotation. I wasn't convinced so I proposed a thought experiment, and now we are both confused. Suppose that we put a rod ( ...
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449 views

Why was the Stark effect discovered much later than the Zeeman effect?

This is strange. The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical ...
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How is it possible to exert a force on a static object?

Assuming mass doesn't change, force is defined as mass * acceleration. Acceleration is the change in velocity as time changes. How is it possible then to exert a force on an object that doesn't move? ...
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Why doesn't a fly fall off the wall?

Pretty simple question, but not an obvious answer at least not to me. I mean you can't just place a dead fly on the wall and expect it to stay there, he will fall off due to gravity. At first I ...
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75 views

Independent canonical coordinate variables?

In Goldstein's Classical Mechanics (2nd ed.) on section 9-1 page 382, there is a discussion about finding a canonical transformation $(q_i,p_i)\rightarrow (Q_j(q_i,p_i,t),P_j(q_i,p_i,t))$ from a given ...
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Stationary-state scattering process

In a stationary-state scattering process of an incoming plane wave, the outgoing spherical wave can be described by $\psi(\vec r) = e^{ikz} + f(\theta) \frac{e^{ikr}}{r}$. My question is, how is this ...
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I dropped my tissue box on a glass table, the box didn't bounce back, table didn't move nor break, what happened?

I have a box, it drops and thus by moving has Kinetic energy, It doesn't penetrate and impacts however the box doesn't rebound nor breaks the table. Its like when I slam my fist on a table but the ...
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46 views

Thermofluid mechanics inclined plane

As shown in the attacked image, a tank has an inclined wall at an angle of 450 to the horizontal. On this wall, there is a 1m square door that is hinged at A and has a simple latch at B. The distance ...
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Spring pendulum system [closed]

Find the Lagrangian and the equations of motion for the system described by the figure using the Lagrange multipliers method. The mass $m$ can slide frictionless along the massless rigid rod of the ...
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2answers
49 views

Creasing of a material at the molecular level

What exactly happens when a material (particularly paper or even cloth or a metal) is folded to form a crease? Why is it that a creased material tends to retain form, while a lightly folded one, '...
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Is it possible to find the G forces of one of the axis rather than the total?

I am investigating the g-forces and acceleration experienced on roller coasters and have data for $x$, $y$ and $z$ acceleration every $0.2$ seconds of the ride as well as the total acceleration and ...
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Eddy current damping heat generation

Background According to this source (page 7): https://deepblue.lib.umich.edu/bitstream/handle/2027.42/109373/me450w10project16_report.pdf?sequence=1 the "braking" torque a magnetic field on a ...
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Question about the apparent loophole in principle of least action

In Lagrangian formalism, given two points $(x_1,t_1)$ and $(x_2,t_2)$, we ask the question which paths $x(t)$ make the action $S=\displaystyle \int_{t_1}^{t_2}L\ \mathrm dt$ stationary and satisfy the ...
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1answer
30 views

How to solve for amplitude w.r.t time for a dad pushing his daughter on the swing with periodic force impulses? [closed]

A Dad is pushing his daughter on a swing. The homogeneous push lasts for α = 10% of the period and is centered around the phase φ = 0. The Fourier series expansion for this is, $$ f(t)=\alpha+\sum_{n=...
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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? Thanks!...
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Density of states and anisotropic distribution functions

We consider a $3D$ dynamical system. Its distribution function is given by the function ${ (\mathbf{x},\mathbf{v}) \mapsto f (\mathbf{x},\mathbf{v})}$, so that $$ \mathrm{d}^{3} \mathbf{x} \, \mathrm{...
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5answers
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Is there a proof from the first principle that the Lagrangian L = T - V?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are ...
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Dynamics of pairwise distances in the $n$-body problem

Consider the $n$-body problem where we are interested in describing the time evolution of $n$ masses interacting through a potential $U$. Let $D$ be the matrix containing all pairwise distances ...
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Coordinate Transformation in Classical Mechanics

The coordinates in one inertial frame are represented by $(x,t)$. Under coordinate transformation, the coordinates in another inertial frame can be represented by $f(x(t),t)$. It can be shown that the ...
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Why rubber is incompressible material?

Why rubber is incompressible material? I know its Poisson's ratio is nearing to 0.5. So I don't understand physically, what it means by 0.5 Poisson's ratio and incompressibility. When I tried ...
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59 views

Born-like measuring rule in classical experiments

this 2011 paper "Born's rule from measurements of classical signals by threshold detectors which are properly calibrated" by Khrennikov investigates the theoretical possibility of Born-like ...
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Different subscripts for $\nabla$ operators while deriving force on system of many particles

Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system: Total (external) force on ...
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How would an increase in temperature affect ooblek's (non newtonian fluid) viscosity?

Due to the fact that Ooblek (cornstarch and water), contains so much water and from what I understand it is non newtonian due to the particles suspended in it, would it therefore be correct to say ...