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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Are time-$t$ maps of a Hamiltonian system with 1 degree of freedom typically twist?

If we take a typical Hamiltonian system $H(q,p)$ with one degree of freedom, and look at its time-$1$ map $(q(0),p(0)) \mapsto (q(t),p(t))$, will it generically satisfy the twist property, e.g. $\...
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134 views

How to properly use Perturbation Theory in classical systems?

Context: If we consider a particle in upwards motion near the Earth's surface and acted by a quadratic drag we get the non-linear eom: $$\frac{dv}{dt}=-g-\frac{b}{m}v^2.$$ We can solve it ...
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2answers
59 views

Is there any general theorem which specifies conditions where the critical solution of an action is unique (for given boundary conditions)? [duplicate]

Consider a classical mechanical system with generalized coordinates $q_i$, $i \in \{1,\dots\,n\}$. And Lagrangian $L$. Given a path $\gamma$ (with coordinates $\gamma_i$) and two times $t_1$ and $t_2$ ...
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Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
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37 views

Photon transmission

I want to know exactly how light travels. Are each photon in a light beam traveling in a cosine function? I'm confused because only when it goes through polarization that it starts to show this type ...
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2answers
64 views

Difference between inviscid and viscous flow

In my lecture notes, I have a load of examples and I want to sort out which egs are viscous flow and which are inviscid flow. It is not always said if the flow is viscous or inviscid. Please can ...
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1answer
34 views

Viscous fluid boundary condition

Consider an incompressible viscous fluid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The flow ...
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77 views

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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37 views

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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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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64 views

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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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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2answers
26 views

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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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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1answer
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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0answers
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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1answer
63 views

Normal reaction [closed]

Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H? I don'...
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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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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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1answer
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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Two axis non linear Inverted Pendulum

I am Electronic Engineering student. Sorry for my english, I am very rusted. I am modeling the inverted pendulum for a Class Project and I wondering if any could answer one question. In this web ...
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0answers
15 views

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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3answers
2k views

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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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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1answer
56 views

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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1answer
44 views

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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2answers
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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17 views

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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1answer
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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1answer
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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2answers
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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4answers
58 views

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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2answers
84 views

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 ( ...
10
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6answers
2k views

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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14 views

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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1answer
98 views

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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1answer
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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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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1answer
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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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0answers
9 views

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 ...
0
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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=...
6
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2answers
944 views

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 ...
3
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2answers
126 views

Stable Sides of Polygon Objects

I have a physics question for you. Let us say a polygon shaped object is stable on a side when the center of mass "falls" inside the base. Is it possible in 2D to build an object that is unstable on ...
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1answer
37 views

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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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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What is the inconsistency between Maxwell's electrodynamics and newtonian mechanics?

As far as I understand, when a modification of a theory is made it is because some observation required this modifcation. Quantum Mechanics is a nice example of that: observations of microscopic ...
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1answer
21 views

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 ...
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2answers
83 views

non constant acceleration problem [closed]

The acceleration of an arrow from a bow falls from $6000m/s^2$ to zero when it leaves the bow after travelling a distance $x=0.75m$. Assuming that this acceleration can be expressed by the linear ...
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1answer
36 views

Regarding $f$ degrees of freedom & $f\!-\!1$ constants & inclusion of these constants

In the classic & famous book "Electromagnetic fields & Interactions" by Richard Becker (Dover publishing), on page 55 (of volume 2) , author says: If the system possesses f degrees of ...