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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Equations of motion for a system of $n$ particles given the potetial [closed]

I am having difficulties on the following question: The equations of motion for a system of n particles are: $$m \ddot{x}_i = - \dfrac{\partial U(x_1,...,x_n)}{\partial x_i}$$ $$\ddot{x}_i = ...
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34 views

What stops the middle point of a power line from falling?

Say you have a system that is a uniformly weighted string with slack suspended from two points; i.e. a power line. There are three forces acting on any given point on this string: string tension ...
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221 views

Why do some impact craters have an elevation in the center?

Why do some impact craters have an elevation in the center? What processes lead to its formation?
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57 views

Decoupling of generalized coordinates in lagrangian

Say you have a lagrangian $L$ for a system of 2 degrees of freedom. The action, S is: $S[y,z] = \int_{t_1}^{t_2} L(t,y,y',z,z')\,dt \tag{1}$ If $y$ and $z$ are associated with two parts of the ...
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62 views

Is there a speed limit for objects falling in gases or liquids? [duplicate]

Let $o$ be a spherical object with mass $m$ and surface $s$. Let $g$ be the gravitational acceleration and $h$ the height. Let the gas where we drop $o$ in have density $d$ and pressure $p$ at ...
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183 views

Is there a rotational equivalent to newtons laws?

Newtons three laws of motion appears to apply only for linear motion: An object remains at rest or moves in a straight line at uniform velocity unless a force is applied. Force is mass times ...
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86 views

Is it true that the self-force prevents a classical particle from falling into a Coulomb potential? What is the physical explanation of this result? [closed]

In 1943 CJ Eliezer published a paper claiming that the self-force prevents a zero angular momentum particle from ever reaching the center of an attractive Coulomb potential (and what's more that it ...
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28 views

Ratio of oscillation amplitudes of a box on a gasket to floor

So the problem is that I have a box and I put it on a gasket to preserve it from vertical oscillations. The gasket is compressed by the box by a quantity of $h$. The floor is oscillating at frequency ...
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70 views

Can you determine acceleration from positions and velocities only?

I just began reading the Landau and Lifshitz book on classical mechanics. It states on the first page of Chapter 1 that: Mathematically, this means that, if all the coordinates $q$ and velocities ...
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53 views

Cart speed and wheel rotation

Say you have a horse drawn cart. Does the outside of the wheel spin at the same velocity that the cart moves forward? The reason I ask is because I am working on a problem where a piece of mud ...
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38 views

Hamiltonian flow?

I was wondering what the Hamiltonian flow actually is? Here is my idea, I just wanted to know if I am correct about this. So let $(x(t),p(t))' = X_{H}(x(t),p(t))$ are the Hamilton's equations and ...
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Mechanical equilibrium : thermodynamics and classical mechanics

A similar question was asked here but mine is a bit different. In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid). In classical mechanics, equilibrium is ...
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Lagrangian $L' = L + \frac{df}{dt}$ gives the same equations of motion

It is well known that when a Lagrangian $L$ is incremented by the total time derivative of a function $f$ that does not depend on the time derivatives of the generalized coordinates, the same ...
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698 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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38 views

How to find the spring coefficient of a simply supported beam?

So I've been searching wikipedia and google but nothing can show how to find the spring coefficient of a simply supported beam with a uniformly distributed load. The spring coefficient, $k$, is ...
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160 views

Can the coefficient of friction be derived from fundamentals?

It is common to want to derive macroscopic laws from what we know microscopically - after all, given a (correct) microscopic description, everything larger should follow. Has it ever been done to ...
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16 views

Does the force of releasing the latch of a spring-latch contraption affects the force generated by the spring?

There is this contraption in my class, where a rod is attached to a latch and a spring. By pulling the latch back behind a piece of metal, the latch is secured, the rod if pulled back and the spring ...
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66 views

Determining the components of the force on a curved surface due to pressure

I have a cross section of a half-tube with a pressure gradient across it causing a force outwards. I am attempting to extract the vertical component (in relation to diagram) of the force on this ...
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60 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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19 views

Motion in a central field in Landau Mechanics

What does this mean when E=U_eff? I don't think this means the first term in E is zero. I don't understand the sentence ' This is a cubic equation for cos(theta)'
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$\mathbf{P}=M\mathbf{v}_{cm}$ for a continuous body?

While restudying some fundamental concepts with greater attention, I have reflected on the following deduction, which I find in my book of mechanics, of the identity of the temporal derivative ...
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Usage of concept of static deflection on classical mechanics (ex. SHM based problems)

Can anyone explain how the concept of static deflection (static displacement) is used in problems of SHM? Explanation by/with an illustration would be even the more helpful. Thank you
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Spring on a rotating disc [closed]

An object (with mass m) is attached with two identic springs (with spring constant k) to the edge and the axis of a rotating disc (with radius r). The object undergoes no friction and is in the middle ...
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48 views

Total angular momentum of a continuous body

I find the definition of total angular momentum $\mathbf{L}$ of a system of $n$ material points with respect to a given point $Q$ as the sum of the momenta $\ell_i=\mathbf{r}_i\times\mathbf{p}_i$ ...
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68 views

Amplitude-phase decomposition as a canonical transformation

I am studying a classical dynamical system defined on $\mathbb{CP}^2$: the phase space is parametrized in terms of three complex coordinates $\psi_i$ ($i=1,2,3$) and Hamilton's equations of motion ...
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116 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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29 views

Acceleration of an oscillating object in a frame of reference that is itself rotating!

I have been reading a paper and due to my limited knowledge of Physics, I can't move ahead. Sorry I do not know latex so, I will snip the paper and paste it here. So here goes it..... I think ...
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Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...
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86 views

How does electromagnetic radiation affect the velocity of a charged particle?

I've heard that the acceleration of a charged particle releases electromagnetic waves. So let's say there is a charged electron moving forwards in a region with a downwards magnetic field. If the ...
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73 views

Interesting approach to Kepler problem

I won't go into the explanation of this idea, because it is explained in this blog post. In this paper, which was featured on John Baez's blog, $\frac {dt}{d\lambda}$ is given as $\frac r V$, where ...
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54 views

How to relate internal energy to atomic motion?

I am trying to conceptualize how atomic motion leads to the thermodynamically-defined internal energy (denoted as $U$ below) through some broad mathematical relationships. I get that the internal ...
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35 views

Thermodynamics of a rubber band

I have a streched rubber band and I know that tension f is proportional to the temperature T when the length is constant. How can I proove that internal energy is only a function of temperature? I ...
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1answer
75 views

General construction of equations of motion for free particles

I've got a question regarding the different Symmetrie-Lie-Groups of Newtonian Mechanics and special realtivity. Is there a canonical way to obtain the equations of motion for a free particle only by ...
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54 views

Classical Hydrogen Atom

I was wondering about the Hamiltonian description of the classical hydrogen atom (two point particles interacting through a Coulumb potential). In particular, I want to know if the fact that ...
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1answer
81 views

Quantum mechanics and Classical limit(s)

I have tried to make sense of this and i am not sure i get it. What i gather from this page about the classical limit is: You need coherent states something like $\hbar \to 0$ is not really enaugh. ...
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27 views

Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
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64 views

Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
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43 views

Particle moving under force $F=-cx^3$ [closed]

A particle with mass $m$ moves under influence of a force $F=-cx^3$, with $c$ a constant. What is the potential energy function $V(x)$? And if it starts to move from rest from position $x=-a$, what ...
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136 views

Thermalization of coupled classical oscillators

I would like to understand if it is possible to perform an experiment, where a bunch of classical harmonic oscillators (e.g., LC circuits or mechanical pendula) coupled in a simple manner (e.g., one ...
2
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1answer
71 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid?

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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239 views

Are there other less famous yet accepted formalisms of Classical Mechanics?

I was lately studying about the Lagrange and Hamiltonian Mechanics. This gave me a perspective of looking at classical mechanics different from that of Newton's. I would like to know if there are ...
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Rain falling into a cart on an incline [closed]

I have a practise question in which a cart on and incline of angle $\alpha$ and starts initially at velocity $v_ 0$. Just as the cart moves off it starts raining vertically and the mass of the rain ...
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50 views

How does one find the phonon frequencies for a 1D anharmonic interaction potential?

Suppose there is a one-dimensional crystal with an anharmonic interaction potential between particles (e.g. $U = ax^2+bx^3$ where $x = d-a$ with $d$ as the distance between two particles and $a$ as ...
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11 views

Good reference on angular motion especially on linear and angular velocity? [duplicate]

I am currently using a book called "Classical Mechanics" by Goldstein, which is a very good text and has amazing introdution to Lagrangian mechanics. Unfortunately not too much is said about angular ...
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Why does the period/frequency of a fan slow down significantly when I taped a piece of rubber band to it?

All of this was done with a standing fan set horizontally on a table. During an experiment, I had to tape a piece of rubber band to one of the standing fan's blade and measured the period of the fan. ...
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1answer
42 views

Which of the Physics textbooks would you recommend I read this quarter (Analytical Mechanics)? [duplicate]

My Analytical Mechanics class this quarter has one required textbook: "Classical Dynamics of Particles and Systems" by Thornton & Marion and three recommended readings: "Mechanics" by Landau ...
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Determine the equation of motion [closed]

The problem is the following. A ring of mass $m=1$ is moving along a circle of radius $R$ without friction. It's tied to a spring (coefficient $k$) of natural length $0$. The other end of the spring ...
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64 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
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Momentum is a cotangent vector?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...