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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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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12 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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2answers
63 views

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
47 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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1answer
62 views

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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1answer
73 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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2answers
150 views

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 ...
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1answer
72 views

Definition of kinetic energy without the second Law of Newton

As I see it, the definition of kinetic energy $$T= {1\over2} m u^2 \text { where $u<<c$}$$ comes by using the definition of work $$W= {\int F\cdot\ dx }$$ and we use for the meaning of ...
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2answers
79 views

Why do particles of equal mass (with one at rest) undergoing elastic collisions scatter at only right angles?

This is from the Section 9.6, page 351 of "Classical Dynamics of Particles and Systems" by Thornton and Marion. By setting a up a system where mass 1 has initial momentum $m_1 u_1$ and mass 2 is at ...
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2answers
279 views

Fluid flow: Force acting on the fluid and the Navier-Stokes equation

Consider a one dimensional fluid flow in a rectangular tube. Typical streams are the poiseuille streams. Consider the case in wich we apply a force on the fluid. The Navier-Stokes equation (for ...
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2answers
94 views

What is the significance of angular frequency $\omega$ with regards to wave functions?

What is the physical significance of $\omega$ in a function like $$ f(x) = Asin(kx + \omega t) $$ The only place that I am familiar with angular frequency is when dealing with circular motion, but ...
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1answer
149 views

What is the physical interpretation of the Poisson bracket [duplicate]

Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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36 views

Ratio between power of chaotic and regular airflow

Turbulent field is created as a result of an impact of an airjet on an edge (the flow velocity is high enough). The field of velocities have a regular and a chaotic component. What I need is to ...
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3answers
106 views

Does the second law of thermodynamics take into consideration of attractive interactions between particles?

If one searches Google or textbooks on 2nd Law of Thermodnamics, one usually finds a statement that is either equivalent or implies the following. The entropy of the universe always increases. But ...
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3answers
155 views

What is a “Reversed Effective Force”?

I have some confusion about the "Reversed effective force" as it appears in the derivation of D'Alembert's principle. In Goldstein d'Alembert's principle is given as: $(F-\dot{p}) \cdot \delta r = ...
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2answers
80 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
2
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2answers
156 views

How do waves have momentum?

A question on a practice test I'm taking is as follows: By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries: A. mass B. energy C. momentum D. ...
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2answers
122 views

Maximum Extension of a Spring [closed]

In the given figure: m= 5kg, F = 30N, K = 700N/m In the figure shown above. the surfaces are friction-less. The blocks are initially at rest and the spring is initially in its natural length. What ...
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2answers
108 views

Phase space Lagrangian?

Reading out of this lecture series we define a phase space Lagrangian $\mathcal L$ to be a function of $4n+1$ variables namely $q,\dot q,p,\dot p,t$. My question is, what space is this function ...
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1answer
82 views

Can we disconnect an object from the pull of gravity using some material? [duplicate]

I have once come across a material/ substance/ compound, or something, that cuts off objects from Earth's gravitational pull. In other words, it would keep the object suspended in the air and will ...
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1answer
65 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
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2answers
537 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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1answer
61 views

When can an autonomous system be written using a Hamiltonian?

If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all ...
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48 views

Higher order principle of isotropy

Let us work with classical mechanics in the substantivalist metaphysics, that is, space and time are seen as absolute. Call $n$-th order of motion any observer such that $n$ is the biggest order of ...
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1answer
87 views

How to find equations of motion when potential is given by inverse-square? [closed]

When potential is $U=-\dfrac{a}{r^2}$ ($a>0$), how can I find $r=r(\phi)$? I'm trying to solve this problem during several hours. From $E=T+U$, and constant angular momentum $L$, I can get the ...
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104 views

When to use Hamiltonian vs Lagrangian?

I currently studying the Lagrangian and Hamiltonian formalisms in classical mechanics, but something I'm not seeing is how do I know which one to use in a given problem? After I find the Lagrangian, ...
2
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1answer
271 views

Lagrangian, Kinetic & Potential energy with two masses connected to three springs

Two masses $m_1$ and $m_2$ are on a frictionless surface. They are connected by three springs with constants $k_1,k_2,k_3$. $k_1$ and $k_3$ are attached to walls and $k_2$ is between the masses. $k_1$ ...
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1answer
65 views

Does it take more effort to move against earth's rotation?

I know that if we stand still, we are traveling at 0 m/s relative to the Earth. But if we move against the rotation of the Earth we lower our speed, so, wouldn't we have to fight against the ...
1
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1answer
46 views

Continuity Equation for Momentum

Momentum is a conserved quantity, which makes me wonder if we can write an equation for the local conservation of momentum in the form of a continuity equation. If we're considering a system of ...
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0answers
23 views

Optimal “Blow up” Configuration

Suppose you have three balls glued together. Two are red and one is blue. The system of balls is blown up by an explosion of pure energy (that conserves the center of mass frame) exactly at the ...
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1answer
56 views

Lagrangian formalism (demonstration)

My question is about the multiplicity of the Lagrangian to a Physics system. I pretend to demonstrate the following proposition: For a system with $n$ degrees of freedom, written by the ...
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1answer
70 views

Effect of Eath's rotation on a ball thrown upwards

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
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1answer
23 views

How to visualize the holonormic constraint $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0

A holonormic $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0 appears in Goldstein's Classical Mechanics Pg 12. Where $i$, and $j$ are particles, however $c_{ij}$ is not defined. How someone deduce the ...
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2answers
93 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
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1answer
67 views

What is a point transformation?

This problem comes from Goldstein. What does $s=e^{\gamma t}q$ mean? Do I just put $q=e^{-\gamma t}s$ into the Lagrangian? But I don't know what that means. I think the point transformation may ...
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2answers
215 views

Adding a total time derivative term to the Lagrangian

This is proof that $L'$ represents same equation of motion with $L$ through Lagrange eq. I understand $L'$ satisfies Lagrange eq, but how does this proof mean $L'$ and $L$ describe same motion of ...
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0answers
37 views

What is the conserved quantity?

Lagrangian $$ \mathcal{L}=\frac{1}{2}mv^2-q\Phi + q\textbf{A} \cdot \textbf{v} $$ is invariant under infinitesimal spatial rotation. In the process of calculating $\delta\mathcal{L}$, the term ...
16
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7answers
801 views

Physics of how the cochlea isolates frequencies along its length?

Can anyone explain the separation of frequencies along the basilar membrane of the cochlea please? (equations would be nice) I understand it being related to the resistance caused by fluid in the ...
2
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0answers
48 views

How did Lord Rayleigh find the volume fraction of argon to air?

In order to isolate for pure nitrogen, Lord Rayleigh and his colleagues took some air and removed oxygen, carbon dioxide, and water vapour, leaving behind what he believed to be pure nitrogen. In ...
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38 views

A rod on an inclined plane

(55th Polish Olympiad in Physics) A rod of length $l$ and mass $m$ was lain on an inclined plane of angle $\alpha$, on the altitude $h$ above the floor. (while $h \gg l)$ Describe the rod's ...
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30 views

A free axis of rotation

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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1answer
160 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
1
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2answers
70 views

Metric and the Lagrangian [duplicate]

Does the Lagrangian formalism require a metric on the configuration manifold $Q$ in order to define a Lagrangian $L$ on the tangent bundle $TQ$? Further, if we specify a metric on the tangent bundle ...
2
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4answers
465 views

Is this solveable? Simultaneous elastic collision of 4 objects in XY plane

I'm writing a computer program/game and can't figure something out; I want to be able to calculate the resulting velocities of 4 particles (hexagons, specifically) after they simultaneously ...
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54 views

How does Zeno of Elea's argument on “motion” make sense? [duplicate]

Zeno of Elea (born c. 500 bce) argued so intensely about motion. In one of his arguments he claims – in simple language – "that it is impossible to slap somebody, since the hand first has to travel ...
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1answer
71 views

Every Galilean transformation can be written as the composition of rotation, translation, and uniform motion

Having heard many good things about Arnold's Mathematical Methods of Classical Mechanics, I picked it up and started going through it. While I think I understand all of the definitions he makes, the ...
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1answer
143 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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41 views

Translation of the Mechanique analytique [closed]

Is there an English translation of the Mechanique analytique by Lagrange that is free? I have tried searching up online, however I only get French originals. The English translations seem all to be ...
2
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1answer
326 views

The g-force of common objects hitting the floor

At my friend's work they have an accelerometer which measures the force with which certain objects hit the ground. He claims that from four feet high, cell phones hit a solid metal surface with a ...
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1answer
75 views

Normal force, work and conservativity

I have searched very much on line, both in this site and elsewhere, but found no proof of whether the normal force is conservative or is not, in general. Clearly, if the force is orthogonal to the ...