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47
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6answers
6k views

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 ...
13
votes
2answers
544 views

Can we quantize Aristotelian physics?

Aristotelian physics, shorn of whatever the historical Aristotle actually believed, is pretty similar to Newtonian physics. Instead of "An object in motion stays in motion unless acted on by an ...
8
votes
2answers
352 views

A false proof of drag force being conservative

Consider a particle moving along some trajectory in the $x$-$y$ plane, in a viscous medium. Then its equation of motion is given by: $$\mathbf{F}_d = - b \mathbf{v} .$$ it's well-known from the ...
8
votes
1answer
263 views

Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + \sum_{i}\...
8
votes
2answers
729 views

Hysteresis and dissipation

Hysteretic phenomena are often linked to dissipation. When there is an hysteresis loop, the dissipated energy can usually be computed as the area of the cycle. For example, in ferromagnetic materials,...
7
votes
4answers
1k views

Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
7
votes
2answers
250 views

Damped oscillator: time-reversal, time-translation and dissipation

The equation of motion of a damped oscillator $$\frac{d^2x}{dt^2}+\gamma\frac{dx}{dt}+\omega_0^2x=0$$ which is invariant under time-translation $t\rightarrow t+a$, but not under time reversal $t\...
6
votes
5answers
180 views

A conceptual doubt regarding Forced Oscillations and Resonance

While studying about the Resonance and Forced Oscillations, I came across a graph in my textbook that is given below:- Now, the author writes As the amount of damping increases, the peak shifts ...
6
votes
3answers
2k views

An example of non-Hamiltonian systems [closed]

I am preparing for the exam. And I need to know the answer to one question which I can't understand. "Give an example of non-Hamiltonian systems: in case of infinite number of particles; for a finite ...
6
votes
1answer
644 views

Lagrangian and Hamiltonian EOM with dissipative force

I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...
6
votes
2answers
638 views

What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function?

I have a problem with one of my study questions for an oral exam: The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov ...
6
votes
0answers
41 views

Crack pattern of safety glass - what gives rise to spider web-like shape

When (laminated) security or shatter-proof glass fractures, the ensuing crack-pattern is often resembling a spider web, with radial and concentric cracks, see e.g. (Source: http://essentialhommemag....
5
votes
4answers
9k views

Would a pendulum swing indefinitely in a frictionless vacuum?

I am attempting to settle a friendly bet. Would a pendulum swing indefinitely in a hypothetical vacuum (i.e. no air resistance) having a hypothetical frictionless bearing (i.e. no energy lost due to ...
5
votes
3answers
2k views

Liouville's theorem and conservation of phase space volume

It can be proved that the size of an initial volume element in phase space remain constant in time even for time-dependent Hamiltonians. So I was wondering whether it is still true even when the ...
5
votes
2answers
444 views

What physical processes may underly the collisional term in the Boltzmann equation, and how do they increase entropy?

Consider particles interacting only by long-range (inverse square law) forces, either attractive or repulsive. I am comfortable with the idea that their behavior may be described by the collsionless ...
4
votes
2answers
168 views

Orbit in the vacuum

As the space is a vacuum and there is no friction in space, Can we assume that, if we place an object in gravity in exactly the right distance from a planet with gravity and in the right acceleration, ...
4
votes
1answer
3k views

Why does friction produce heat?

What causes two objects sliding against each other to produce heat? Why don't they generate visible light or something else?
4
votes
2answers
304 views

What makes quantum decoherence different from dissipation?

From my understanding quantum decoherence and dissipation are completely different ways of modelling information loss to the environment. Dissipation can be modeled using the Caldeira-Leggett model ...
4
votes
1answer
169 views

Is a particle subject to dissipation proportional to its velocity a Hamiltonian system?

Why or why not? I'm pretty sure that this isn't a Hamiltonian system because it involves a dissipation term, but using the Hamiltonian flow it gives me that the system is Hamiltonian.
3
votes
1answer
170 views

What is the physical interpretation of the linear coefficient in this ODE for projectile motion?

For the second order ODE governing the position of a projectile subject to air resistance $$ m\frac{d^2x}{dt^2} +k\frac{dx}{dt}+mg=0 \quad k>0, \> x(0)=0, \> x'(0)=V>0 $$ a non-...
3
votes
2answers
100 views

Dissipative forces and reversible processes

A book that I have contains the following lines: For a process to be reversible, the dissipative forces such as viscosity and friction should be absent. My question is why?
3
votes
1answer
56 views

Lagrangian for second-order system

Given an $n$-dimensional second-order system $$\ddot q^i-\sum_{j=1}^n A^i_j\dot q^j=0,$$ where $A$ is a constant matrix, is it possible to find a Lagrangian such that the above equation is the ...
3
votes
1answer
89 views

Is there an abstract notion of heat within a microscopical system?

The microstates of a system are said to be unobservable. I can introduce the entropy as a measure of the number of microstates, which lead to the same macroscopic variables. So in this detailed ...
3
votes
0answers
47 views

Friction in Lagrangian Method [duplicate]

A uniform, flexible chain of length $l$, mass $m$, hangs off a frictionless table-top of height greater than $l$. The length of the part of rope hanging off is $x$. Gravity accelerates the part of the ...
3
votes
0answers
106 views

Are gravitational waves dissipated and what is the mechanism? [duplicate]

I was amazed by the fact that we have been able to detect gravitational waves created thousands of year before they were observed. My surprise is that any wave phenomena I know it is always dissipated,...
3
votes
0answers
72 views

Liouville's theorem for systems with dissipation described by a single hamiltonian

Following this link, one can treat dissipation in the lagrangian by using a factor $e^{\frac{t \beta}{ m}}$ in addition to the Lagrangian $L_0$ of a system without disspation: $ L_0[q, \dot{q}] = \...
3
votes
1answer
84 views

Intuitive explanation for subsonic Fanno flow

In most situations in physics, the effect of kinetic friction is to reduce the macroscopic kinetic energy of a system and convert it into heat, thereby increasing its temperature. but in the case of ...
2
votes
4answers
163 views

Why current loses its energy?

Can someone explain or give a link to explanation why current looses its energy? For example in simple circuit with lamp. I understand that the energy is spent for heating and lighting. But how ...
2
votes
1answer
117 views

Do time-invariant Hamiltonians define closed systems?

In classical mechanics, every time-invariant Hamiltonian represents a closed dynamical system? Can every closed dynamical system be represented as a time-invariant Hamiltonian? Or are there closed ...
2
votes
1answer
282 views

Mathematical form of chemical potential difference and entropy production

I'm trying to understand the form of the 'force' which drives chemical reactions, ie. the difference in chemical potential, also sometimes called the 'affinity'. $$\Delta \mu = - kT ln \frac{J_+}{J_-}$...
2
votes
0answers
73 views

Quantization of non-variational systems?

In undergraduate courses the introduction to Hamiltonian mechanics usually starts from a Newtonian view point. One has equations of motions of the form (not sure if it is ok to use covariant notation ...
2
votes
0answers
68 views

Wronskian of complex second order linear differential equation

While studying certain analogue gravity models I came across a differential equation of the form: \begin{align} \frac{d^2y}{dz^2} + \omega^2 (z)~ y(z) = 0 \end{align} where $z$ is a complex variable ...
2
votes
3answers
148 views

Where does the energy go when engine braking?

If you're in gear in a car and not accelerating, the car slows down faster than it would from just air resistance and tire deformation. In normal braking, the energy is turned into heat from the brake ...
1
vote
5answers
268 views

What happens to the kinetic energy of a dropped ball when it comes to rest on the ground?

If we want to drop a ball from a height, we calculated that potential energy at bottom is zero and we say it is converted into kinetic energy. At that movement, if it is a kind of sand, we find it ...
1
vote
2answers
151 views

Do transformers lose energy?

EDIT: The title should rather be how/why transformers lose energy My idea of a transformer is that it is composed of two separate wire windings around some metal core. The purpose is to increase/...
1
vote
8answers
464 views

Why not use our own light production to produce new energy instead of wasting it?

Why don't we use our own light production at night (I mean home, buildings, streets,..., lighting) to charge photovoltaic panels instead of wasting it?
1
vote
2answers
234 views

Appearance of the Jerk Term in Dynamics of Mass-Spring-Damper System

I am coming from the computer science territory and have not a long trace in mechanics. My background in derivation of the system dynamics could be summarized with utilization of the ...
1
vote
1answer
159 views

How is energy dissipated in a travelling em wave

How is energy dissipated in a travelling em wave. Will there be any dissipation if it were to travel trough vaccum ?
1
vote
1answer
40 views

What kind of damping is this $F = -ax|x'|$?

From Applied Mathematics by Logan: A mass hanging on a spring is <...> governed by $$mx'' = -ax|x'| - kx$$ where $-ax|x'|$ is a nonlinear damping force. I looked up "nonlinear damping" ...
1
vote
2answers
71 views

Why does a ball eventually stop?

I was wondering, if the force of friction with the ground does not make any work on the ball and just give it the necessary torque to rotate (hence the consideration of static friction coefficient in ...
1
vote
1answer
274 views

Perpetual motion machine with magnets [duplicate]

I have been recently made aware of the following motor, which uses two magnets and a wheel to generate motion, and the creator of this machine claims that this motion is perpetual. Here is a ...
1
vote
3answers
175 views

Diffuse laser light in a surface

Im building a laser target. It consists of a box, with a black plexiglass circle in the center of one of its sides, and a larger white circle around it. The black for the inside shots, and the white ...
1
vote
1answer
274 views

Lagrangian formalism application on a particle falling system with air resistance

I have this problem, with a first-step resolution: $$...$$ So, I just don't know why they put the term $\frac{\partial F}{\partial \dot{z}}$ in Euler-Lagrange's equations. Why? I know that the ...
1
vote
3answers
790 views

Are there any non-dissipative non-conservative forces?

Although the question stands for itself, I would like to know that if the answer has to be no then does any particular law forbids the existence of such forces; and if there are such forces then what ...
1
vote
2answers
301 views

Behaviour of individual terms in Einstein-Smoluchowski fluctuation-dissipation relation

Consider a bath of Brownian particles at temperature $T$. If we sprinkle some larger particles in this (eg: pollen grains in water or dust motes in air), they'll diffuse with diffusion constant $D$ ...
1
vote
1answer
47 views

Help with my bouncy ball lab (I know the factors just not how to approach them) [closed]

In my physics lab we need to determine the factors that account for the energy "loss" during a high bounce ball bounce. I know that energy is "lost" (not really) to heat, air resistance, and sound. ...
1
vote
0answers
137 views

Friction in Lagrangian formulation

We know the Lagrange equations are: $$\frac{\partial \mathcal{L}}{\partial q_i}-\frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\partial \dot{q_i}}\right)=0.$$ Then, when we add friction in there, we ...
1
vote
1answer
101 views

Power of viscous friction on a falling sphere

I have derived a simple model of a rotameter using an homogeneous solid ball in a rigid cone where a fluid flows. I consider 4 forces: Weight, Buyancy, Viscous Friction and Drag. I have written my ...
0
votes
2answers
89 views

Difference between stiffness and damping?

I understand stiffness as the extent to which an object (e.g. a mass spring) resists deformation from an applied force, or the rigidity of an object. And I understand damping as the energy ...
0
votes
3answers
106 views

A moving bus suddenly stops. Is its momentum destroyed?

Absolutely not but how does momentum transfer to surrounding (ground, air particles)?