[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
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137 views
In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?
I know that force is the negative gradient of the potential:
$$\textbf{f} = -\boldsymbol{\nabla} u$$
where force $\textbf{f}$ is a vector and $u$ is a scalar.
This is a relatively soft question, ...
3
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3answers
1k views
What is the physical meaning of diffusion coefficient?
In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another ...
3
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1answer
375 views
Can relativistic kinetic energy be derived from Newtonian kinetic energy?
Relativistic kinetic energy is usually derived by assuming a scalar quantity is conserved in an elastic collision thought experiment, and deriving the expression for this quantity. To me, it looks ...
3
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1answer
278 views
The form of Lagrangian for a free particle
I've just registred here, and I'm very glad that finally I have found such a place for questions.
I have small question about Classical Mechanics, Lagrangian of a free particle. I just read Deriving ...
3
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2answers
218 views
The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available
If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
3
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2answers
485 views
Classical car collision
I have a very confusing discussion with a friend of mine.
2 cars ($car_a$ and $car_b$) of the same mass $m$ are on a collision course. Both cars travel at $50_\frac{km}{h}$ towards each other.
They ...
3
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1answer
165 views
Quantum $n$-body problem
Is the quantum $n$-body problem as difficult as the classical $n$-body problem?
Or quantum mechanics allows to get a simpler exact solution?
Suppose there are 3 particles with uniform potential ...
3
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1answer
271 views
Finding the tension in rope tied to ladder using the principle of virtual work
A ladder $AB$ of mass $m$ has its ends on a smooth wall and floor (see figure). The foot of the ladder is tied by an inextensible rope of negligible mass to the base $C$ of the wall so the ladder ...
3
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1answer
86 views
Orbits for space missions
I am just wondering say if there is an expedition where some astronauts are sent to the moon, how do they choose the trajectory for the spaceshuttle (or whatnot)? I mean there are many possible ...
3
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2answers
134 views
Does locality emerge from (classical) Lagrangian mechanics?
Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
3
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1answer
382 views
When is the principle of virtual work valid?
The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints.
Goldstein says something I don't understand. He says ...
3
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2answers
178 views
Why doesn't phase space contain acceleration/forces?
I'm watching some Physics lectures on the internet by Leonard Susskind:
http://www.youtube.com/watch?v=pyX8kQ-JzHI&feature=BFa&list=PL189C0DCE90CB6D81&lf=plpp_video
In this lecture, and ...
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2answers
273 views
What are some interesting calculus of variation problems? [closed]
That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
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2answers
444 views
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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3answers
358 views
D'Alembert's Principle: Where does $-Q_j$ come from?
This is a follow-up question to D'Alembert's Principle and the term containing the reversed effective force.
From the second term of Eq. (1.45)
$$\begin{align*}
\sum_i{\dot{\mathbf{p}}_i \cdot ...
3
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1answer
831 views
what is uniform velocity?
i have a very basic question from school days. what does it mean to say an object is moving with uniform speed? it seems to me now that it should be an unit dependent concept.
for example if speed is ...
3
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4answers
371 views
Rolling stone on a frictional surface
Consider a spherical rigid stone rotating with angular velocity $\omega$ being dropped vertically onto a horizontal rigid surface with the coefficient of friction $\mu$. Can the stone roll on the ...
3
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3answers
111 views
Physical interpretation of Poisson bracket properties
In classical Hamiltonian mechanics evolution of any observable (scalar function on a manifold in hand) is given as
$$\frac{dA}{dt} = [A,H]+\frac{\partial A}{\partial t}$$
So Poisson bracket is a ...
3
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1answer
84 views
Calculating the path of a ball with spin moving across a table
A ping pong ball is rolling over a smooth (but not frictionless) table. During its travel, a clockwise spin is placed on the ball. The ball's path is changed to move to the right (in perspective from ...
3
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1answer
227 views
Intuition behind classical virial theorem
I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
3
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1answer
382 views
Differences of behaviour of a particle in a box in quantum theory between that in classic physics
Can anyone help me enlist 3 major differences between the quantum and classical physics of the behaviour of a particle in a box? I would like some insight into the differences without solving PDEs ...
3
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3answers
122 views
Virtual differentials approach to Euler-Lagrange equation - necessary?
I'm currently teaching myself intermediate mechanics & am really struggling with the d'Alembert-based virtual differentials derivation for the Euler-Lagrange equation. The whole notion of, and ...
3
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2answers
205 views
Bowling ball on a rubber sheet
After reading a layman's guide to general relativity, I began to wonder what shape a bowling ball on a large rubber sheet would produce. For simplicity, I would like to assume that Hooke's law applies ...
3
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2answers
191 views
Classical Limit of Commutator
In Dirac's book on quantum mechanics (4th ed., pgs 87-88), he seems to give a very elementary argument as to how the commutator [X,P] reduces to the Poisson brackets {x,p} in the limit h_bar->0. ...
3
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2answers
448 views
Classical Limit of the Feynman Path Integral
I understand that in the limit that h_bar goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...
3
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2answers
353 views
Connections between classical and quantum mechanics?
I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
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2answers
890 views
why is mechanical waves faster in denser medium while EM waves slower?
Why is it that mechanical waves/longitudinal waves/sound travel faster in a denser/stiffer medium as in steel compared to say air, while EM waves/trasverse waves/light travels slower in a (optically) ...
3
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1answer
156 views
How can you tell a model explosion from the real thing?
Movies and TV shows frequently show buildings being bombed, cars blowing up, etc. Frequently these are really explosions of miniatures filmed up close.
Aside from the speed that the explosion ...
3
votes
2answers
351 views
“Work” when biking up a hill
So, when biking, I noticed that when going up hills, it was less tiring if I went up them more quickly. This is not total Work done as is Force * Distance, as that should be the same.
But the longer ...
3
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2answers
132 views
what's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional ...
3
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2answers
72 views
Conservation of Linear Momentum at the point of collision
This is a pretty basic conceptual question about the conservation of linear momentum.
Consider an isolated system of 2 fixed-mass particles of masses $m_1$ and $m_2$ moving toward each other with ...
3
votes
2answers
124 views
A partial differential equation for kinetic energy
The kinetic energy of a point particle of mass $m$ and speed $v$ is $K = \frac{1}{2}mv^2$. An elementary mathematics textbook I saw asked one to show that
$$ \frac{\partial K}{\partial ...
3
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1answer
111 views
all the 1-dimensional problems in newtonian mechanics are solvable?
i mean given a system with a conserved Energy in one dimension
$$ E= \frac{p^{2}}{2m}+V(x) $$
then the 'solution' to this problem is implicitly given by
$$ t(x)= \frac{1}{2m} ...
3
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1answer
155 views
Is there any case in classical mechanics where Newton's (strong) third law doesn't hold?
Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system ...
3
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1answer
279 views
Writing equation for amplitude of driven harmonic oscillator in Lorentzian form
This harmonic oscillator is driven and damped, with the form:
$$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$
Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + ...
3
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1answer
99 views
What are the fields in this problem?
In problem 3 of chapter 2 of Landau Lifshitz "Mechanics," I don't understand the meaning of the fields as defined in the following statement:
Which components of momentum and angular momentum are ...
3
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1answer
173 views
Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?
I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude:
$$F(r, t) = \frac{k}{r^2}e^{-at}$$
...
3
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3answers
235 views
Particles as a limit of classical field theory
A common academic exercise has been to show that classical mechanics is a limit of quantum mechanics, usually by putting $\hbar \rightarrow 0$.
Similarly is it possible to show that a limit to field ...
3
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1answer
270 views
Rotating/Translating Disk
I was trying to understand an aspect of rotational dynamics and thought of a problem to help me learn. I'm sure this problem has been considered by countless people in the past, but I'm having some ...
3
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1answer
476 views
Conservation of linear and angular momentum
Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
3
votes
1answer
256 views
How do you know if a coordinate is cyclic if its generalized velocity is not present in the Lagrangian?
Goldstein's Classical Mechanics says that a cyclic coordinate is one that doesn't appear in the Lagrangian of the system, even though its generalized velocity may appear in it (emphasis mine). For ...
3
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2answers
1k views
Lagrangian of two particles connected with a spring, free to rotate
Two particles of different masses $m_1$ and $m_2$ are connected by a massless spring of spring constant $k$ and equilibrium length $d$. The system rests on a frictionless table and may both oscillate ...
3
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1answer
304 views
A Question about Virtual Work related to Newton's Third Law
In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as,
$$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$
...
3
votes
2answers
237 views
Hamilton's equations in terms of initial conditions
I'm trying to understand the way that Hamilton's equations have been written in this paper. It looks very similar to the usual vector/matrix form of Hamilton's equations, but there is a difference.
...
3
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1answer
764 views
Is it possible to break bulletproof glass with your voice?
In The Adventures of Tintin, an opera singer (the Milanese Nightingale) broke a bulletproof glass case using her voice. Is that scientifically possible?
From the Wikipedia page, a typical bulletproof ...
3
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1answer
157 views
What does this infinitesimal Eulerian change describe?
This is a question I originally posted in math.se which received an answer that was far too mathematically sophisticated for what I wanted; given that basic multivariable calculus was used through out ...
3
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1answer
183 views
Is there a Newton's third law for the em field?
There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges.
Can the same be done in an analagous way to ensure Newton's ...
3
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3answers
187 views
Are quantum mechanics and determinism actually irreconcilable? [closed]
As a preface, I am not a physicist. I'm simply interested in abstract physics and fundamental principles of the universe and such. As such, if you can provide an answer for the layman (as ...
3
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3answers
182 views
Is there a mathematical relationship here or am I looking for relations when there are none?
When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
3
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2answers
767 views
Normal Forces and Ferris Wheels
At the moment, I am reading an example problem regarding what was alluded to in the title. In this example problem, they say, "Based on experiences you may have had on a ferris wheel or driving over ...
