Linked Questions
29 questions linked to/from Norton's dome and its equation
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Ball spontaneously rolling down hill [duplicate]
I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time.
This leads to some interesting ...
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Do identical starting conditions always lead to identical outcomes?
My friend and I are discussing whether or not physical phenomena are deterministic. Let's say, for example, that we have a 3-dimensional box with balls inside of it upon which no gravitational forces ...
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How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories?
Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the container is ...
- 3,705
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History of interpretation of Newton's first law
Nowadays it seems to be popular among physics educators to present Newton's first law as a definition of inertial frames and/or a statement that such frames exist. This is clearly a modern overlay. ...
user4552
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What situations in classical physics are non-deterministic?
In Sean Carroll's book "The Big Picture," he states (chapter 4, page 35):
Classical mechanics, the system of equations studied by Newton and
Laplace, isn't perfectly deterministic. There are ...
- 3,407
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5
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Infinite series of derivatives of position when starting from rest
Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
- 141
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Reversibility = non-causality. Can this be right?
I read yesterday the Norton Dome's paper, which shows that some Newtonian systems can be non-causal, based on specific solutions of Newton's laws. The author justifies the solutions in very nice, ...
- 3,447
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What's the intuitive reason that phase space flow is incompressible in Classical Mechanics but compressible in Quantum Mechanics?
One of the most important results of Classical Mechanics is Liouville's theorem, which tells us that the flow in phase space is like an incompressible fluid.
However, in the phase space formulation ...
- 10.1k
18
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5
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604
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Does the mass point move?
There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $...
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When can phase trajectories cross?
It's said in elementary classical mechanics texts that the phase trajectories of an isolated system can't cross. But clearly they can, for example for the pendulum, the trajectories look like this:
...
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Paths in phase space can never intersect, but why can't they merge?
Page 272 of No-Nonsense Classical Mechanics sketches why paths in phase space can never intersect:
Problem: It seems to me this reasoning only implies that paths can never "strictly" ...
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Why is classical mechanics determinism based on position and momentum only and not forces and scattering rules?
Consider a closed system (say a box) of $n$ particles. There is a well-known idiom/meme/law in classical mechanics that says that the position and momentum of those $n$ particles is all that is needed ...
- 61
2
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3
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607
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Singularity in Newton's gravitational law [duplicate]
If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite?
May someone please clarify it to me?
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4
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Is Norton's dome valid (or does $\frac{d^2 \vec{p}}{dt^2} = \vec{0} \implies \frac{d^n \vec{p}}{dt^n} = \vec{0} \ \forall \ n > 2$)?
I came across Norton's dome and I don't agree that it proves anything.
First, here's an obviously ridiculous and completely nonsensical example that I constructed from thinking about simple harmonic ...
- 123
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When motion begins, do objects go through an infinite number of position derivatives?
This might be a very vague and unclear question, but let me explain. When an object at rest moves, or moves from point $A$ to point $B$, we know the object must have had some velocity (1st derivative ...
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