All Questions
Tagged with complex-systems newtonian-mechanics
21 questions
3
votes
1
answer
43
views
Self-confinement of $N$-body gravitational systems
Consider $N=2$ point particles (each having unit mass) interacting via Newtonian gravity in the usual 3-dimensional space. There is a simple criterion to assess whether the system is bounded or not: ...
- 5,244
3
votes
1
answer
41
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Shadowing Lemma and Numerical Integration
Shadowing lemma tells that any pseudo-trajectory (numerically integrated trajectory) from some initial condition $x_0$ is the exact trajectory of a different initial condition $x_1$.
Q: Is this ...
- 61
2
votes
0
answers
87
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Connections between the Classical and Quantum Three-body Problem?
If mathematicians somehow find an exact analytical solution to the three-body problem, would that help solve the Schrödinger equation exactly and analytically for the helium atom?
And more generally, ...
- 129
1
vote
0
answers
48
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Two-body problem + shield
Let us consider two point charges, one positive, one negative, interacting via Coulomb force.
In the absence of any other force, this system constitutes an elementary example of two-body problem, and ...
- 1,252
4
votes
3
answers
318
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Mathematically proving that it is always possible for a rigid body to maintain its rigidity
Consider a rigid body $\mathcal{B}$ modeled by a system of $n$ point masses $B_1,B_2,\dots, B_n$ constrained to keep constant distance from each other. I wonder how it is possible to mathematically ...
- 404
0
votes
2
answers
214
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Dynamics: why do physicists include derivatives like $\dot{\theta}$ in the state space for a system like a pendulum?
I come from statistics, so my experience with physics is spotty, especially on some simple stuff. I have been working on some applications related to control theory lately, and was looking at some ...
- 181
2
votes
1
answer
249
views
How many equations of motion? The higher order derivatives are highly correlated
Note: the bounty text above states "second order linear differential equations". It is an empirical observation that this is the case for the particular system I'm studying, please read &...
- 111
0
votes
0
answers
58
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Stability of deformed planets
Motivated by this question and first line of this answer, I want to ask if we were describe the evolution of an orientable continuous simply connected physical body having mass distribution based on ...
- 8,040
1
vote
1
answer
236
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Are all orbits of the conservative pendulum homoclinic?
I don't understand this statement:
"The homoclinic orbit is characterized by $E = mgl$. When $E < mgl$, the pendulum is tracing other orbits."
If energy is conserved, then $E_0 = E$ ($E$...
- 202
0
votes
1
answer
39
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About natural frequencies in non-excited pendulums and Poincaré sections
How can a Poincaré map be defined for a double pendulum (or Furuta pendulum) when these systems don't have external excitations?
0
votes
1
answer
667
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Is an 'angle of slope' really the same on Earth and Moon? [closed]
I know (and it's easy to proof the formula), that the maximum angle at which an object will stay static on a slope being at an $\alpha$ angle to the ground is
$$\tan \alpha = \mu$$
where $\mu$ is the ...
- 135
0
votes
1
answer
428
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Double Pendulum - equation of angle with respect to time [closed]
First of all I am in grade 12, last year of my IB diploma programme. I'm familiar with derivatives and integrals but nothing as complex as these Lagrangians, Hamiltonians or other university-level ...
8
votes
2
answers
1k
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Will double or triple pendulums sync when they are on a platform they can affect?
what i am talking about is something along the lines of this video, http://www.youtube.com/watch?v=5v5eBf2KwF8
where 30 metronomes sync themselves on a table. Will the same happen with double or ...
- 83
3
votes
3
answers
215
views
Can you remain balanced if your CG passes in front of your toes?
Can you remain balanced if your CG passes in front of your toes? I'm looking at the physics of walking. It's described as a controlled fall for good reason.
What I'm interested in is whether you can ...
- 51.7k
2
votes
1
answer
221
views
Physical interpretation of the canonical scalar product in linear dynamics
Consider a unforced, undamped, linear mechanical system with a finite number of degrees of freedom. Its (second order) dynamical equations can be gathered in a matrix equation
$$M\ddot X + K X=0$$
...
- 744
-1
votes
1
answer
424
views
Time it takes for a mass in a linked pendulum to flip?
I have created Mathematica code that simulates a double pendulum. So I've numerically solved for $\theta_{1}(t)$ and $\theta_{2}(t)$. I have also found the momentum from the Lagrangian as well.
My ...
17
votes
4
answers
13k
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What creates the chaotic motion on a double pendulum?
As we know, The double pendulum has a chaotic motion. But, why is this? I mean, the mass of the two pendulums are the same and they have the same length. But, what makes its motion random?
I'm just ...
- 1,107
2
votes
2
answers
2k
views
Two suns, one moon, and one planet?
I have a question about how would seasons and the moon cycle be affected in a system where one planet orbits Sun #1, and Sun #1 orbits a second sun. Online I found this description:
"Type II: "...
- 21
4
votes
1
answer
3k
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About Poincare section for the double pendulum
I am reading Prof. Louis N. Hand's Analytical Mechanics. In the chapter about chaos, it introduces the concepts of Poincare section based on the example of double pendulum. Also, it plot the section ...
- 2,383
0
votes
1
answer
780
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How to find the value of the parameter a in this transfer function? [duplicate]
Possible Duplicate:
How to find the value of the parameter $a$ in this transfer function?
I am given a transfer function of a second-order system as:
$$G(s)=\frac{a}{s^{2}+4s+a}$$
and I need to ...
- 1,158
1
vote
1
answer
183
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How to find the value of the parameter $a$ in this transfer function?
I am given a transfer function of a second-order system as:
$$G(s)=\frac{a}{s^{2}+4s+a}$$
and I need to find the value of the parameter $a$ that will make the damping coefficient $\zeta=.7$. I am not ...
- 1,158