All Questions
Tagged with celestial-mechanics classical-mechanics
29
questions
0
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1
answer
269
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Derivation of the equation of a hyperbolic orbit from the conic section expression derived via the orbit equation
So I'm looking to derive the equation of a hyperbolic orbit from the general expression for a conic section $$r=\frac{l}{e\cos\theta+1}$$ that you get out of solving the orbit equation for an inverse-...
CommunityBot
- 1
3
votes
1
answer
429
views
Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?
In the book of Classical Mechanics by Goldstein, at page 88, it is given that:
$$
\frac{d^{2} u}{d t^{2}}+u=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right) .
$$
The preceding equation is such ...
CommunityBot
- 1
15
votes
2
answers
512
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Regularization: What is so special about the Coulomb/Newtonian and harmonic potential?
I wanted to know if the procedure for regularization of the Coulomb potential outlined in Celletti (2003): Basics of regularization theory could be generalized to arbitrary polynomial potentials. So ...
CommunityBot
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3
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43
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Explicit construction of action-angle variables for the two-fixed-centers problem
After studying action-angle variables and Eulers two-fixed-center problem in a course on mechanics and symplectic geometry, I understand that a two-fixed-center system is Liouville integrable and ...
- 207k
5
votes
1
answer
191
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How are Lie series used as canonical transformations in perturbation theory?
I have a few questions on how to use Lie series as a canonical transformation, which are widely used in perturbation theory (celestial mechanics).
I know that these series are related to a Taylor ...
- 2,536
4
votes
0
answers
129
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Why Kepler problem is equivalent to a free particle on 4 dimensional sphere?
In trying to understand Laplace-Runge-Lenz vector, I read in Wikipedia
that the Kepler problem is mathematically equivalent to a particle moving freely on the surface of a four dimensional hypersphere....
- 9,368
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113
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Applications of Hamiltonian formalism in classical or celestial mechanics
I am looking for a reference (or just a brief explanation) to applications of the Hamiltonian formalism to classical mechanics, e.g. to planetary motion.
In all known to me textbooks on classical ...
- 207k
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votes
2
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388
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DART crash on Dimorphos: computation of orbital period change
What is the distribution of expected changes in the period of Dimorphos' orbit around Didymos when the spacevehicle DART crashes against it?
- 1,106
2
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0
answers
151
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Harmonic and subharmonic orbits in central fields
Using Newton's theorem of revolving orbits one can easily obtain orbits for central forces containing inverse cube terms, such as
$$F(r)=F_0(r)+\frac{(1-k^2)|B|}{r^3},$$
from known orbits for $F_0$. ...
- 17.8k
2
votes
2
answers
165
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A doubt in a Wikipedia article discussing Bertrand's theorem
Wikipedia while deriving Bertrands theorem writes after some steps:
...For the orbits to be closed, $β$ must be a rational number. What's more, it must be the same rational number for all radii, ...
- 5,371
2
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1
answer
126
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A doubt in a Wikipedia article discussing Bertrand's Theorem in Central force motion
Wikipedia on Bertrand's theorem, when discussing the deviations from a circular orbit says:
...The next step is to consider the equation for $u$ under small perturbations ${\displaystyle \eta \equiv ...
- 207k
1
vote
1
answer
203
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Bertrands theorem, Hooke's law and closed orbit [closed]
Bertrand's Theorem says: the only forces whose bounded orbits imply closed orbits are the Hooke's law and the attractive inverse square force.
I'm looking at the Hooke's law $f=-k r$ and try to see ...
- 25k
2
votes
2
answers
231
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Is there a variable mass Verlete like integration algorithm?
I'm currently modeling the explosion of a star. For my simulation, I use a Verlete like integration algorithm. This is quite common in celestial mechanics modeling. The thing is that now that I have ...
- 4,276
3
votes
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answers
447
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Story about a mathematician, a dinner party, and the three-body problem
I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
1
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0
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69
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Time taken to collide [duplicate]
Two point masses m1 and m2, separated initially by distance d, move towards each other under mutual gravitational force.
Find the time they take to collide?
The main problem I'm having is to solve the ...
- 111