All Questions
14
questions
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votes
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answers
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 ...
2
votes
0
answers
151
views
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
views
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, ...
- 1,270
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 ...
- 1,270
2
votes
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 ...
- 1,270
0
votes
1
answer
269
views
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-...
1
vote
0
answers
49
views
How did most of the math and physics formulae that govern our lifestyle and help us in space exploration come into being? [closed]
I realise that this isn't a very academic question, but after watching movies like First Man and Interstellar, it got me wondering:
How did all these formulas that we use on a regular basis come into ...
- 131
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 ...
- 2,283
3
votes
1
answer
420
views
Feynman's Lost Lecture: what is the significance of $\frac{d\mathfrak{v}}{d\theta}=-\frac{GMm}{\left|\mathfrak{L}\right|}\hat{\mathfrak{r}}?$
My question pertains to a fact used by Richard Feynman in his so-called
Lost Lecture. http://books.wwnorton.com/books/Feynmans-Lost-Lecture/.
I have only skimmed the book, so I have much more to learn ...
- 2,015
-2
votes
1
answer
115
views
Spirals in newtonian celestial mechanics?
I know Kepler's laws, Newton's laws, and that conic sections are the trajectories of noncolliding two point masses. But I wonder about a point mass A eventually colliding with point mass B.
In ...
- 926
15
votes
2
answers
512
views
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 ...
- 9,890
-2
votes
1
answer
223
views
Impact of Moon's gravitational pull on Earth [closed]
What speed does the Moon's gravitational pull impart to Earth?
0
votes
1
answer
247
views
Problem: Spectroscopy of a binary system
The Problem is:
For a binary system (2 Stars) with Orbital Period of $P =4.822 days = 416620.8 second$ and inclination $i=90$ and with speeds very less than $3 .10^8 m/s$. Their orbital planes around ...
- 115
12
votes
3
answers
893
views
What could cause an asymmetric orbit in a symmetric potential?
My question can be summarized as:
Given a potential with a symmetry (e.g. $z\rightarrow-z$), should I expect orbits in that potential to exhibit the same symmetry? Below is the full motivation for ...
- 18.5k