All Questions
Tagged with celestial-mechanics classical-mechanics
11
questions with no upvoted or accepted answers
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
4
votes
0
answers
129
views
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....
- 449
3
votes
0
answers
43
views
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 ...
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
0
answers
447
views
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 ...
- 139
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
1
vote
0
answers
168
views
Planar Precession Frequency of Orbit
What is the general relation between orbital precession $\Phi$, orbital frequency $\Omega$ and a radial perturbation frequency $\omega$?
For certain cases the answer is "clear", for example:
1) If $\...
- 683
1
vote
0
answers
53
views
Sign of the action for the harmonic osccilator?
I am confused about the derivation of the action $S(x,\mathbf{J})$ for a harmonic oscillator as given at page 219 in "Galactic Dynamics", J.Binney-S. Tremaine, 2nd Ed. 2008. The part of the derivation ...
0
votes
0
answers
113
views
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 ...
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-...
0
votes
0
answers
37
views
How can I measure the stability of a many body gravitational system?
Suppose I have an N body planetary system interacting via gravity. Suppose I know the positions and momenta at t=0. How do I know if this system is stable (indefinitely)? By stable I mean the ...
- 1,601