Skip to main content
Physics

Return to Question

Notice added Book Recommendation by Qmechanic♦
added 62 characters in body; edited tags; Post Made Community Wiki
Source Link
Qmechanic ♦
Qmechanic ♦
  • 206.6k
  • 48
  • 566
  • 2.3k

After studying action-angle variables and Eulers two-fixed-center problemEulers two-fixed-center problem in a course on mechanics and symplectic geometry, I understand that a two-fixed-center system is Liouville integrable and therefore (as long as the orbits are bounded) there exists a transformation to action-angle variables.

What I'm wondering is whether there is any book or paper where someone has done this transformation explicitly, or even just explored the question and found that the transformation can't be expressed in terms of elementary/known special functions. Is anybody here aware of such a source?

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 therefore (as long as the orbits are bounded) there exists a transformation to action-angle variables.

What I'm wondering is whether there is any book or paper where someone has done this transformation explicitly, or even just explored the question and found that the transformation can't be expressed in terms of elementary/known special functions. Is anybody here aware of such a source?

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 therefore (as long as the orbits are bounded) there exists a transformation to action-angle variables.

What I'm wondering is whether there is any book or paper where someone has done this transformation explicitly, or even just explored the question and found that the transformation can't be expressed in terms of elementary/known special functions. Is anybody here aware of such a source?

Source Link
Gnome Ann
Gnome Ann
  • 11
  • 1

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 therefore (as long as the orbits are bounded) there exists a transformation to action-angle variables.

What I'm wondering is whether there is any book or paper where someone has done this transformation explicitly, or even just explored the question and found that the transformation can't be expressed in terms of elementary/known special functions. Is anybody here aware of such a source?