Author | Siegel, Carl Ludwig. author |
---|---|
Title | Lectures on Celestial Mechanics [electronic resource] : Reprint of the 1971 Edition / by Carl Ludwig Siegel, Jรผrgen K. Moser |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-87284-6 |
Descript | XII, 290 p. online resource |
One. The Three-Body Problem -- ยง 1. Covariance of Lagrangian Derivatives -- ยง 2. Canonical Transformation -- ยง 3. The Hamilton-Jacobi Equation -- ยง 4. The Cauchy Existence Theorem -- ยง 5. The n-Body Problem -- ยง 6. Collision -- ยง 7. The Regularizing Transformation -- ยง 8. Application to the Three-Body Problem -- ยง 9. An Estimate of the Perimeter -- ยง 10. An Estimate of the Velocity -- ยง 11. Sundmanโs Theorem -- ยง 12. Triple Collision -- ยง 13. Triple-Collision Orbits -- Two. Periodic Solutions -- ยง 14. The Solutions of Lagrange -- ยง 15. Eigenvalues -- ยง16. An Existence Theorem -- ยง 17. The Convergence Proof, -- ยง18. An Application to the Solutions of Lagrange -- ยง 19. Hillโs Problem -- ยง 20. A Generalization of Hillโs Problem -- ยง 21. The Continuation Method -- ยง 22. The Fixed-Point Method.. - -- ยง 23. Area-Preserving Analytic Transformations -- ยง 24. The Birkhoff Fixed-Point Theorem -- Three. Stability -- ยง 25. The Function-Theoretic Center Problem -- ยง 26. The Convergence Proof -- ยง 27. The Poincarรฉ Center Problem -- ยง 28. The Theorem of Liapunov -- ยง 29. The Theorem of Dirichlet -- ยง 30. The Normal Form for Hamiltonian Systems -- ยง31. Area-Preserving Transformations -- ยง 32. Existence of Invariant Curves -- ยง 33. Proof of the Lemma -- ยง 34. Application to the Stability Problem -- ยง 35. Stability of Equilibrium Solutions -- ยง 36. Quasi-Periodic Motion and Systems of Several Degrees of Freedom -- ยง 37. The Recurrence Theorem