Lectures on Celestial Mechanics

The Three-Body Problem: Covarinace of Lagarangian Derivatives.- Canonical Transformation.- The Hamilton-Jacobi Equation.- The Cauchy-Existence Theorem.- The n-Body Poblem.- Collision.- The Regularizing Transformation.- Application to the Three-Bdy Problem.- An Estimate of the Perimeter.- An Estimate of the Velocity.- Sundman's Theorem.- Triple Collision.- Triple-Collision Orbits.- Periodic Solutions: The Solutions of Lagrange.- Eigenvalues.- An Existence Theorem.- The Convergence Proof.- An Application to the Solution of Lagrange.- Hill's Problem.- A Generalization of Hill's Problem.- The Continuation Method.- The Fixed-Point Theorem.- Area-Preserving Analytic Transformations.- The Birkhoff Fixed-Point Theorem.- Stability: The Function-Theoretic Center Problem.- The Convergence Proof.- The Poincaré Center Problem.- The Theorem of Liapunov.- The Theorem of Dirichlet.- The Normal Form of Hamiltonian Systems.- Area-Preserving Transformations.- Existence of Invariant Curves.- Proof of Lemma.- Application to the Stability Problem.- Stability of Equilibrium Solutions.- Quasi-Periodic Motion and Systems of Several Degrees of Freedom.- The Recurrence Theorem.Kalme, C. I. is the author of 'Lectures on Celestial Mechanics' with ISBN 9783540586562 and ISBN 3540586563.