Differential Equations 1n Celestial Mechanics

  • Form of the Integrals of Planetary Theory
  • THEORIES OF NEWCOMB AND LINDSTEDT**
  • POINCARE’S THEORY
    • POINCARE’s TRANSFORMATION
    • VESSIOT’S TRANSFORMATION
  • BOHLIN’S THEORY
    • POINCARE.’s FORMULATION OF LINDSTEDT’s THEORY***
  • WHITTAKER’S THEORY
    • WHITTAKER’S TRANSFORMATION
    • ADELPHIC INTEGRAL
    • THE THIRD INTEGRAL
    • INTEGRALS DEVELOPABLE ABOUT A SINGULAR POINT
  • ALMOST PERIODIC DIFFERENTIAL EQUATIONS
    • INTEGRAL OF A QUASI-PERIODI FUNCTION
    • SECULAR CONSTANT

Problem of Uniform Convergence

  • BOREL SERIES AND LIOUVILLE NUMBERS
    • BOREL SERIES
    • CLASS OF BAIRE
    • THE QUESTION OF GYLDEN’S PROBABILITY THEOREM
  • REFINEMENT BY PETERSSON AND WINTNER
    • PETERSSON’ S REFINEMENT
    • WINTNER’S DISCUSSION BASED ON THE THEORY OF ALMOST PERIODIC FUNCTIONS
  • TRIGONOMETRIC SERIES
    • TRIGONOMETRIC SERIES
    • SOLUTION BY TRIGONOMETRIC SERIES
    • ELEVATION OF THE DEGREE OF FORMAL CONVERGENCE
    • GROUPING OF TERMS
  • DIVERGENCE OF BOHLIN’S SERIES
    • DIVERGENCE OF LINDSTEDT’ S SERIES
    • DIVERGENCE OF BOHLIN’S SERIES
    • MECHANISM OF DIVERGENCE OF BOHLIN’ S SERIES
  • ASYMPTOTIC INTEGRALS OF LITTLEWOOD
    • LITTLEWOOD’S THEOREMS
    • PROOF OF THE FUNDAMENTAL THEOREM
  • Stability Problem
    • LIAPOUNOV STABILITY
      • DEFINITION OF STABILITY
      • CHARACTERISTIC NUMBERS
      • LIAPOUNov’s DIRECT METHOD
      • CONVERSE OF LIAPOUNOv’s THEOREMS
  • MOTION NEAR AN EQUILIBRIUM POINT
    • BOHL’S THEOREMS
    • ASYMPTOTIC SOLUTIONS
  • PERRON’S STABILITY CRITERION
    • PERRON’S STABILITY CRITERION
    • KINEMATIC SIMILARITY
  • TOPOLOGY OF THE ST ABILITY DOMAIN
    • LINEAR OPERATORS
    • STRONG STABlLITY
    • STABILITY IN ABSTRACT SPACE
    • APPLICATION TO CONTROLS
    • STABILITY OF RIGID·BODY ROTATION