# Accession Number:

## AD0483126

# Title:

## FORMAL STABILITY OF HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1966-05-01

# Pagination or Media Count:

## 42.0

# Abstract:

Motion near periodic solutions is characterized by the eigen-values of the linear terms of the differential equation in local coordinates. When these local coordinates have purely imaginary characteristic roots the possibility of stability exists. When these roots are commensurable with the frequency of the periodic solution the system is in general unstable. It was believed that there were an infinite set of algebraic conditions necessary for formal stability. These are herein to reduce to two for a Hamiltonian system with two degrees of freedom. Author

# Descriptors:

- *HAMILTONIAN FUNCTIONS
- *N BODY PROBLEM
- PERIODIC VARIATIONS
- METAMATHEMATICS
- MATRICES(MATHEMATICS)
- STABILITY
- DIFFERENTIAL EQUATIONS
- SURFACES
- BOUNDARY VALUE PROBLEMS
- STEEPEST DESCENT METHOD
- SEQUENCES(MATHEMATICS)
- SERIES(MATHEMATICS)
- MOTION
- CELESTIAL MECHANICS
- FUNCTIONS(MATHEMATICS)
- POLYNOMIALS
- COMPLEX NUMBERS

# Subject Categories:

- Celestial Mechanics
- Theoretical Mathematics
- Mechanics