Intrinsic stability of periodic orbits

Details Intrinsic stability of periodic orbits Intrinsic stability of periodic orbits

Jun 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..40..111h&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 40, no. 2, 1987, p. 111-153.

Computer Science

7

Numerical Stability, Orbital Mechanics, Orbits, Degrees Of Freedom, Equations Of Motion, Potential Flow, Riccati Equation, Velocity Distribution

Scientific paper

Families of orbits of a conservative, two degree-of-freedom system are represented by an unsteady velocity field with components u(x,y,t) and v(x,y,t). It is shown that a necessary condition for stable periodic orbits is satisfied when the orbit-averaged divergence is zero, which results in bounded normal variations. A sufficient condition for stability is derived from the requirement that tangential variations do not exhibit secular growth. In a steady, divergence-free field, velocity component functions u(x,y) and v(x,y) may be continued analytically from any initial condition, except when velocity is parallel to ∇U or at equilibria. In an unsteady field, the orbit-averaged divergence is zero when the vorticity function is periodic. When such a field exists, initial conditions for stable periodic orbits may be determined analytically.

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