The swinging spring - Invariant curves formed by quasi-periodic solutions. III

Details The swinging spring - Invariant curves formed by quasi-periodic solutions. III The swinging spring - Invariant curves formed by quasi-periodic solutions. III

Jun 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975a%26a....41..187h&link_type=abstract

Astronomy and Astrophysics, vol. 41, no. 2, June 1975, p. 187-198.

Astronomy and Astrophysics

Astrophysics

6

Astrodynamics, Celestial Mechanics, Orbital Mechanics, Springs (Elastic), Invariance, Numerical Stability, Pendulums, Periodic Functions

Scientific paper

Invariant curves in the surface of section y = 0 are presented for the planar spring-pendulum problem. A set of nine energy levels is investigated. At each level, the quasi-periodic solutions are identified with families of symmetric periodic solutions previously obtained. The formation of chains of islands is seen to correspond to the emergence of stable higher order (long-period) periodic solutions. Also, a new form of asymmetric periodic solution with nonperpendicular crossings of the vertical axis was found at the energy level C = - 0.25. This new family of solutions, which resembles the letter u rotated from the vertical through a small angle and then distorted somewhat in the vertical direction, is stable at the energy levels C = - 0.25.

Affiliated with

Also associated with

No associations

Rating

The swinging spring - Invariant curves formed by quasi-periodic solutions. III does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The swinging spring - Invariant curves formed by quasi-periodic solutions. III, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The swinging spring - Invariant curves formed by quasi-periodic solutions. III will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-747968