Computer Science – Numerical Analysis
Scientific paper
Apr 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ap%26ss..61..287k&link_type=abstract
Astrophysics and Space Science, vol. 61, no. 2, Apr. 1979, p. 287-316.
Computer Science
Numerical Analysis
1
Dynamic Response, Gravitational Effects, Motion Stability, Numerical Analysis, Periodic Functions, Elastic Systems, Mesh, Pendulums, Springs (Elastic)
Scientific paper
A systematic and detailed discussion of the 'gravitational' spring-pendulum problem is given for the first time. A procedure is developed for the numerical treatment of non-integrable dynamical systems which possess certain properties in common with the gravitational problem. The technique is important because, in contrast to previous studies, it discloses completely the structure of two-dimensional periodic motion by examining the stability of the one-dimensional periodic motion. Through the parameters of this stability, points have been predicted from which the one-dimensional motion bifurcates into two-dimensional motion. Consequently, families of two-dimensional periodic solutions emanated from these points are studied. These families constitute the generators of the mesh of all the families of periodic solutions of the problem.
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