A Method for Computing Families of Periodic Orbits Based on Unconstrained Optimization
نویسندگان
چکیده
A new efficient method is presented for the numerical computation of families of periodic orbits of systems with three or more degrees of freedom. This method is based on a well-known procedure using the variational equations as well as on unconstrained optimization techniques. This combination accelerates the convergence of previous schemes. The new composite method has been implemented here on an example of interest to Celestial Mechanics.
منابع مشابه
On the Application of Optimization Methods to the Determination of Members of Families of Periodic Solutions
The techniques used for the numerical computation of families of periodic orbits of dynamical systems rely on predictor-corrector algorithms. These algorithms usually depend on the solution of systems of approximate equations constructed from the periodicity conditions of these orbits. In this contribution we transform the rootfinding procedure to an optimization one which is applied on an obje...
متن کاملA New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems
In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The globa...
متن کاملThe modified BFGS method with new secant relation for unconstrained optimization problems
Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. U...
متن کاملPeriodic Orbits of the N-Body Problem
We give a fast, accurate, and highly convergent algorithm for computing periodic orbits of the N-body problem. The Lindstedt-Poincaré technique from perturbation theory, Fourier interpolation, the dogleg strategy devised by Powell for trust region methods in unconstrained optimization, proper handling of the symmetries of the Hamiltonian, and a simple mechanism to eliminate high frequency error...
متن کاملComputing Periodic Orbits of Nonlinear Mappings through Particle Swarm Optimization
Periodic orbits of nonlinear mappings are very useful for the study of dynamical systems. In this paper, a new approach for computing periodic orbits through the global minimization of a properly defined objective function, using the Particle Swarm Optimization method, is introduced. Experimental results on wellknown and widely used nonlinear mappings indicate that the algorithm is robust, it i...
متن کامل