Algebraic Structure and Poisson’s Integral Theory of f(R) Cosmology

Abstract

In this paper, the algebraic structure and the Poisson's integral theory of f (R) cosmology are presented. Firstly, the Hamilton canonical equations are derived for the system. Secondly, the contravariant algebraic forms of f (R) cosmology are obtained. Thirdly, the Lie algebraic structure admitted and Poisson's integral methods are investigated for f (R) cosmology. Further, the first integrals and solution of f (R) cosmology are given. Finally, an example is given to illustrate the results.

Lie Algebraic Structure and Poisson Conservation Law for One Class of Multi-Dimensional Coupled Oscillators

“…In recent years, the research on the algebraic structure and conservation law of dynamical systems has achieved a series of important results [1][2][3][4]. The results demonstrate that the Lagrange equations and Hamilton equations all have compatible algebraic structure and Lie algebraic structure, and the corresponding Poisson conservation law is also obtained.…”

Algebraic Structure and Poisson Integral Method of Snake-Like Robot Systems

“…Mei and Shi [15] have extended this method to non-holonomic constrained mechanical systems. Fu et al have studied the algebraic structure and Poisson's theory of the relativistic Birkhoffian system, rotational relativistic dynamical system, mechanico-electrical coupling system, and f (R) cosmology system [16][17][18]. In this paper, we make an effort in this direction and demonstrate the applications of the algebraic structure and Poisson's theory of dynamical systems to snake-like robot system.…”