Titlebook: Symplectic Geometric Algorithms for Hamiltonian Systems; Kang Feng,Mengzhao Qin Book 2010 Springer-Verlag Berlin Heidelberg 2010 Contact s

TRACE

Symplectic Difference Schemes for Hamiltonian Systems,e areas and the phase volume. Thus, preserving the canonicity of transition of difference schemes from one time step to the next is also important in the numerical solutions of Hamiltonian systems. The goal of this chapter is to find some simple symplectic schemes, i.e., to identify which one, among

interpose

The Calculus of Generating Functions and Formal Energy,tions is dependent on the chosen coordinates. One would like to know under what circumstance will the construction of generating functions be independent of the coordinates. The generating functions are deeply associated with the conservation laws, so it is important to study their properties and co

思想

Composition Scheme,oint schemes. Here, we only deal with one-step reversible schemes. We will introduce the concept of adjoint methods and some of their properties. We will show that there is a self-adjoint scheme of even order in every method. Using the self-adjoint schemes with lower order, we can construct higher o

maladorit

CARE

Contact Algorithms for Contact Dynamical Systems,ymmetric, but is also a very interesting structure — the contact structure. In this chapter, we apply the ideas of preserving Lie group and Lie algebra structure of dynamical systems in constructing symplectic algorithms for Hamiltonian systems to the study of numerical algorithms for contact dynami

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EVICT

Lee-Variational Integrator,e other hand, motivated by the symplectic property of Lagrangian mechanics, a version of discrete Lagrangian mechanics has been developed and variational integrators that preserve discrete symplectic 2-form have been obtained [., but variational integrators obtained in this way fix the time steps an

albuminuria

Structure Preserving Schemes for Birkhoff Systems,ion of Hamiltonian mechanics. In this chapter, the symplectic geometry structure of Birkhoffian system is discussed, and the symplecticity of Birkhoffian phase flow is presented. Based on these properties, a way to construct symplectic schemes for Birkhoffian systems by the generating function metho

神秘

investigate

Introduction,and even expert systems has been developed. With the development of the modern mechanics, physics, chemistry, and biology, it is undisputed that almost all physical processes, whether they are classical, quantum, or relativistic, can be represented by an Hamiltonian system. Thus, it is important to solve the Hamiltonian system correctly.