Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

This paper gives a review of integration algorithms for finite dimensional mechanical
systems that are based on discrete variational principles. The variational technique gives a …

The purpose of this paper is to survey some recent advances in variational integrators for
both finite dimensional mechanical systems as well as continuum mechanics. These …

This paper concerns heteroclinic connections and resonance transitions in the planar
circular restricted 3-body problem, with applications to the dynamics of comets and asteroids …

This thesis presents the beginnings of a theory of discrete exterior calculus (DEC). Our
approach is to develop DEC using only discrete combinatorial and geometric operations on …

The use of the symmetries of a physical system in the study of its dynamics has a long
history that goes back to the founders of c1assical mechanics. Symmetry-based tech niques …

We present a theory and applications of discrete exterior calculus on simplicial complexes of
arbitrary finite dimension. This can be thought of as calculus on a discrete space. Our theory …

多柔体系统动力学主要研究由多个具有运动学约束, 存在大范围相对运动的柔性部件构成的动力
学系统的建模, 计算和控制. 多柔体系统不仅具有柔体大变形导致的几何非线性 …

The purpose of this paper is to review and further develop the subject of variational
integration algorithms as it applies to mechanical systems of engineering interest. In …

The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …