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CONNECTIONS AND GEODESIC CHARACTERISTIC OF EQUATIONSOF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS

Applied Mathematics and Mechanics(English Edition) 1998年第9期19卷 837-842页

作者：罗绍凯郭永新梅凤翔 Shangqiu Teachers College Shangqiu P. R. China Department of Applied Mechanics Peking Institute of Technology Beijing P. R. China

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.

关键词： 1-jet bundle dynamical flow vertical endomorphism connection geodesic

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A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 659-688页

作者： Alexandre CABOUSSAT Roland GLOWINSKI Haute Ecole de Gestion de Genève HES-SO//University of Applied Sciences Department of Mathematics University of Houston

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

关键词： Eikonal equation Minimal and maximal solutions Regularization methods Penalization of equality constraints dynamical flow Operator splitting Finite element methods

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Connections on Phase Space of AutonomousMechanical Systems with Constraints

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Journal of Beijing Institute of Technology 1997年第3期6卷 213-220页

作者：郭永新梅凤翔北京理工大学应用力学系

The covariance of a dynamical flow with respect of a connection on tangent burdle is put forward The connection of an autonomous constrained mechanical system is found whose geodesic equations are equations of motion of the systems The connection is determined by dynamical functions and constraints of the system of the system and is reduced to the usual dynarmical connection of the dynamical flow is second drder homogmogeneous one.

关键词： vertical endomorphism coection dynamical flow geodesic

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