tailieunhanh - An algorithm for deriving equations of motion of constrained mechanical system

The article deals with the form of equations of motion of mechanical system with constraints. For holonomic systems the number of differential equation is equal to the degrees of freedom, without regard to the number of chosen coordinates. The possibilities of computer processing (symbolical and numerical) are shown. Two simple examples demonstrate the described technique. | VietRam Journal of Mechanics, NCST of Vietnam Vol. ~1, 1999, No 1 (36 - 44) AN ALGORITHM FOR DERIVING EQUATIONS OF MOTION OF CONSTRAINED MECHANICAL SYSTEM DINH VAN PHONG Hanoi University of Technology, Vietnam ABSTRACT. The article deals with the form of equations of motion of mechanical system with constraints. For holonomic systems the number of differential equation is equal to the degrees of freedom, without regard to the number of chosen coordinates. The possibilities of computer processing (symbolical and numerical) are shown. Two simple examples demonstrate the described technique. 1. Introduction There are a lot of techniques for building equations of motion of mechanical systems. The conventional approaches could be divided into two groups, see .[7], [8]. In the first one, a minimal set of Lagrangian variables, equal to a degree of freedom, is chosen, in order to define the system configuration. The number of differential equations is minimal and equal to a degree of freedom. The drawback of this technique is complexity of equations of motion and even the computer processing {. by recursive algorithm) is time consuming. The second group of methods uses a larger number of coordinates in combination with constraints. The form of system of equations is simple, permitting computer generations. However~ a final mixed system of differential-algebraic equations is large, including not only Lagrangian coordinates, but also so-called Lagrange multipliers. The total equations consist of differential equations which number is equal to number of chosen coordinates, and equations of constraints. In the present paper we will show that it is possible to derive the equations of motion with only a minimum of differential equations. Moreover there exists the possibility of calculation of reaction forces. 2. The form of equations of motion Let us consider the dynamical system with m degrees of freedom. For this system we choose n Lagrangian coordinates qi, i = 1,

• Cơ khí - Chế tạo máy
• Vietnam Journal of Mechanics
• Deriving equations of motion of constrained mechanical system
• The possibilities of computer processing
• Motion of mechanical system
• Symbolical and numerical
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
• Languages Gibian and special operators
• The application FEM
• Betts miller janjic convective parameterization scheme
• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
• The gulf of Tonkin
• The kinetic energy distribution
• Duality in the analysis of responses to nonlinear systems
• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
• Aerodynamics of a wing in surface effect ship
• Theory and experiment
• Wing in surface effect ship
• The aerodynamic characteristics
• The Institute of Mechanics
• The error estimate
• The convergence rate for h
• p refinement
• The finite element analysis
• Three dimensional elastostatic mechanics problems
• Some initial experimental results
• Free water layer formation in horizontal pipes
• Water layer formation
• Hanoi Institute of Mechanics
• Bending vibration of beam elements under moving loads
• Considering vehicle braking forces
• Fluctuations of structures
• Beam elements according
• Continuous element for vibration analysis
• Thick shells of revolution
• Continous Element Method
• Finite element solutions
• Natural frequencies and harmonic responses
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• Buckling analysis of simply supported composite laminates subjected
• In plane compression load
• A novel mesh ffree method
• Alternative numerical technique
• Mesh free method
• A three story building
• Hedge algebras based fuzzy controller
• The structural system
• The El Centro earthquake
• Three story building against earthquake
• Laminar separation phenomenon combining with numerical calculations
• The turbulent separation
• The laminar separation
• Experimental study on mechanical properties
• Three phase polymer composite reinforced
• Glass fibers and titanium oxide particles
• Polymer composite reinforced
• Three phase composite
• Dynamic characteristics of elastically supported beam subjected
• A compressive axial force and a moving load
• The implicit Newmark method
• The Galerkin finite element method
• The axial force
• Eccentrically stiffened functionally graded plates and shallow shells
• Von Karman Donnell sense
• The formulation of governing equations
• The classical shell theory
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Evaluating structural safety based on fuzzy set theory
• Evaluating structural safety
• The fuzzy reliability
• Simple beam structure