TAILIEUCHUNG - Canonical equations for a constrained mechanical system

In the present work the author proposes a form of canonical equations for a constrained mechanical system applying usefully for holonomic and nonholonomic systems. These equations are constructed by the help of the principle of compatibility [1]. Such a form of canonical equations will be used comfortable for studying dynamic of a multibody system. | Journal of Mechanics, NCNST of Vietnam T. XVI, 1994, No 1 {43- 48) CANONICAL EQUATIONS FOR A CONSTRAINED MECHANICAL SYSTEM DO SANH Hanoi Technology Univers£ty §1. INTRODUCTION In many theoretical studies it is convenient to transform Lagrange's equations to the canonical form where the canonical variables are introduced for substuting the Lagrange's ones. It is a set of 2n variables { qi, pi} (i = 1, n) and in these variables the motion of a system is described by 2n ordinary differential equations of the first order. First, as known the cano~ical equations was established for a conservative holomonic mechanical system, Late~ a similar form was expended for a nonconservative mechanical system and nextly, for a nonholonomic system (the form of canonical equations with undefined multipliers} [2, 3, 8]. However, the above mentioned estsblished form of canonical equations haven't many practice senses. In the present work the author proposes a form of canonical equations for a constrained mechanical system applying usefully for holonomi_c and nonholonomic systems. These equations are constructed by the help of the principle of compatibility [1]. Such a form of canonical equations will be used comfortable for studying dynamic of a multibody system. §2. CANONICAL EQUATIONS FOR A CONSTRAINED MECHANICAL SYSTEM Let us consider a holonomic mechanical system. The position of the system is defined by Lagrange's coordinates qi (i = ~). There exists a force function U of active forces. Hamilton reduced the differential equations of motion to a very significant form called the Hamilton canonical equations. For the aim of establishing canonical equations, instead of variables qi we introduced new variables Pi (i = 1, n), that is: 8T Pi = aqi () where T is the kinetic energy of. the system which is assumed to be positive define quadratic form. The variables Pi are known as impulses and are cOnjugates of the Lagrange's coordinates. Since the highest order of form with .

• Cơ khí - Chế tạo máy
• Journal of Mechanics
• Canonical equations for a constrained mechanical system
• Constrained mechanical system
• Holonomic and nonholonomic systems
• Ordinary differential equations
• Vietnam Journal of Mechanics
• 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
• The cohesive crack growth in concrete beams in bending
• by Fracture mechanics and the finite element method
• The construction of the program CGPTROl
• Investigate two dimensional models
• Journal of technology and science education
• Self assessment exercises in continuum mechanics with autonomous learning
• Self assessment exercises in continuum mechanics
• Self assessment exercises
• Practice GRAPAU of the RIMA Project
• 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
• Flight mechanics experiment onboard nasa’s zero gravity aircraft
• Method to promote STEM
• Microgravity programs with NASA
• Hands on experimental design
• Reduced gravity program with NASA
• Methodology for developing teaching activities and materials
• Developing teaching activities and materials
• Fluid mechanics courses
• Undergraduate engineering programs
• 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