THEORY MECHANICS2Chapter14 D'alembert'sprincipleCollege of Mechanical and VehicleEngineering王晓君
College of Mechanical and Vehicle Engineering 王晓君 Chapter 14 D'alembert's principle THEORY MECHANICS
Chapter14D'alembert'sprinciple> 14. 1 D' Alembert's principle for particles 14.2 D'Alembert's principle for particle systems> 14.3 Simplification of a rigid body inertial force system
➢ 14. 1 D' Alembert's principle for particles ➢ 14. 2 D'Alembert's principle for particle systems ➢ 14. 3 Simplification of a rigid body inertial force system Chapter 14 D'alembert's principle
Chapter14D'alembert'sprincipleGeneraltheorems of dynamicsDynamics of asystemofnonfreeparticlesD'alembert(Also known asS principlestatic methodCharacteristics: To study the problem of dynamics in thesame way that statics studies the problem of equilibrium
Dynamics of a system of nonfree particles General theorems of dynamics D'alembert' s principle Characteristics: To study the problem of dynamics in the same way that statics studies the problem of equilibrium. (Also known as static method) Chapter 14 D'alembert's principle
14.1D'alembert'sprincipleI,The inertia forceLet the particle M with mass m move along the trajectoryshown in the diagram. The main force acting on the particle Mat a certain instant is , the constraint reaction is N, and itsacceleration is a.According to the basic equations of dynamics, _ F gwe havema=F+NVF+N+(-ma)=0rewrite this asaFg =-maDedineFg It's called the inertial force of the particle.The inertial force: the magnitude of avirtual force acting on aparticle is equal to the product of the mass of the particle and themagnitude of its acceleration, in the opposite direction ofitsacceleration
Let the particle M with mass move along the trajectory shown in the diagram. The main force acting on the particle M at a certain instant is , the constraint reaction is , and its acceleration is . m F N a g F M F N a According to the basic equations of dynamics, we have ma F N = + rewrite this as F + N + (−ma) = 0 Dedine F ma g = − The inertial force: the magnitude of a virtual force acting on a particle is equal to the product of the mass of the particle and the magnitude of its acceleration, in the opposite direction of its acceleration. 14.1 D'alembert's principle Ⅰ. The inertia force g F ——It's called the inertial force of the particle
14.1D'alembert'sprincipleII.D'Alembert's principle ofa particleThe inertialforces are introduced into Newton's secondlaw:F+F+Fg =0-D'Alembert'sprincipleofaparticleThat is: at any instant of a particle's motion, the counterforceof theprincipal dynamic constraint acting on the particle and theforce ofinertia assumed on the particle constitute the formalequilibrium force system, which is D'Alembert's principle of theparticle
Ⅱ. D'Alembert's principle of a particle The inertial forces are introduced into Newton's second law： + + = 0 g F FN F ——D'Alembert's principle of a particle That is: at any instant of a particle's motion, the counterforce of the principal dynamic constraint acting on the particle and the force of inertia assumed on the particle constitute the formal equilibrium force system, which is D'Alembert's principle of the particle. 14.1 D'alembert's principle