SITYOTHEORY MECHANICS1902Theoretical MechanicsCollege of Mechanicaland VehicleEngineeringWangXiaojun
Theoretical Mechanics THEORY MECHANICS College of Mechanical and Vehicle Engineering Wang Xiaojun
Part3DynamicsIntroductionDynamics studies the relationship between the mechanicalmotion ofan objectanditsforce.Mechanicalmodel:particleand particle system(includingrigid body)Two kinds of problems in dynamics:(1) Given the law of motion ofthe object, find the force acting on the object;(2) Given the force acting on the object and the initial conditions of motion, findthemotionlawoftheobject
Part3 Dynamics Introduction Dynamics studies the relationship between the mechanical motion of an object and its force. Mechanical model: particle and particle system (including rigid body). Two kinds of problems in dynamics: （1）Given the law of motion of the object, find the force acting on the object; （2）Given the force acting on the object and the initial conditions of motion, find the motion law of the object
Chapter10Basic equations ofparticle dynamicsFundamental lawofdynamicsDifferentialequations of particlemotionTwokindsofproblemsinparticledynamics
Chapter10 Basic equations of particle dynamics 引 言 • Fundamental law of dynamics • Differential equations of particle motion • Two kinds of problems in particle dynamics
10.1 FundamentallawofdynamicsFirst Law (Law ofinertia)If no force is exerted on any particle, it will remain in its original state of static oruniform motion in a straight lineThe property that a particle keeps its original motion state unchanged is called inertiaIn fact, there is no particle under no force, and if the force system acting on theparticle is the equilibrium force system, it is equivalent to the particle under no forceThe law states that force is what changes the motion of a particleSecondLaw (Law ofrelationshipbetweenforce and acceleration)The acceleration obtained by a particle underforce is directly proportionaltothe force force and inversely proportional to the mass ofthe particle. Thedirectionof accelerationis the same as the directionof force
First Law (Law of inertia) If no force is exerted on any particle, it will remain in its original state of static or uniform motion in a straight line. The property that a particle keeps its original motion state unchanged is called inertia. In fact, there is no particle under no force, and if the force system acting on the particle is the equilibrium force system, it is equivalent to the particle under no force. The law states that force is what changes the motion of a particle. Second Law (Law of relationship between force and acceleration) The acceleration obtained by a particle under force is directly proportional to the force force and inversely proportional to the mass of the particle. The direction of acceleration is the same as the direction of force. 10.1 Fundamental law of dynamics
10.1 Fundamental law of dynamicsFor ma= Fa =mThe above equation is the starting particle for deriving other dynamic equations, which iscalled the fundamental equation of dynamics.When aparticle is acted upon by several forcesat the same time, the above formula F should be understood as the resultant of these forces.parity conservation:1、 The relationship between force and acceleration is instantaneous, that is, the changeofforcetotheparticlemotionstateinacertaininstantisreflectedbytheaccelerationdetermined in that instant. The force does not directly determine the velocity of the particleandthedirectionofthevelocity canbe completely differentfromthedirectionoftheforce2、 If two equal forces act on two particles with different masses, the larger the mass is, thesmaller the acceleration will be.The smaller the mass, the greater the acceleration
m F a = or ma F = The above equation is the starting particle for deriving other dynamic equations, which is called the fundamental equation of dynamics. When a particle is acted upon by several forces at the same time, the above formula should be understood as the resultant of these forces. parity conservation： 1、The relationship between force and acceleration is instantaneous, that is, the change of force to the particle motion state in a certain instant is reflected by the acceleration determined in that instant. The force does not directly determine the velocity of the particle, and the direction of the velocity can be completely different from the direction of the force. 2、If two equal forces act on two particles with different masses, the larger the mass is, the smaller the acceleration will be. The smaller the mass, the greater the acceleration. F 10.1 Fundamental law of dynamics