重庆大学机械系统动力学1

1、1ME Graduate Course: Dynamics2Grade In-class Practice (20%) （A project might be included） Final exam (80%)3Reference Books Advanced Engineering Dynamics (2nd Edition, Jerry Ginsberg, Cambridge University Press 1995) PPT (Pay attention to all the examples) Where to find these materials? Password: dy1

2、1114Introductory concepts Dynamics: Kinematics and kinetics of particles, rigid bodies and continua Kinematics: Studies motion without its cause Kinetics: Relates forces and torques to motion5 Foundations of Dynamics Newtons laws I. The existence of inertial reference frame II. In an inertial frame,

3、 F=ma III. Action and reaction forces are equal and act in opposite directions Apply to particles, systems of particles & Rigid bodies/systems of rigid bodies Newtonian mechanics: Motion of bodiesatomic scale Speed of motionsthe speed of light6Two approaches to build equations of motion Vectoria

4、l dynamics Newtons laws Motion is described in physical coordinates and their derivatives Analytical dynamics Lagrangian-Hamiltonian approach (scalar)Newtons laws to obtain equations of motion7)t (kx)t ( xm Newtons laws to obtain equations of motion8)t (kx)t ( xm Solve by assuming that）tsin(A)t ( xn

5、The equation becomes:）tcos(A)t ( xnnThen we will have:）2tsin(A-)t ( xnn ）2tsin(kAtsin(Am-nnnNewtons laws to obtain equations of motion By substituting the initial conditions:910）tsin(A)t ( xnLagranges equations1112What will be covered? Kinematics Particle kinematics Relative motion Kinematics of rig

6、id bodies Analytical Mechanics Vibration Matlab 13Chapter 1. Particle Kinematics Interest is on defining quantities such as position, velocity and acceleration Need to specify a reference frame and a coordinate system in which to actually write the vector expressions. Choose the coordinates naturall

7、y fit known aspects of the motion14Cartesian coordinates151617Cylindrical and polar coordinates18 Unit vectors in terms of i, j, k Position VelocityFor Acceleration 19Spherical Coordinates Position Velocity Acceleration20 Extrinsic coordinate systems Rectangular Cartesian Coordinates Cylindrical Coo

8、rdinates Spherical Coordinates Intrinsic coordinates Path Variables: The definition of the unit vectors and of the position relies on knowledge of the path21Path Variables22)(1lim_0sesrtPs232425Joint Kinematical Descriptions Relation between two sets of orthogonal unit vectors in a plane The velocity may be expressed in terms of either set of unit vectors26 Substitute the relation betwe