文档介绍：理论力学 Theoretical Mechanics
运动学第五章点的运动学
力学教研室
Kinematics of a Particle
Kinematics
Introduction
Kinematics is a subject which mainly studies the geometrical characteristics of body’s motion, we just emphasize the equations of motion, path, velocity and acceleration, without considering the corresponding factors, such as force and mass.
Dynamics includes Kinematics and ics, while the kinematics is the basement of Dynamics.
Kinematics
Introduction
The motion is absolute, while the description of motion is relatively, because they are different if the different bodies are chosen as the reference bodies (参考体).
In kinematics, we study the geometrical characteristics of two models: Particle (particle system) and rigid bodies
Reference body, reference frame
Kinematics of a particle
Equation of motion about a particle
Equation of path: 轨迹方程
Equation of motion about a particle
Equation of motion: 运动方程
Kinematics of a particle
Equation of motion - Vector
Equation of motion about a particle
Path of Particle M
OM------ r Radius Vector
Kinematics of a particle
Equation of motion – Rectangular coordinates:
Equation of motion about a particle
Unit vector i, j, k
Remove the coefficient t, we will obtain the equation of path:
Kinematics of a particle
Equation of motion – Curvilinear coordinates:
Equation of motion about a particle
Kinematics of a particle
Sample problem 1
Sample problem 1
Ellipsograph (椭圆规)
Determine the equation of motion and path of point A, B, C, M.
Kinematics of a particle
Sample problem 1
Sample problem 1
Equation of motion A:
Equation of motion B:
Equation of motion M:
Equation of Path M:
Kinematics of a particle
Sample problem 1
Sample problem 1
Equation of Motion C:
Motion path of C is a circle with radius l and center O
Chose the point O’ as the start point of curvilinear coordinate, then the equation of motion C: