Engineering Mechanics II

Aim

The purpose of the course is to give the students an understanding knowledge of the basic laws of rigid body mechanics, and ability to independently apply the laws on concrete problems. After the course the student should:

• Know the definitions of the fundamental concepts used in rigid body mechanics, such as velocity, angular velocity, acceleration, angular acceleration, linear momentum, angular momentum, mass moment of inertia, linear impulse, angular impulse, power, work and energy.
• Be able to derive expressions for, and also compute, the entities above for problems of an engineering nature.
• Be able to draw free body diagrams, formulate kinematic constraint equations, formulate Euler's laws and derive the ordinary differential equations that describe how bodies move.
• Be able to solve these differential equations numerically for mechanical systems with at most three degrees of freedom using MATLAB.
• Be able to perform simpler derivations of results in rigid body mechanics.
• Be able to describe the outcome of simpler mechanical experiments in qualitative terms.
• Be able to identify results that are clearly unreasonable.

Content

Planar kinematics of rigid bodies (veclocity and acceleration relations, instant center of velocity, relative motion). Planar kinetics of rigid bodies (Euler's laws of motion, mass moment of inertia, power, work energy, impulse, angular impulse, impact). Spatial kinematics of rigid bodies (angular velocity vector, velocity and acceleration relations). Spatial kinetics of rigid bodies (Euler's laws of motion, mass moment of inertia matrix, fixed axis rotation, Euler's equations, work, energy, impulse, angular impulse, impact, gyro dynamics).