Engineering Mechanics - Dynamics

Aim

The goal of the course is to give the student familarity with the basic laws of dynamics and the skill to apply them independently to actual problems. After the course, the student should be able to:

• Define the basic concepts in mechanical engineering as force, couple, equilibrium, velocity, acceleration, angular velocity, angular acceleration, linear impulse and linear momentum, angular impulse and angular momentum, mechanical work, energy and gyroscopic motion.
• Apply the above concepts and definitions to problems related to engineering mechanics.
• Perform simple derivations of theorems and expressions used in dynamics of particles and dynamics of rigid bodies.
• Draw free body diagrams, formulate kinematic constraints and derive the governing equations for mechanical problems by using Euler laws of motion for rigid bodies.
• Identify calculation results that are clearly incorrect.

Content

Particle kinematics (velocity and acceleration in natural, cartesian, and polar coordinates). Particle kinetics (laws of motion, power, work, energy, impulse, momentum, angular impulse, angular momentum, impacts). Planar kinematics of rigid bodies (veclocity and acceleration relations, instant center of velocity, kinematic constraints). Planar kinetics of rigid bodies (Euler's laws of motion, mass moment of inertia, power, work, energy). Spatial kinematics of rigid bodies (time differentiation in different reference frames, angular velocity vector, angular acceleration vector, velocity and acceleration relations). Spatial kinetics of rigid bodies (Euler's laws of motion, mass moment of inertia matrix, fixed axis rotation, imbalance, gyro dynamics).