Mechanics (Dynamics)

COURSE CONTENT

Kinematics of Particles: Introduction to Dynamics, Rectilinear Motion of Particles, Position, Velocity, and Acceleration, Determination of the Motion of a Particle, Uniform Rectilinear Motion, Uniformly Accelerated Rectilinear Motion, Motion of Several Particles, Curvilinear Motion of Particles, Position Vector, Velocity, and Acceleration, Rectangular Components of Velocity and Acceleration, Motion Relative to a Frame in Translation, Tangential and Normal Components, Radial and Transverse Components.

Kinetics of Particles: Newton’s Second Law, Introduction, Newton’s Second Law of Motion, Linear Momentum of a Particle, Rate of Change of Linear Momentum, Equations of Motion, Dynamic Equilibrium, Angular Momentum of a Particle, Rate of Change of Angular Momentum, Equations of Motion in Terms of Radial and Transverse Components, Motion under a Central Force. Conservation of Angular Momentum, Newton’s Law of Gravitation, Trajectory of a Particle under a Central Force, Application to Space Mechanics, Kepler’s Laws of Planetary Motion.

Kinetics of Particles: Energy and Momentum Methods, Introduction, Work of a Force, Kinetic Energy of a Particle, Principle of Work and Energy, Applications of the Principle of Work and Energy, Power and Efficiency, Potential Energy, Conservative Forces, Conservation of Energy, Motion under a Conservative Central Force, Application to Space Mechanics, Principle of Impulse and Momentum, Impulsive Motion, Impact, Direct Central Impact, Oblique Central Impact.

Systems of Particles: Introduction, Application of Newton’s Laws to the Motion of a System of Particles, Effective Forces, Linear and Angular Momentum of a System of Particles, Motion of the Mass Center of a System of Particles, Angular Momentum of a System of Particles about Its Mass Center, Conservation of Momentum for a System of Particles, Kinetic Energy of a System of Particles, Work-Energy Principle. Conservation of Energy for a System of Particles, Principle of Impulse and Momentum for a System of Particles, Variable Systems of Particles, Steady Stream of Particles, Systems Gaining or Losing Mass.

Kinematics of Rigid Bodies: Introduction, Translation, Rotation about a Fixed Axis, Equations Defining the Rotation of a Rigid Body about a Fixed Axis, General Plane Motion, Absolute and Relative Velocity in Plane Motion, Instantaneous Center of Rotation in Plane Motion, Absolute and Relative Acceleration in Plane Motion, Analysis of Plane Motion in Terms of a Parameter, Rate of Change of a Vector with Respect to a Rotating Frame, Plane Motion of a Particle Relative to a Rotating Frame, Coriolis Acceleration, Motion about a Fixed Point, General Motion, Three-Dimensional Motion of a Particle Relative to a Rotating Frame, Coriolis Acceleration, Frame of Reference in General Motion,

Plane Motion of Rigid Bodies: Forces and Accelerations, Introduction, Equations of Motion for a Rigid Body, Angular Momentum of a Rigid Body in Plane Motion, Plane Motion of a Rigid Body. D’Alembert’s Principle, A Remark on the Axioms of the Mechanics

of Rigid Bodies, Solution of Problems Involving the Motion of a Rigid Body, Systems of Rigid Bodies, Constrained Plane Motion.

Plane Motion of Rigid Bodies: Energy and Momentum Methods, Introduction, Principle of Work and Energy for a Rigid Body, Work of Forces Acting on a Rigid Body, Kinetic Energy of a Rigid Body in Plane Motion, Systems of Rigid Bodies, Conservation of Energy, Power, Principle of Impulse and Momentum for the Plane Motion of a Rigid Body, Systems of Rigid Bodies, Conservation of Angular Momentum, Impulsive Motion, Eccentric Impact.

Kinetics of Rigid Bodies in Three Dimensions: Introduction, Angular Momentum of a Rigid Body in Three Dimensions, Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body, Kinetic Energy of a Rigid Body in Three Dimensions, Motion of a Rigid Body in Three Dimensions, Euler’s Equations of Motion, Extension of D’Alembert’s Principle to the Motion of a Rigid Body in Three Dimensions, Motion of a Rigid Body about a Fixed Point, Rotation of a Rigid Body about a Fixed Axis, Motion of a Gyroscope. Eulerian Angles, Steady Precession of a Gyroscope, Motion of an Axisymmetrical Body under No Force.

LEARNING OUTCOMES

The course is the main introductory lesson in the concepts of Dynamic Loading of Structures and the time dependence of the operating loads of a structure.

The course aims to introduce students to the basic concepts of kinematics and the dynamics of a structure.

The solid-body approach is the necessary first step to calculate the operating loads of a structure or a structural component / member.

The course introduces the concepts of kinematic constraints as well as the concepts of load transfer at the joints/connections of the members of a structure.

With the successful completion of the course the learning outcomes are:
• The realization of the time dependence of the operational loads on any structure and the significance of the dynamic characteristics of the mechanical systems in their response.
• The ability to calculate dynamic loads in operating structures and in their members in 2 and 3 dimensions.
• The ability to design and implement trajectories by the members of a structure and to calculate the velocities and accelerations at any point of the structure in 2D and 3D.
• The ability to combine kinematic and dynamic analysis at every step of of the operating envelop, regardless of the potential problem approach (Material Point, System of Material Points, Rigid Body and Systems of Rigid bodies).
• Awareness of the fact that the dynamic loads that will be calculated using the assumption of rigid body are the operating loads of each structure that we want to design and dimension.

This knowledge is necessary and is used in many subsequent courses of Mechanical and Aeronautical Engineering (Strength of Material, Machine Elements, Light weight structures, Material Behavior, Finite Elements Methods for Structural Analysis, Composite Engineering, etc.)