Aims

The aims of the course are to:

• Show how the concepts of kinematics are applied to rigid bodies.
• Explain how Newton's laws of motion and the equations of energy and momentum are applied to rigid bodies.
• Develop an appreciation of the function, design and schematic representation of mechanical systems.
• Develop skills in modelling and analysis of mechanical systems, including graphical, algebraic and vector methods.
• Show how to model complex mechanics problems with constraints and multiple degrees of freedom.
• Develop skills for analyzing these complex mechanical systems, including stability, vibrations and numerical integration.

Objectives

As specific objectives, by the end of the course students should be able to:

• Specify the position, velocity and acceleration of a rigid body using > graphical, algebraic and vector methods.
• Understand the concepts of relative velocity, relative acceleration and instantaneous centres of rigid bodies.
• Apply Newton's laws and d'Alembert's principle to determine the acceleration of a rigid body subject to applied forces and couples, including impact in planar motion.
• Determine the forces and stresses in a rigid body caused by its motion.
• Apply Lagrange's equation to the motion of particles and rigid bodies under the action of conservative forces
• Identification of equilibrium points, and linearization around equilibrium points
• Linearization around equilibrium points to extract stability information, vibrational frequencies and growth rates.
• Use of the "Effective potential'' when J_z is conserved.
• Understand chaotic motion as observed in simple non-linear dynamics systems
• Understand simple gyroscopic motion.

Content

Introduction and Terminology

Kinematics

• Differentiation of vectors (4: pp 490-492)
• Motion of a rigid body in space (3: ch 20)
• Velocity and acceleration images (1: p 124)
• Acceleration of a particle moving relative to a body in motion (2: pp 386-389)

Rigid Body Dynamics

• D'Alembert force and torque for a rigid body in plane motion (4: pp 787-788)
• Inertia forces in plane mechanisms (1: pp 200-206)
• Method of virtual power (4: pp 429-432)
• Inertia stress and bending (1) Ch 5

Lagrange's Equation

• Introduction to  Lagrange's Equation (without derivation)
• Concept of conservative forces
• Application to the motion of particles and rigid bodies under the action of conservative forces

Non-linear dynamics

• Solution of equations of motion for a double pendulum
• Illustration of motion on a phase plane
• Concept of chaos and the sensitivity to initial conditions

Gyroscopic Effect

• Introduction to gyroscopic motion (2: pp 564-571)

REFERENCES

(1) BEER, F.P. & JOHNSTON, E.R. VECTOR MECHANICS FOR ENGINEERS: STATICS AND DYNAMICS
(2) HIBBELER, R.C. ENGINEERING MECHANICS – DYNAMICS (SI UNITS)
(3) MERIAM, J.L. & KRAIGE, L.G. ENGINEERING MECHANICS. VOL.2: DYNAMICS
(4) PRENTIS, J.M. ENGINEERING MECHANICS

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 26/08/2020 09:22