Part One I › Division II II › Section 126 126

Mechanics of Particles, Rigid Bodies, and Deformable Bodies: Elasticity, Vibrations, and Flow

Subject Outline

AThe principles of classical mechanics
- 1The fundamental parameters and concepts of classical mechanics: matter, space, motion, time
- 2Statics, the equilibrium of systems at rest: force, friction
- 3Dynamics: motion of systems
  - aKinematics: motion of particles and rigid bodies without consideration of the forces producing the motion
    - iVelocity and acceleration
    - iiRotation about a fixed axis
    - iiiMotion in a circular path
    - ivSimple harmonic motion
    - vRelative motion
  - bKinetics: motion of bodies under the action of forces upon them
    - iNewton's laws of motion: the law of inertia, the law of force, the law of action and reaction
    - iiMotion under a constant force
    - iiiBallistics: phenomena and laws of projectiles and their propulsion, flight, and impact
    - ivThe motion of the pendulum
    - vNewton's law of universal gravitation
    - viKepler's laws of planetary motion
  - cImpulse and momentum
  - dWork and power
  - eEnergy
    - iThe concepts of energy and energy conservation
    - iiForms of energy and examples of energy transformations associated with each energy form
    - iiiThe equivalence of mass and energy
  - fThe conservation of momentum
- 4Mechanics of nonrigid bodies
  - aThe collision of bodies or particles: centre of mass system, elastic collisions, inelastic collisions
  - bStiffness in mechanical vibrations
- 5Motion in a rotating frame of reference: inertia forces and Coriolis forces
- 6Mechanics of complex systems
  - aThe principle of virtual work
  - bThe rotation of spinning tops and gyroscopes
  - cThe precession and nutation of rotating bodies
  - dLagrange's and Hamilton's equations of motion
BCelestial mechanics
- 1The scope and history of celestial mechanics
- 2The two-body problem and perturbations that cause the orbits of planets and satellites to deviate from ellipses
- 3The three-body problem
- 4The general n-body problem
CRelativistic mechanics in inertial systems of reference
- 1Mechanical foundations of special relativity
- 2Relativistic kinematics
- 3The relationship between gravitational mass and inertial mass
DThe stress dynamics of elastic materials
- 1The phenomenon of elasticity: stress-strain relationships
- 2Elasticity in viscous and crystalline bodies
- 3Elastic constants
- 4The theory of elasticity: mathematical expressions defining elastic properties
EVibrations of elastic bodies
- 1The nature of vibrations: natural or free vibrations, damped and forced vibrations
- 2Vibrators and their sources of energy
- 3Types of vibrational waves: their properties and modes of propagation
- 4The behaviour of materials undergoing vibration
- 5Detection and utilization of vibrations [see 723.F.6.and 735.K.2.]
FFluid mechanics, including gas dynamics
- 1General properties of fluids, ideal and actual: mechanical and thermodynamic properties
- 2Fluid statics and equilibrium
  - aThe basic equation of fluid statics
  - bFluid forces on plane and curved surfaces: analysis of forces, buoyancy, stability of floating and submerged bodies
- 3Fluids in motion: hydrodynamics and aerodynamics
  - aFrictionless one-dimensional fluid flow
  - bFlow in pipes and channels: laminar flow, turbulent flow, special types of flow
  - cGeneral two- and three-dimensional flow: mathematical conditions, vorticity, boundary layers, drag
  - dCompressible fluid flow: isentropic flow, shock waves
GRheological phenomena: deformation and flow
- 1Continuum mechanics
  - aKinematics of deformation and flow: strain, shear, compression, elongation
  - bDynamics: balance of forces and torques
- 2Constitutive equations: stress-deformation relations in different media
- 3Yield strength of materials: fracture and fatigue