Theoretical Mechanics I

Opublikowano: 04.04.2014 21:58

Subject name Theoretical Mechanics I
Type of subject               Basic
Summary ECTS 5
Form of course 30h lecture, 30h exercises
Lecturer                           Prof. Włodzimierz Kurnik, Ph.D., D.Sc.
A brief outline:
Lecture
  • Subject of Mechanics, its branches and fields. Basic notions, Newton’s laws. Historic outline.
  • Mass geometry. Mass and grawity centers. Moments of inertia of bodies and figures.
  • Statics: models of rigid bodies, forces, constraints and types of supports, geometric and analytical conditions of equilibrium, dry friction and its effects in statics.
  • Kinematics of a particle: position, velocity and acceleration of a particle in Cartesian and cylindrical/polar coordinate systems and in the natural directions.
  • Dynamics of a particle: equations of motion of a free and constrained particle, momentum and angular momentum laws, kinetic energy law.  
  • Dynamics of multiparticle systems: equations of motion, constraints, momentum, angular momentum and kinetic energy laws.
  • Kinematics of a rigid body: description of spatial position of a rigid body, Euler’s angles. Velocities and accelerations of a rigid body in translation, plane motion, rotation about fixed point and fixed axis.
Exercises
  • Calculations of moments of inertia and mass centers of rigid bodies.
  • Solving problems of statics: calculating support and joint forces, equilibrium positions, dry friction effects for rigid bodies and mechanisms.
  • Determining motions, velocities and accelerations of particles in various reference frames.  
  • Deriving differential equations of motion of a free and constrained particle, solving and discussing the results.
  • Making use of momentum, angular momentum and kinetic energy laws to solve dynamical problems of a particle.
  • Solving dynamical problems of multiparticle systems.
  • Calculating positions, velocities and accelerations of points in a rigid body in particular motions: translation, plane motion, rotation about fixed axis and regular precession.
Reference resources Reference resources are available here.