Theoretical Mechanics II

Opublikowano: 01.12.2014 13:35

Subject name Theoretical Mechanics II
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
  • Motion of a particle in a moving reference frame. Velocity and acceleration of a particle in a resultant motion. Coriolis acceleration. Dynamics of relative motion.
  • Dynamics of a rigid body: kinetic energy, momentum and angular momentum laws. Dynamics of a rigid body in translation, plane motion (incl. Dynamics of vehicles), rotation about fixed axis (incl. bearing reactions of unbalancerd rotors) and rotation about fixed point (incl. gyroscopic effect).
  • Elements of analytical mechanics: constraints and generalized coordinates of multibody systems, virtual displacements, virtual work and d’Alembert’s principles. Lagrange’s equations.
  • Impact phenomena. Collision of a particle with a fixed barrier. Collision of two particles. Impact center of a body. Collision of two bodies in plane motions.
  • Dynamics of a particle with variable mass. Equation of motion of a particle with continously varying mass. Examples and applications.
Exercises
  • Determining velocities and accelerations of a particle in its resultant motion.
  • Deriving and solving dynamic equations of relative motion of a particle in a moving reference frame.
  • Calculating velocities and accelerations in a rigid body from the momentum, angular momentum and kinetic energy laws.
  • Determining dynamic bearing reactions of unbalanced rotors.
  • Solving dynamic problems of plane motions of a rigid body (incl. rolling vheel).
  • Deriving dynamic equations of motion of multibody systems by means of Lagrange equations.
  • Solving impact problems of particles and rigid bodies in plane motions.
  • Solving exemplary dynamical problems of a particle with variable mass.