# The list of topics for the entry exam to the AGH Doctoral School in discipline Electronics and Electrical Engineering

1. Mechanics: The principles of Newton's dynamics. The principle of conservation of momentum. The principle of energy conservation. Number of degrees of freedom of the mechanical system, classification of constraints. Cases of reduction of a general system of forces. Kinematics of a rigid body about a fixed point. Eulerian angles. Methods of generation of equations of motion of multibody systems.

1. Strength of materials: Stress-strain diagrams; the characteristic material properties. Moments of areas: first moment of area, centroid of area, moments of inertia, Steiner theorem. Stress tensor and strain tensor; special causes: plane stress, plane strain, spatial stress state, spatial strain state. Generalized Hooke’s. Stress components under general loading conditions, the definition of principal stresses. Mohr’s circle. Pure bending, internal moment and stress relations, differential equation for the elastic curve of a beam. Circular shafts in torsion – distribution of the shearing stresses, equations for maximum shearing stress and angle of twist in the elastic range. Material effort, strength theories, equivalent stress. Stress concentration phenomenon. Engineering stress and strain vs. true stress and strain. Wöhler curve, fatigue life determination based on nominal stress approach. Stress intensity factor, its role and application in fracture mechanics.

1. Construction and operation of machines: Characteristics of belt drives and their application in machine design. Problems of transmission shafts design and calculations. Design of bolted joints working under static and varying load conditions. Construction of bearing systems with application of rolling-element bearings. Factors influencing the fatigue strength of machine elements. Characteristics of contemporary permanent joints. Strength conditions of statically loaded machine elements. Application and functions of lubricants in machine building.

1. Drive systems: the construction, operation and modelling of electric, hydraulic and pneumatic drives and actuators.
1. Acoustics: The properties of the sound and its sources. Contemporary applications of acoustics. Methods for conditioning of the acoustics of rooms. What is audio engineering for?

1. Robotics: The construction and modelling of robots. Simple and inverse kinematics task. Statics and dynamics problems. Control Systems in Robotics. What is the accuracy and repeatability of the manipulator. What are the Euler angels and what are the advantages of using them to describe the orientation of the effector of the robot. What is the number of degrees of freedom of manipulator.  What are the holonomic constraints and whether the mobile robot can be a holonomic object.

1. Modelling: Linear and nonlinear models of objects mechanical and electrical and technological processes. Classical mechanic, fluid mechanics and thermodynamics problems. Static and dynamic characteristics of dynamic objects (time and frequency domain). Structural dynamics, partial differential equations usage for object modelling. Eigenproblem of the multidimensional objects (mode shapes).