Course detail
Analytical Mechanics and Mechanics of Continuum
FSI-9AMK Acad. year: 2025/2026 Summer semester
The subject consists of tree significantly stand-alone parts.
The first part – Analytical mechanics – describes the mechanical system from the point of variation principles. From them the equations of motion are derived. The mutual equivalence of principles and their equivalence to Newton´s laws are proved.
The second part deals with tensors. It comes out from vector and vector components definition. The calculus rules and some special tensors are defined. The close connection between second order tensors and matrices is presented.
The third part – Mechanics of continuum – consist of classical theory of elasticity and hydromechanics with derivation of basic motion equations. The spreading of tension waves in elastic medium and change of their energy are described. The origin of shock wave in liquid and resultant changes of medium is explained. The attention is paid also to transmission processes in liquid and plain tasks solution.
Language of instruction
Czech
Supervisor
Department
Entry knowledge
Basic knowledge of differential calculus, functions of many variables or complex variable functions.
Rules for evaluation and completion of the course
The exam has a written and an oral part.
Attendance at lectures is not compulsory, but is recommended.
Aims
Analytical mechanics creates an apposite base both the mutual binding bodies system motion solution and understanding the structure of statistic and quantum physics.
The main objective of the mechanics of continuum is to demonstrate the different progress of medium description in comparison with analytical mechanics. In mechanics of continuum we come out from concept of field of proper vector and from the analysis of that field we derive the physical processes and the results of these processes.
In analytical mechanics the students will have a clear idea of practical application of second order Lagarange´s equations for solution of system bodies motion under different type of bonds.
In mechanics of continuum, on the base of theoretical knowledge, they will be cognizant of estimation the shape of tension or flux field and analyse the possibility of critical states generation inside these fields.
The study programmes with the given course
Programme D-IME-P: Applied Mechanics, Doctoral, recommended course
Programme D-ENE-P: Power Engineering, Doctoral, recommended course
Programme D-APM-P: Applied Mathematics, Doctoral, recommended course
Type of course unit
Lecture
20 hours, optionally
Syllabus
Analytical mechanics: Principle of virtual work, d´Alembert´s principle, Lagarange´s equations of second order, the other differential principles. Hamilton´s principle, Hamilton´s function, Hamilton´s canonical equation.
Tensors: Definition of tensor, operations with tensors, isotropic tensors, the second order symmetric tensor, quadric, principal axes of tensor. Characteristics of tensors from point of matrix theory.
Mechanics of continuum: Tensor of tension, tensor of deformation, generalized Hook´s low, elastic body energy, spreading and reflection of tension waves. Basic theorems of liquid kinematics, hydrostatics, basic theorems of liquid dynamics, shock wave in liquid and the origin of discontinuousness. Plane tasks, fluxional function velocity potential, complex potential, and description of plain flux field.