Course detail

# Analytical Mechanics and Mechanics of Continuum

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.

Learning outcomes of the course unit

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.

Prerequisites

Basic knowledge of differential calculus, functions of many variables or complex variable functions.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

M. Macur: Úvod do analytické mechaniky a mechaniky kontinua, díl I. a II. VUT v Brně 1995, 1996. (CS)
M. Brdička, L. Samek, B. Sopko: Mechanika kontinua. Academia, Praha 2000. (CS)
J. Horský: Mechanika ve fyzice. Academia, Praha 2001. (CS)
W. Kaufmann: Technische Hydro-und Aeromechanik. Springer-Verlag Berlin/Goettingen/Heidelberg 1958. (DE)
V. Trkal: Mechanika hmotných bodů a tuhého tělesa. Nakladatelství ČSAV, Praha 1956. (CS)
S. S. Bhavikatti: Mechanics of Solids, New Age Int. 2010 (EN)
S.P. Timoschenko, J. Gudier.: Teorija uprugosti. Překlad . Nauka, Moskva 1975. (CS)
S. P. Timoschenko, J. Goodier.: Theory of Elasticity (Third ed.). McGraw-Hill, New York 1970. (EN)
L. Meyrovitch: Analytical Methods in Engineering. New York: Mc.Graw-Hill, 1978. (EN)
G. T. Mase, G. E. Mase: Continuum Mechanics for Engineers (Second ed.). CRC Press 1999 (EN)
H. Goldstein, C. P. Poole, J. L. Safko: Classical Mechanics, Addison Wesley, San Francisco, 2011. (EN)
A. Bertram: Elasticity and Plasticity of Large Deformations - An Introduction (Third ed.). Springer 2012 (EN)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

The exam has a written and an oral part.

Language of instruction

Czech, English

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

Attendance at lectures is not compulsory, but is recommended.

Classification of course in study plans

• Programme D-APM-K Doctoral, 1. year of study, summer semester, 0 credits, recommended
• Programme D-IME-P Doctoral, 1. year of study, summer semester, 0 credits, recommended

• Programme D4P-P Doctoral

branch D-APM , 1. year of study, summer semester, 0 credits, recommended

• Programme D-ENE-P Doctoral, 1. year of study, summer semester, 0 credits, recommended

#### Type of course unit

Lecture

20 hours, optionally

Teacher / Lecturer

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.