Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Analytical Mechanics (17.M44031)

Native organizations units: Chair of Technical Mechanics

Type of studies	Title
Master Academic Studies	Technical Mechanics and Technical Design (Godina: 1, Winter)

General information:

Category	Professional-applicative
Scientific or art field	Mechanics
Interdisciplinary	Yes
ECTS	6

Educational goal:

To learn fundamental principles and methods of analytical mechanics applied to systems with finite number of degrees of freedom; to understand basic notions, definitions and usage of mechanics in problem posing and problem solving tasks; to develop abilities and skills related to applications of contemporary mathematical tools and information technologies in problem solving.

Educational outcome:

Ability to generate dynamical models of multibody systems by different methods recognizing uniqueness of mechanics; to recognize general notions of kinematics and dynamics of systems and its usage in the analysis of motion; possibility to practice individually, work hard, think creatively, communicate with other engineers, show understanding and skills, and apply the collected knowledge to robotic systems regarding simulations of motion and predictions of their behaviour in time domain.

Course content:

General considerations of constrained mechanical systems. Real, possible and virtual displacements. Simultaneous variations: Lagrange's, Jordan's and Gauss's. Lagrange's multipliers. The Lagrange equations of the first kind. Differential variational principles: the D'Alembert-Lagrange principle, Jordan's principle, Gauss's principle. General equation of statics. Generalized coordinates, velocities and accelerations. The D'Alembert-Lagrange principle in terms of generalized coordinates. The Lagrange equations of the second kind for holonomic and nonholonomic systems. The canonical equations of Hamilton. Kane's equations. Quasi-coordiantes. The Gibbs'Appell equations. Acceleration energy. The Udwadia-Kalaba equations. The integral variational principle of Hamilton. The form of the Lagrange function for different mechanical systems and corresponding stationarity conditions. The Poisson brackets. Transformational features of the D'Alembert-Lagrange principle. Noether theorem. Canonical transformations. The Hamilton-Jacobi equation. Basic stability theory. The Lyapunov function. The Lyapunov theorems. Direct methods of variational calculus. Examples start with simple problems and proceed to real engineering applications such as vehicle motion, robotic systems with rigid and flexible segments, application of the Laplace transform method to nonlinear problems.

Teaching methods:

Lectures, presentations of real problems, exercises comprising Mathematica and Matlab tools. Homeworks chosen to check understanding of the introduced both notions and methods. Exam is either classical or given in form of a seminar work where the introduced tools are to be recognized at a chosen paper from leading international journal covering mechanical problems. The latter is to be done through individual work with each student separately. The exam ends with informal talk on introduced notions and methods.

Literature:

Authors	Title	Year	Publisher	Language
F.R. Gantmaher	Analitička mehanika	1965	Naučna knjiga, Beograd	Serbian language
D.R. Merkin	Introduction to the Theory of Stability	1996	Springer-Verlag, Berlin	English
Leipholz, H.	Stability theory	1970	Academic Press, New York	English
Simić, S.	Analitička mehanika	2006	Fakultet tehničkih nauka, Novi Sad	Serbian language
Aleksandar Bakša, Miroslav Vesković	Stabilnost kretanja	1996	Matematički fakultet, Beograd	Serbian language
P.G. Drazin	Nonlinear systems	1992	Cambridge University Press, Cambridge	English
Haug, E.J.	Computer Aided Kinematics and Dynamics of Mechanical Systems, Volume I: Basic methods	1989	Allyn and Bacon, Boston	English
H.K Khalil	Nonlinear systems	2000	Pearson Education Int. Inc., New Jersey	English
B. Brogliato	Nonsmooth mechanics	1999	Springer, London	English