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.

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.

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-coordinates. The Gibbs'Appell equations. Acceleration energy. The integral variational principle of Hamilton. The form of the Lagrange function for different mechanical systems and corresponding stationarity conditions. 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 include lectures, computing practice, and consultations. The stress is on understanding during the presentations. Different methods are used for the same system. Numerical and analytical approximations of the solutions are also presented. Computer practice is held in order to visualize learnt concepts, compare efforts needed for simulations and model predictions and investigations of “what if” scenarios. Apart from regular consultations, there are also pre-examination consultations with the direct preparation for the evaluation of the course content understanding, with computer animation and the Internet guide. Practice part of the examination – exercises which were passed during the semester are valid only in the first occurring examination term. Oral part of the examination is only for the students who pass the practical part.