COURSE GOALS: The principle objectives of the course Classical Mechanics 2 are the introduction of fundamental laws and methods of classical mechanics, further development of acquired mathematical skills and their applications to selected physical problems, and the preparation of students for more advanced courses in theoretical physics.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics;
1.2. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena);
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem;
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.3. use mathematical methods to solve standard physics problems;
4. COMMUNICATION SKILLS
4.3. present their own research results at education or scientific meetings;
4.4. use the written and oral English language communication skills that are essential for pursuing a career in physics, informatics and education;
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon completing the course Classical mechanics 2, students will be able:
* to derive the equation of motion for a particle in a noninertial system, analyse the effects of noninertial forces, in particular the influence of the Coriolis force on the motion of a particle close to the surface of the Earth;
* to determine the points of equilibrium for a system with an arbitrary number of degrees of freedom, examine their stability and linearize the equations of motion for stable equilibrium points;
* to determine the normal modes for a system of coupled harmonic oscillators, describe the vibrations of molecules, in particular those with two and three atoms, analysing the vibrational modes in one and two atomic 1D crystal lattice.
* to formulate the variational principle, derive Euler-Lagrange equations and apply them to various physical systems, including those with forces of constraints;
* to formulate the D'Alambert's principle and apply it to problems of static equilibrium;
* to discuss Hamilton's formulation of classical mechanics, explain the concept of the phase space and sketch the phase portrait of an arbitrary conservative system with one degree of freedom;
* to understand the concepts of old quantum theory and (phase space quantization).
* to discuss the Hamilton-Jacobi formulation of classical mechanics, construct global constants of motion by separating Hamilton-Jacobi equation and derive the Schrödinger's equation by using the analogy between geometrical and physical optics;
* Motion in a non-inertial frame of reference. The effects of the Coriolis force. Example: a particle falling freely close to the surface of the Earth.
* Oscillations of systems with more than one degree of freedom. Normal modes of oscillations.
* Vibrations of molecules and 1D one and two atomic crystal lattice.
* Variational principle. Lagrange's formulation of classical mechanics. Systems with constraints.
* D'Alambert's principle and conditions for static equilibrium.
* Hamilton's formulation of classical mechanics. Phase space.
* Old quantum theory and quantization of the harmonic oscillator
* Hamilton-Jacobi formulation of classical mechanics. Hamilton-Jacobi equation.
* Geometrical interpretation of the Hamilton-Jacobi function, relation to the geometrical optics. Connections with quantum mechanics.
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend classes, participate actively in solving problems and solve homework. Furthermore, students are required to pass two written examinations during the semester.
GRADING AND ASSESSING THE WORK OF STUDENTS:
At the end of the course a written and oral examination is held for students who have successfully completed the requirements of the course.
- Murray R. Spiegel, ''Theory and problems of Theoretical Mechanics'', Schaum's outline series
- Skripta: T. Nikšić, ''Klasicna mehanika 2'', online.
- H. Goldstein, C. P. Poole, J. L. Safko (2001), ''Classical Mechanics'' (3rd edition ed.). Addison-wesley.