Elements of Theoretical Mechanics 390-ERS-2EMT
Elements of classical mechanics is a one-semester course involving three hours of lectures and three hours of tutorials per week.
The goal of this course is to introduce the Lagrangian and Hamiltonian formulations of classical mechanics, as well as to discuss the basic applications of these formalisms to the description of the dynamics of systems of point masses and rigid bodies.
Lecture topics:
Newtonian dynamics
Conservative forces and energy
Constraints and generalised coordinates
The Principle of Virtual Work
d'Alembert's Principle
Lagrange Equations
Conservation laws
Variational calculus
The Action and Hamilton's principle
Hamilton's canonical equations
The two-body problem
The small oscillations approximation
Rigid body dynamics
The goal of the tutorials is for the students to acquire practial experience and expertise in analysing the motion of classical mechanical systems and developing a modest level of computational proficiency.
Topics discussed:
Review of selected topics in mathematical analysis
Conservative forces and energy
Constraints and generalised coordinates
Lagrange equations
Variational calculus
Hamilton's principle
Hamiltons canonical equations
The two-body problem
Small oscillations
Rigid body dynamics
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
The student understands the notions of: the relativity of motion, reference frame, constraints, forces of reaction, virtual displacements, generalized coordinates. The students is able to introduce generalized coordinates, find the lagrangian and the hamiltonian, and work out the equations of motion. In some cases the student is able to solve these equations and analyse the result.
The student understands the role, origin and meaning of conservation laws and their relation to symmetries.
The student is able to find equilibria of mechanical systems and analyse small oscillations about them; understands the origin of Kepler's laws and the description of planetary orbits; has mastered the basics of classical mechanics to a degree which constitutes a good foundation for future studies.
K_W08
K_W20
K_U03
K_U18
Assessment criteria
Oral examination; the student has to demonstrate both a command of the theory as well as the ability to solve simple problems.
Bibliography
Obligatory:
John R. Taylor, Classical Mechanics (2 volumes)
Suplemental:
L. Landau i E. Lifszyc, Mechanics
H. Goldstein, Theoretical Mechanics
G. L. Kotkin, W.G. Serbo, Problems in classical mechanics
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: