Classical Mechanics And Special Relativity
The course gives a review to the basic principles and introduction to
advanced methods of mechanics, emphasizing the relationship between dynamical
symmetries and conserved quantities, as well as classical mechanics as a
background to quantum mechanics. This course is also designed to help the
student acquire an understanding of the formalism and concepts of relativity as
well as its application to physical problems.
Topics include: Lagrangian mechanics and the variational principle,
central force motion, theory of small oscillations, Hamiltonian mechanics,
canonical transformations, Hamilton-Jacobi Theory, rigid body motion, and
continuous systems, Lorentz transformation among others.
The aim of this
course is to continue with and consolidate the Mechanics studied in level one.
Its ideas link with other courses on oscillations and waves. It further introduces
students to classical dynamics and Special Relativity.
By the end of this
course, the student should be able to:
- Use Newtonian mechanics with forces and torques
to solve problems in Cartesian and curvilinear coordinates.
- Solve mechanics problems using work-energy, and
conservation of energy, momentum and angular momentum.
- Solve and analyze rigid-body problems.
- Solve mechanics problems in non-inertial frames.
- Use Lagrangian mechanics to obtain the equations
of motion for a variety of problems, including the use of generalized
coordinates and cyclic coordinates.
- Use perturbation and similar techniques to
linearize equations of motion to analyze stability and study coupled systems
using normal modes.
- Analyse the Lorentz transformation equation.
- Prepare students for advanced course in
A student completing
the course is expected to demonstrate knowledge and understating of:
§ Newton’s laws of
motion, potentials, conservation of energy, momentum and angular momentum.
§ the postulates of
Special Relativity and their consequences in terms of Time dilation and length
transformations, relativistic kinematics and the relation between mass and
§ problems using the
conservation of angular momentum and total energy
§ problems in
rotating frames identify normal modes for oscillating systems
§ Find normal modes
for systems with many degrees of freedom by applying symmetry arguments and
§ Lagrangian and Hamiltonian formulations of classical