Courses MA1241 & MA1242 - Classical Mechanics I & II

Course Outline for MA1241

• Introduction.
Mechanics as the basis of Physics.
Description of some modern applications of Mechanics and some topics of current research: Non-linear Dynamics and Chaos; Fluid Dynamics and Turbulence; Non-linear phenomena in Astrophysics; Cosmology and the structure of the Universe.

• Mathematical preliminaries.
Vectors and their role in Mechanics. Elements of vector algebra.

• Kinematics.
Position, velocity, acceleration and how they are related to each other.
Differentiation and integration of vectors.

• Newton's Laws: the foundations of Classical Mechanics.
Description of Newton's three laws of dynamics and their analysis through ideal experiments.
Applications of Newton's laws to elementary physical systems.

• Linear momentum.
Dynamics of multi-particle systems. Centre of mass. Conservation of momentum. Impulse.

• Work and Energy.
Definition of work and the work-energy theorem. Potential and kinetic energy. Conservative and non-conservative forces. Conservation of energy.

• Angular Momentum.
Angular momentum of a point-like mass. Motion with angular momentum. Conservation of angular momentum.

Course Outline for MA1242

• Some mathematical aspects of forces and energy. Gradient. Stokes' Theorem.

• More on Momentum and Energy. Flow of mass: dynamics of systems with varying mass. The rocket equation. Elastic and inelastic collisions. Centre of mass frame.

• More on angular momentum.
Fixed axis of rotation. Motion combining translation and rotation.

• Rigid body motion.
Angular velocity and angular momentum as vectors. The gyroscope, precession.

• Gravity.
Historical background: from Brahe and Kepler to Newton and from Newton to Einstein.
Newton's law of gravitation. Inertial and gravitational mass. Experimental tests. Limits of validity.
Applications: elementary systems; astronomical and astrophysical systems.

• Central forces.
Two-body problem, reduced mass. General properties of central force motion.

• Non-inertial frames and fictitious forces.
Accelerating, but non-rotating frames. Rotating coordinate systems. Centrifugal and Coriolis forces. Tidal forces. Rotating bucket and Mach's principle.
The Equivalence Principle, origins of General Relativity.

Galilean transformations. Principle of Relativity.

• Elements of fluid dynamics.

Back to course home page