MA1242 - Classical Mechanics I & II
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
• Mathematical preliminaries.
Vectors and their role in
Mechanics. Elements of vector algebra.
Position, velocity, acceleration
and how they are related to each other.
Differentiation and integration of
• 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.
• 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
collisions. Centre of mass frame.
• More on angular momentum. Fixed
combining translation and rotation.
• Rigid body motion.
Angular velocity and angular
momentum as vectors. The gyroscope, precession.
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
Applications: elementary systems;
astronomical and astrophysical systems.
• Central forces.
Two-body problem, reduced mass.
General properties of central force motion.
• Non-inertial frames and
Accelerating, but non-rotating
frames. Rotating coordinate systems. Centrifugal and Coriolis forces.
Tidal forces. Rotating bucket and Mach's principle.
Principle, origins of General Relativity.
Principle of Relativity.
• Elements of fluid