### Module Details

 The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
 Title CLASSICAL MECHANICS Code MATH228 Coordinator Dr PEL Rakow Mathematical Sciences Rakow@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2023-24 Level 5 FHEQ Second Semester 15

### Aims

To provide an understanding of the principles of Classical Mechanics and their application to dynamical systems.

### Learning Outcomes

(LO1) To understand the variational principles, Lagrangian mechanics, Hamiltonian mechanics.

(LO2) To be able to use Newtonian gravity and Kepler's laws to perform the calculations of the orbits of satellites, comets and planetary motions.

(LO3) To understand the motion relative to a rotating frame, Coriolis and centripetal forces, motion under gravity over the Earth's surface.

(LO4) To understand the connection between symmetry and conservation laws.

(LO5) To be able to work with inertial and non-inertial frames.

(S1) Applying mathematics to physical problems

(S2) Problem solving skills

### Syllabus

Foundations of classical mechanics: Newton's laws of motion, inertial and non-inertial reference frames, energy principles. Applications to simple dynamical systems under various force systems Newton's law of gravitation and its application to motions of planetary bodies and the orbits of satellites. Motion relative to a rotating frame, coriolis and centripetal forces, motion under gravity over the earth's surface,. Rigid body dynamics: centre of mass, angular velocity and momentum principles. Plane motions of laminae, simple 3-dimensional rigid body motions with reference to practical examples such as the orbiting space station, and the axis of rotation of the earth.

### Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH101 Calculus I 2022-23; MATH102 CALCULUS II 2022-23; MATH103 Introduction to Linear Algebra 2022-23

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Final assessment  90    50
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Class test  60    50