Module Code - Title:
MS4414
-
THEORETICAL MECHANICS
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
MS4403
MS4613
Rationale and Purpose of the Module:
To introduce students to the fundamental concepts of theoretical mechanics.
To prepare students by developing the basic mathematical skills in theoretical mechanics.
To emphasise applications of vector calculus and ODEs.
Syllabus:
Kinematics: reference frames, motion in one dimension, motion with constant acceleration, kinematics in three dimensions, uniform circular motion, centripetal acceleration
Dynamics: mass, force, NewtonÆs laws of motion, friction, Newton's Law of Gravity, planetary motion
Conservation laws: momentum, angular momentum, energy (kinetic energy, potential energy as gradient of force)
Oscillatory motion: free and forced pendulum, resonance, parametric resonance
Introduction to the Hamiltonian and Lagrangian mechanics
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
1. Understand basic mechanical concepts, such as reference system, velocity, acceleration, force.
2. Understand and be able to apply NewtonÆs Laws.
3. Understand and be able to apply the concepts of momentum and energy and their conservation.
4. Be able to apply NewtonÆs Law of Gravity to basic problems of celestial mechanics.
5. Understand the basic concepts of the Hamiltonian approach to mechanics, such as Hamiltonians, Hamiltonian equations, and Poisson brackets.
6. Understand the basic concepts of the Lagrangian approach to mechanics and its connections with the Hamiltonian approach.
7. Understand the concept of stability and be able to apply it to basic mechanical problems.
Affective (Attitudes and Values)
None
Psychomotor (Physical Skills)
None
How the Module will be Taught and what will be the Learning Experiences of the Students:
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
P. Smith, R. C. Smith (1996)
Mechanics
, Wiley
F. Scheck (1999)
Mechanics: From Newton's Laws to Deterministic Chaos
, Springer
Other Relevant Texts:
Programme(s) in which this Module is Offered:
Semester(s) Module is Offered:
Module Leader:
Eugene.Benilov@ul.ie