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ACM20050

Academic Year 2025/2026

Dynamics of Classical Systems (ACM20050)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Assoc Professor Miguel Bustamante
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This course starts by developing the principles of Newtonian Mechanics for particles, systems of particles and rigid bodies. It focuses on applications of Newton's laws with an emphasis on problem solving. Interesting aspects ranging from variational principles to dynamical systems will be considered.

[Introduction to dynamical systems] Systems of coupled ordinary differential equations (linear and nonlinear). Number of degrees of freedom. Nullclines. Fixed points. Constants of motion. Gradient systems. Non-dimensionalization. Linear stability of solutions near fixed points.

[Newton’s laws of motion] Revision of Newton's laws of motion and the concept of kinetic and potential energy. Conservative force fields and conservation of energy. Equilibrium of a particle and stability of equilibrium.

[Central forces and planetary and satellite motion] Motion in a plane is discussed with a focus on central forces. Newton’s law of gravitation. Determination of the orbit from the central force. Kepler’s laws of planetary motion and the motion of satellites.

[Moving coordinate systems] Non-inertial coordinate systems. Rotating coordinate systems. Velocity and acceleration in a moving frame. Coriolis and centripetal acceleration.

[Systems of Particles] Centre of mass. Momentum of a system of particles. Motion of the centre of mass. Angular momentum of a system of particles. Total external moment acting on a system and its relation to the angular momentum.

About this Module

Learning Outcomes:

On completion of this module students should be able to


1. Identify fixed points of nonlinear systems.

2. Use linear stability analysis to classify fixed points.

3. Plot trajectories and phase portraits.

4. Analyse the stability of equilibrium positions of a particle.

5. Solve orbit problems in mathematical terms.

6. Explain the concepts of planetary and satellite orbits including Kepler's laws.

7. Derive expressions for the velocity and acceleration in a rotating frame.

8. Explain the concepts of angular velocity, angular momentum for a system of particles.

9. Understand the relation between the angular momentum and total external moment acting on a system.

Student Effort Hours:
Student Effort Type Hours
Lectures

31
Tutorial

12
Specified Learning Activities

15
Autonomous Student Learning

42
Total

100

Approaches to Teaching and Learning:
Lectures and problem classes (tutorials).

Requirements, Exclusions and Recommendations
Learning Recommendations:

Recommended first modules in Calculus, Linear Algebra, and Differential Equations.


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Closed-book end-of-trimester exam, of 2-hour duration, scheduled by UCD Assessment.
 End of trimester
Duration:
2 hr(s)
 Standard conversion grade scale 40% No
80
 No
Exam (Open Book): Open-book in-class exam during a lecture time slot. Exact date to be defined, from within Weeks 4-5-6. Week 4, Week 5, Week 6 Standard conversion grade scale 40% No
10
 No
Exam (Open Book): Open-book in-class exam during a lecture time slot. Exact date to be defined, from within Weeks 8-9-10. Week 8, Week 9, Week 10 Standard conversion grade scale 40% No
10
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Assoc Professor Anthony Cronin Tutor
Sarah Murphy Tutor

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Fri 14:00 - 14:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 11:00 - 11:50
Spring Tutorial Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Tues 11:00 - 11:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 12:00 - 12:50
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