 # Module # PHY1020 : Dynamics

• Offered for Year: 2020/21
• Module Leader(s): Dr Cora Uhlemann
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 2 Credit Value: 10 ECTS Credits: 5

#### Aims

To introduce the mathematical methods required for the modelling and description of physical dynamic systems.

Module outline
In mathematics and physics, dynamics is the study of movement and change over time, in ways that can be described by mathematical equations or systems of equations. The aim is to explain and predict past and future patterns using basic principles of mathematics. Objects of interest might be tiny particles or huge stars, there might be a single object or very many. In addition to working in normal physical space, solving problems with differential equations (such as Newton's laws), the concept of phase space, which describe all the possible states of a system, is introduced; working in phase space, using geometrical methods, greatly assists in the understanding of dynamical systems.

#### Outline Of Syllabus

Particle dynamics: differentiation and integration of a vector-valued function; position, velocity and acceleration vectors in Cartesian and polar coordinates.

Newton's laws of motion and energetics: forces and linear momentum; angular momentum; kinetic and potential energies; motion under gravity; variable mass problems.

Pendulum motion and phase-space analysis: small amplitude, simple harmonic motion; damped and forced oscillations; introduction to phase-space analysis; large amplitude motion and nonlinear oscillations; 2D motion, double pendulums, and chaos.

Orbital motion: Newton's law of gravity; equations of orbital motion; Kepler's laws.

Multiple particles: two body system including reduced mass; introduction to N-body case; centre of mass.

#### Teaching Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

#### Assessment Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.