CLASSICAL DYNAMICS

Description

Much of the way that mathematicians model the physical world today relies on the mathematical framework set out by Newton in the 17th century. In this module, we take as our starting point Newton’s laws of motion and examine how they may be applied to study the dynamics of particles and mechanical systems. This module provides a foundation for MAT3008 Lagrangian and Hamiltonian Dynamics. Indicative content includes: Introduction: Vectors and vector differentiation. Frames of reference. Displacement, velocity, acceleration and momentum. Units. Forces: Newton’s laws of motion. Inertial reference frames. Examples of forces such as gravity, normal forces, friction, air resistance and spring tension. Dynamics under forces, e.g. projectile motion, simple harmonic motion and damped simple harmonic motion. Dimensional Analysis: Applications of dimensional analysis in physical real-world systems. Work and Energy: Work done. Kinetic and potential energy. Conservation of energy. Conservative forces and potentials. Systems of Particles: Conservation of momentum. Elastic and inelastic collisions. Angular motion: Polar coordinates. Angular momentum and torque. Central forces. Circular motion. Non-inertial reference frames (if time permits): Newton’s second law in accelerating reference frames. Rotating reference frames. Coriolis and centrifugal forces. This module aims to (1) Introduce students to the mathematical concepts and results in Classical Dynamics including Newton's laws of motion, forces, work and energy, dimensional analysis and reference frames and (2) to enable students to use Newton's laws to analyse physical real-world problems, and solve the resulting ordinary differential equations of motion and interpret the solutions. Attributes Developed 001 Students will understand the concepts of force and momentum. They will understand Newton's laws of motion and be able to apply them to simple mechanical systems. KC 002 Students will be able to calculate simple solutions of the equations of motion, such as projectile motion and the motion of a mass on a spring. KC 003 Students will use dimensional analysis to identify parameters in simple physical real-world systems. KCT 004 Students will understand the concepts work and power, and kinetic and potential energy. They will be able to calculate the work done by a force using line integrals. KC 005 Students will be able to calculate the dynamics of collisions for systems of particles. KC 006 Students will understand the concepts of torque and angular momentum. They will be able to apply Newton's laws of motion for angular motion in rotating systems. KC