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Module Title |
Mechanics
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Module Code |
MS339
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School |
School of Mathematical Sciences
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Online Module Resources
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| Module Co-ordinator | Dr David Reynolds | Office Number | X138E |
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Level |
3
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Credit Rating |
7.5
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Pre-requisite |
None
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Co-requisite |
None
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Module Aims
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•To present principles of linear and angular momentum, and conservation of energy
•To present theory of central forces
•To present as a case study in mathematical modelling, the derivation of Kepler’s Laws from inverse square law of attraction
•To present Lagrange’s and Hamilton’s equations of motion
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Learning Outcomes
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•Students will be able to formulate and solve standard one-dimensional problems in mechanics
•Students will know methods for solving elementary first and second order linear equations
•Students will know how to analyse central force problems
•Students will understand how to use Lagrange’s equations to find equations of motion
•Students will understand that Lagrange’s equations are necessary for action to be stationary
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Indicative Time Allowances
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Hours
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Lectures |
0
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Tutorials |
0
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Laboratories |
0
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Seminars |
0
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Independent Learning Time |
112.5
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Total |
112.5
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Placements |
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Assignments |
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NOTE
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Assume that a 7.5 credit module load represents approximately 112.5 hours' work, which includes all teaching, in-course assignments, laboratory work or other specialised training and an estimated private learning time associated with the module.
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Indicative Syllabus
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•Solving Ordinary Differential Equations Separable equations, first order linear equations, second order homogeneous equations with constant coefficients, particular solutions of inhomogeneous equations using method of undetermined coefficients
•Kinematics Velocity and acceleration and their representations in polar coordinates, types of motion such as rectilinear, circular, simple harmonic
•Newton’s Second Law for Particle mass, momentum, forces; discussion of Newton’s Laws; examples involving projectiles, linear oscillators and resonance; power; conservative forces and potential energy; conservation of energy; stability
•Central forces Consequences of conservation of angular momentum and energy; geometry of conic sections; Kepler''s laws; exact solution in case of inverse square law of attraction, application to motion of planets, comets and satellites, Hamilton’s first integral
•Principles of Dynamics Moving cartesian coordinate systems; angular velocity; velocity and acceleration relative to moving coordinate systems; principles of linear and angular momentum for finite systems of particles; principle of inertia and inertial frames; centre of mass; action and reaction; two-body problem
•Analytical Dynamics generalised coordinates; Lagrange''s equations and lagrangians, hamiltionians and Hamilton''s equations; Lagrange’s equations as necessary condition for critical action
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| Assessment | | Continuous Assessment | 25% | Examination Weight | 75% |
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Indicative Reading List
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J. .M. Knudsen & P.G. Hjorth, Elements of Newtonian Mechanics, Springer-Verlag (1995).M. Lunn, A First Course in Mechanics, Oxford University Press, (1991).D. Acheson, From Calculus to Chaos, Oxford University Press, (1997).
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Programme or List of Programmes
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| BSSA | Study Abroad (DCU Business School) |
| BSSAO | Study Abroad (DCU Business School) |
| ECSA | Study Abroad (Engineering & Computing) |
| ECSAO | Study Abroad (Engineering & Computing) |
| HMSA | Study Abroad (Humanities & Soc Science) |
| HMSAO | Study Abroad (Humanities & Soc Science) |
| MS | BSc in Mathematical Sciences |
| SHSA | Study Abroad (Science & Health) |
| SHSAO | Study Abroad (Science & Health) |
| Archives: | |
