Advanced Mechanics
This course will enable the students to –
- Acquaint the students with mechanical systems under generalized coordinate systems, virtual work, energy and momentum.
- Aware about the mechanics developed by Newton, Lagrange's, Hamilton.
- Understand the motion of fluid and develop concept, models.
- Understand the techniques which enable us to solve the problems of fluid flow.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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DMAT 703 |
Advanced Mechanics (Theory)
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The students will be able to –
CO87: Construct General equation of motion of a rigid body under fixed force, no force and impulsive force. CO88: Describe Motion in three dimensions with reference to Euler's dynamical and geometrical equations, Motion under no forces, Motion under impulsive forces. CO89: Analyze the Derivation of Lagrange’s Equations to holonomic Systems. Understand the motion of top, concept of the Hamilton Equations of Motion and the Principle of Least Action. CO90: Distinguish the basic principles of ideal fluid, such as Lagrangian and Eulerian approach, conservation of mass etc. CO91: Use Euler and Bernoulli's equations and the conservation of mass to determine velocity and acceleration for incompressible and non-viscous fluid. CO92: Differentiate between rotational and irrotational flow, stream functions, velocity potential and able to construct complex potential due to sink, source and doublets. |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Giving tasks
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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D'Alembert's principle, General equations of motion of a rigid body, Motion of centre of inertia and motion relative to centre of inertia, Motion about a fixed axis: Finite forces moment of effective forces about a fixed axis of rotation, Angular momentum, Kinetic energy of a rotating body about a fixed line, Equation of motion of the body about the axis of rotation, Principle of conservation of energy.
Motion in three dimensions with reference to Euler's dynamical and geometrical equations, Motion under no forces, Motion under impulsive forces, Motion of a top.
Lagrange's equations for holonomous dynamical system, Energy equation for conservative field, Small oscillations, Motion under impulsive forces, Hamilton's equations of motion, Conservation of energy, Hamilton's principle and principle of least action.
Kinematics of ideal fluid, Lagrange's and Euler's methods, Equation of continuity in cartesian, cylindrical and spherical polar coordinates, Boundary surface, Stream-lines, path-lines, velocity potential, Rotational and irrotational motion.
Euler's hydrodynamic equations, Bernoulli's theorem, Helmholtz equations, Cauchy's integral, Motion due to impulsive forces. Motion in two-dimensions, Stream function, Complex potential, Sources, Sinks, Doublets, Images in two dimensions: image of a source with regard to a plane, image of a source with regard to a circle.
- M.D. Raishinghania, Dynamics, S.Chand & Co. New Delhi, 2016.
- J.L. Bansal and P.R. Sharma, Dynamics of a Rigid Body, Jaipur Publishing House, Jaipur, 2009.
- P.P. Gupta and G.S. Malik, Rigid Body of Dynamics-I, Krishna Prakashan, 2014.
- M.D. Raisinghania, Fluid Dynamics, S. Chand & Co. New Delhi, 2016.
- K.P. Goyal and J.K. Gupta, Fluid Dynamics, Pragati Prakashan, Meerut, 2011.
- Patrick Hamill, Intermediate Dynamics, Jhones & Barlett Publication, 2010.
- S.L. Loney, Dynamics of a Particle and Rigid body, Maxford Books Pub, 2003.
- Schaum's Outlines, Fluid Mechanics, McGraw-Hill Education, 1 edition, 2007.
- F. Chorlton, Text book of Fluid Dynamics, CBS Publications, New Delhi, 2004.
- Milne Thomson, Theoretical Hydrodynamics, Macmillan, 3rd Edition, 1955.
