Dynamics of a Rigid Body
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.
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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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24MAT 125 |
Dynamics of a Rigid Body (Theory) |
CO25: Construct the general equation of motion of a rigid body about a fixed axis and apply D’Alembert’s principle to some real time applications. CO26: Analyze the concept of motion of a rigid body in two dimensions, rolling and sliding friction, rolling and sliding of a uniform rod and a uniform sphere. CO27: Describe motion in three dimensions with reference to Euler's dynamical and geometrical equations, motion under no forces and motion under impulsive forces. CO28: Analyze the derivation of Lagrange’s equations for holonomic systems. Understand the motion of a top. CO29: Distinguish the concept of the Hamilton Equations of Motion and the Principle of Least Action. CO30: Contribute effectively in course-specific interaction. |
Approach in teaching: Interactive Lectures, Discussion, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, Topic presentation, Assigned tasks |
Quiz, Class Test, Individual projects, Open Book Test, Continuous Assessment, 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.
Equations of motion in two dimensions, Kinetic energy of a rigid body, Moment of momentum, Rolling and sliding friction, Rolling of a sphere on a rough inclined plane, Sliding of a rod, Sliding and rolling of a sphere on an inclined plane, Sliding and rolling of a sphere on a fixed sphere, Equations of motion of a rigid body under impulsive forces, Impact of a rotating elastic sphere on a fixed horizontal rough plane, Change in kinetic energy due to the action of impulse.
Motion in three dimensions with reference to Euler's dynamical and geometrical equations, Motion under no forces, Motion under impulsive forces, Conservation of momentum (linear and angular) and energy for finite as well as impulsive forces.
Lagrange's equations for holonomic dynamical system, Energy equation for conservative field, Small oscillations, Motion under impulsive forces.
Motion of a top: Equation of motion of a top, Range of , Steady motion of a top, Stability conditions.
Hamilton's equations of motion, Conservation of energy, Hamilton's principle and principle of least action.
- 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.
- S.L Loney, The Elementary on the Dynamics of a Particle and the Rigid Bodies, GK Publications Ltd., 2012.
SUGGESTED READING
- E.T. Whittaker, A Teatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, 1988.
- J.L. Synge and B.A. Griffith, Principles of Mechanics, McGraw-Hill, New York, 1959.
- M. Ray and H.S. Sharma, Text Book on Dynamics of Rigid Body, Student’s friend &Company, 1960.
- Patrick Hamill, Intermediate Dynamics, Jhones & Barlett Publication, 2010.
- S.L. Loney, Dynamics of a Particle and Rigid body, Maxford Books Pub, 2003.
e- RESOURCES
- https://epgp.inflibnet.ac.in/Home/ViewSubject?catid=ZLCHeZEhCZ8yCri36nSF3A==
- https://www.physics.rutgers.edu/~shapiro/507/book3.pdf
- https://engineering.purdue.edu/~xe/Forms%20For%20Website/FE%20Review/S2017/Dynamics%20Notes.pdf
JOURNALS
