Dynamics of a Rigid Body

Paper Code: 
MAT125
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 
This course will enable the students to
  1. Acquaint the students with mechanical systems under generalized coordinate systems, virtual work, energy and momentum. 
  2. Aware about the mechanics developed by Newton, Lagrange's, Hamilton.

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper Title

MAT125

Dynamics of a Rigid Body

(Theory)

The students will be able to –

 

CO25: Construct General equation of motion of a rigid body under fixed force, no force and impulsive force. CO26: Apply D’Alembert’s Principle on some real time applications.

CO27: Analyse the concept of Motion of a rigid body in two dimensions, Rolling and sliding friction, rolling and sliding of uniform rod and uniform sphere.

CO28: Describe Motion in three dimensions with reference to Euler's dynamical and geometrical equations, Motion under no forces, Motion under impulsive forces.

CO29: Analyze the Derivation of Lagrange’s Equations to holonomic Systems. Understand the motion of top.

CO30: Distinguish the concept of the Hamilton Equations of Motion and the Principle of Least Action.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Reading assignments, power point presentation

 

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation

 

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation, Individual and group projects

 

Unit I: 
I
15.00
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.
   
Unit II: 
II
15.00
Motion of a rigid body in two dimensions: 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. 
    
Unit III: 
III
15.00
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.
   
Unit IV: 
IV
15.00
Lagrange's equations for holonomous dynamical system, Energy equation for conservative field, Small oscillations, Motion under impulsive forces, Motion of a top.
 
Unit V: 
V
15.00
Hamilton's equations of motion, Conservation of energy, Hamilton's principle and principle of least action.
 
Essential Readings: 
  • 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.
  • J.L. Synge and B.A. Griffith, Principles of Mechanics, McGraw-Hill, New York, 1942.
  • 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.
  • S.L. Loney, A Text Book on Dynamics of Particle and Rigid Body, AITBS Publishers & Distributers, 1991.
  • E.T. Whittaker, A Teatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, 1965.
 
Academic Year: 
2021-2022
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