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Advanced Mechanics [1]

Paper Code: 
25DMAT703
Credits: 
6
Contact Hours: 
90.00
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.
  3. Understand the motion of fluid and develop concept, models
  4. Understand the techniques which enable us to solve the problems of fluid flow.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

25DMAT

703

 

 

 

 

 

 

 

Advanced Mechanics

(Theory)

 

 

 

 

 

 

 

CO101: Construct the general equation of motion of a rigid body under fixed and impulsive force about a fixed axis.

CO102: Describe Motion in three dimensions with reference to Euler's dynamical and geometrical equations. Understand the motion of the top under given conditions.

CO103:  Analyze the Derivation of Lagrange’s Equations to holonomic Systems. Concept of the Hamilton Equations of Motion and the Principle of Least Action.

CO104: Distinguish the basic principles of ideal fluid, Such as Lagrangian and Eulerian approach, Conservation of mass, etc.

CO105: Differentiate between rotational and irrotational flow, Stream functions, Velocity potential and be able to construct complex potential due to sink, Sourceand doublets.

CO106: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Assigned tasks

 

 

 

Quiz, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
D'Alembert's principle and applications
12.00
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 of a rigid body 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: 
Motion of a rigid body in Three Dimension
12.00
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
 
Unit III: 
Lagrange's and Hamilton's equation of Motion
12.00
Lagrange's equations for holonomous dynamical systems, 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.
 
Unit IV: 
Kinematics of ideal fluid
12.00
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.
 
Unit V: 
Equation of Motion of fluid
12.00
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.
 
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.
  • M.D. Raisinghania, Fluid Dynamics, S. Chand & Co. New Delhi, 2016.
  • K.P. Goyal and J.K. Gupta, Fluid Dynamics, Pragati Prakashan, Meerut, 2011.
References: 
  • 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.

 

e- RESOURCES
 

 

JOURNALS
 
Academic Year: 
2025-2026 [8]

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Links:
[1] https://maths.iisuniv.ac.in/node/1451
[2] https://www.physics.rutgers.edu/~shapiro/507/book3.pdf
[3] https://engineering.purdue.edu/~xe/Forms%20For%20Website/FE%20Review/S2017/Dynamics%20Notes.pdf
[4] https://mdu.ac.in/UpFiles/UpPdfFiles/2020/Jan/Fluid_Dynamics_final.pdf
[5] https://www.inderscience.com/jhome.php?jcode=ijdsde
[6] https://www.springer.com/journal/40435
[7] https://www.begellhouse.com/journals/fluid-mechanics-research.ht
[8] https://maths.iisuniv.ac.in/academic-year/2025-2026