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Course Co-ordinated by IIT Roorkee
Dr. S. P. Harsha
IIT Roorkee


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The course aims to expose the students to basic principles governing the motion of mechanical systems and to develop their skills in analysis and control of their motion.

Mechanics of particle motion, momentum and energy principles. Hamilton's, D' Alembert's principle, Lagrange's equation applied to conservative and nonconservative systems. Space and body fixed co-ordinates, Euler angles, multibody systems, planer dynamic analysis. Stability of dynamical systems, Liapunov's direct method and theorems, Routh's stability criteria. Open and closed loop systems, proportional, integral and derivative control actions and their characteristics.


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Basic Concepts:

  • Inertial Coordinate System.

  • Fundamental Laws of Motion.

  • Mechanics of Particles and System of Particles.

  • Principle of Linear and Angular Momenta.

  • Work-energy principles.



Lagrangian Dynamics:

  • Degrees of Freedom.

  • Generalized Coordinates and Generalized Forces.

  • Holonomic and Nonholonomic Constraints, Lagrange's Equation from D'Alembert's Principles.

  • Application of Lagrange's equation for Conservative and Non-conservative Autonomous Systems with holonomic and Nonholonomic Constraints.

  • Applications to systems with very Small Displacements and Impulsive Motion.

  • Hamilton Principle from D'Alembert's Principle.

  • Lagrange Equation from Hamilton's Principle.



Multi-body Dynamics:

  • Space and Fixed body Coordinate Systems.

  • Coordinate Transformation Matrix.

  • Direction Cosines, Euler Angles.

  • Euler Parameters.

  • Finite and Infinitesimal Rotations.

  • Time Derivatives of Transformations Matrices.

  • Angular Velocity and Acceleration Vectors.

  • Equations of Motion of Multi-Body System.

  • Newton-Euler Equations.

  • Planer Kinematic and Dynamic Analysis.

  • Kinematic Revolute Joints.

  • Coordinate Partitioning, Equations of Motion.

  • Joint Reaction Forces.

  • Simple Applications of Planer Systems.



Stability of Motion:

  • Fundamental Concept in Stability.

  • Autonomous Systems and Phase Plane Plots.

  • Routh's Criteria for Stability.

  • Liapunv's Method.

  • Liapunov's Stability Theorems.

  • Liapunov's Function to Determine Stability of the System.



Control System Dynamics:

  • Open and Close Loop Systems.

  • Block Diagrams.

  • Transfer Functions and Characteristics Equations.

  • Proportional Integral and Derivative Control actions and their Characteristics.


Understanding of dynamics of physical systems: UG level course on mechanical system dynamics.

  1. "Advanced Engineering Dynamics", J. H. Ginsberg, Harper and Row.

  2. "Methods of Analytical Dynamics", L. Meirovitch, McGraw Hill Inc.

  3. "Dynamics of Physical Systems", R. H. Canon, McGraw Hill Inc.

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