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.
Inertial Coordinate System.
Fundamental Laws of
Mechanics of Particles and System of Particles.
Linear and Angular Momenta.
Degrees of Freedom.
Coordinates and Generalized Forces.
Holonomic and Nonholonomic
Constraints, Lagrange's Equation from D'Alembert's
Application of Lagrange's equation for Conservative and
Non-conservative Autonomous Systems with holonomic and Nonholonomic
Applications to systems with very Small
Displacements and Impulsive Motion.
Hamilton Principle from
Lagrange Equation from Hamilton's
Space and Fixed body Coordinate Systems.
Coordinate Transformation Matrix.
Direction Cosines, Euler Angles.
Finite and Infinitesimal Rotations.
Derivatives of Transformations Matrices.
Angular Velocity and
Equations of Motion of Multi-Body System.
Planer Kinematic and Dynamic Analysis.
Kinematic Revolute Joints.
Coordinate Partitioning, Equations of
Joint Reaction Forces.
Simple Applications of Planer
Stability of Motion:
Fundamental Concept in Stability.
Autonomous Systems and Phase Plane Plots.
Routh's Criteria for
Liapunov's Stability Theorems.
Liapunov's Function to Determine Stability of the System.
Control System Dynamics:
Open and Close Loop Systems.
Transfer Functions and Characteristics Equations.
Proportional Integral and Derivative Control actions and their
Understanding of dynamics of physical
systems: UG level course on mechanical
"Advanced Engineering Dynamics", J. H. Ginsberg, Harper and Row.
"Methods of Analytical Dynamics", L. Meirovitch, McGraw Hill Inc.
"Dynamics of Physical Systems", R. H. Canon, McGraw Hill Inc.
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